diff --git a/.github/workflows/publish.yaml b/.github/workflows/publish.yaml new file mode 100644 index 0000000..4e6a7b8 --- /dev/null +++ b/.github/workflows/publish.yaml @@ -0,0 +1,40 @@ +name: Publish Python package + +on: + push: + tags: + - "v*.*.*" # Manual tagging of the commit on the main branch should trigger publish action + +permissions: + contents: read + id-token: write + +jobs: + publish: + runs-on: ubuntu-latest + + environment: + name: pypi + + steps: + - name: Checkout code + uses: actions/checkout@v4 + + - name: Set up Python + uses: actions/setup-python@v5 + with: + python-version: "3.11" + + - name: Install build tools + run: | + python -m pip install --upgrade pip + python -m pip install build twine + + - name: Build package + run: python -m build + + - name: Check package + run: twine check dist/* + + - name: Publish package + uses: pypa/gh-action-pypi-publish@release/v1 \ No newline at end of file diff --git a/.github/workflows/test.yaml b/.github/workflows/test.yaml index c2d1386..eecf0b9 100644 --- a/.github/workflows/test.yaml +++ b/.github/workflows/test.yaml @@ -2,12 +2,14 @@ name: Run Python tests on: push: - branches: [ main ] # - add for limiting it only to pushes on a main branch - paths: # triggers testing action if only any python / 2 other files have been changed + branches: [ main ] # - add for limiting it to be triggered only by pushes to the main branch + paths: # triggers testing action if only any Python / listed files have been changed - '**.py' - 'requirements.txt' + - 'pyproject.toml' - '.github/workflows/test.yaml' pull_request: + branches: [ main ] jobs: test: @@ -15,7 +17,7 @@ jobs: strategy: matrix: - python-version: ["3.8", "3.9", "3.10", "3.11"] + python-version: ["3.8", "3.11", "3.12", "3.13"] steps: - name: Checkout code # loads code from a repo @@ -31,7 +33,7 @@ jobs: python -m pip install --upgrade pip pip install pytest pip install -e . - pip install numba + pip install "numba>=0.57.1" - name: Run tests run: pytest diff --git a/.gitignore b/.gitignore index ad8e2ca..4fbd09e 100644 --- a/.gitignore +++ b/.gitignore @@ -16,6 +16,11 @@ Documents/ .idea/ .vscode/ src/zernpy/calculations/*.jpg +src/zernpy/ignored/ +!Command_Hints_Mypy_Ruff.txt + +# tests bound to the local environments +run_all_local_tests.cmd # Byte-compiled / optimized / DLL files __pycache__/ diff --git a/Command_Hints_Mypy_Ruff.txt b/Command_Hints_Mypy_Ruff.txt new file mode 100644 index 0000000..7a82bf9 --- /dev/null +++ b/Command_Hints_Mypy_Ruff.txt @@ -0,0 +1,3 @@ +mypy src/zernpy - command for checking files for comforming to typing rules +ruff check src tests - command for checking files for comforming to formatting rules +ruff check --fix - command for checking + fixing found formatting issues \ No newline at end of file diff --git a/MANIFEST.in b/MANIFEST.in index 118344b..5ccc678 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -1,3 +1,2 @@ -exclude src/zernpy/*.png - -recursive-exclude src/zernpy/readme_images * +recursive-exclude tests * +recursive-exclude src/zernpy/tests * diff --git a/README.md b/README.md index da9b439..8b93f78 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,8 @@ ### 'zernpy' - Python package for calculation real-valued Zernike polynomials and associated 2D PSF kernels +[![Tests](https://github.com/sklykov/zernpy/actions/workflows/test.yaml/badge.svg)](https://github.com/sklykov/zernpy/actions/workflows/test.yaml) +[![PyPI](https://img.shields.io/pypi/v/zernpy)](https://pypi.org/project/zernpy/) +[![License](https://img.shields.io/github/license/sklykov/zernpy)](https://github.com/sklykov/zernpy/blob/main/LICENSE) +[![Lint](https://img.shields.io/badge/lint-ruff-informational)](https://github.com/astral-sh/ruff) #### Project description and references This project is designed to compute the parameters, real values, and properties of Zernike polynomials using both exact (analytical) and recursive equations. diff --git a/build_api_dict_pdoc.bat b/build_api_dict_pdoc.cmd similarity index 69% rename from build_api_dict_pdoc.bat rename to build_api_dict_pdoc.cmd index 74b8206..eda613e 100644 --- a/build_api_dict_pdoc.bat +++ b/build_api_dict_pdoc.cmd @@ -1,2 +1,2 @@ -pdoc ./src/zernpy/zernikepol.py ./src/zernpy/zernpsf.py -o ./docs/api --logo ../for_favicon.png --logo ../for_favicon.png --no-show-source --footer-text "zernpy ver. 0.1.0, 2026 Sergei Klykov" +pdoc ./src/zernpy/zernikepol.py ./src/zernpy/zernpsf.py -o ./docs/api --logo ../for_favicon.png --logo ../for_favicon.png --no-show-source --footer-text "zernpy ver. 0.1.1, 2026 Sergei Klykov" timeout /t 25 diff --git a/docs/api/search.js b/docs/api/search.js index 8c8bcd2..cc690e4 100644 --- a/docs/api/search.js +++ b/docs/api/search.js @@ -1,6 +1,6 @@ window.pdocSearch = (function(){ /** elasticlunr - 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oMain script with the class definition for accessing Zernike polynomial initialization, calculation and plotting.

\n\n

Also, provides a few functions useful for fitting set of Zernike polynomials to an image with phases.

\n\n

@author: Sergei Klykov, @year: 2026, @licence: MIT

\n"}, "zernpy.zernikepol.ZernPol": {"fullname": "zernpy.zernikepol.ZernPol", "modulename": "zernpy.zernikepol", "qualname": "ZernPol", "kind": "class", "doc": "

Define the Zernike polynomial class and associated calculation methods.

\n"}, "zernpy.zernikepol.ZernPol.__init__": {"fullname": "zernpy.zernikepol.ZernPol.__init__", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.__init__", "kind": "function", "doc": "

Initialize of the class for Zernike polynomial definition as the object.

\n\n
Parameters
\n\n
    \n

  • **kwargs (orders or index for Zernike polynomial initialization expected as key=value pairs):\nAcceptable variants for key=value pairs arguments:

    \n\n

    1) n=int, m=int with alternatives: \"radial_order\" for n; \"l\", \"azimuthal_order\", \"angular_frequency\" for m;

    \n\n

    2) osa_index=int with alternatives: \"osa\", \"ansi_index\", \"ansi\";

    \n\n

    3) noll_index=int with alternative \"noll\";

    \n\n

    4) fringe_index=int with alternative \"fringe\"

    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Raised if the specified orders (m, n) or index (OSA, Noll...) have inconsistencies like:
    • \n
\n\n

for specified orders:\n1) m < 0 or n < 0; 2) m or n is not int; 3) (self.__n - abs(self.__m)) % 2 == 0;

\n\n

4) if n > 54 - because the polynomials with higher orders are meaningless due to very slow calculations;

\n\n

for indices - see the raised error message.

\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n

[2] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[3] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n
Returns
\n\n
    \n
  • ZernPol class instance.
    • \n
\n", "signature": "(**kwargs)"}, "zernpy.zernikepol.ZernPol.get_indices": {"fullname": "zernpy.zernikepol.ZernPol.get_indices", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_indices", "kind": "function", "doc": "

Return the tuple with following orders: ((m, n), OSA index, Noll index, Fringe index).

\n\n
Returns
\n\n
    \n
  • tuple: with elements: (tuple (azimuthal (m), radial (n)) orders, OSA index, Noll index, Fringe index)
    • \n
\n\n

All indices are integers.

\n", "signature": "(self) -> Tuple[Tuple[int, int], int, int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_mn_orders": {"fullname": "zernpy.zernikepol.ZernPol.get_mn_orders", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_mn_orders", "kind": "function", "doc": "

Return tuple with the (azimuthal, radial) orders, i.e. return (m, n).

\n\n
Returns
\n\n
    \n
  • tuple: with the (azimuthal, radial) orders for the initialized Zernike polynomial.
    • \n
\n", "signature": "(self) -> Tuple[int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_polynomial_name": {"fullname": "zernpy.zernikepol.ZernPol.get_polynomial_name", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_polynomial_name", "kind": "function", "doc": "

Return string with the conventional name (see references for details) of polynomial up to 7th order.

\n\n
Parameters
\n\n
    \n
  • short (bool, optional):\nIf True, this method returns shortened name. The default is False.
    • \n
\n\n
References
\n\n

[1] Up to 4th order: Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n

[2] 5th order names: from the website https://www.telescope-optics.net/monochromatic_eye_aberrations.htm

\n\n

6th order - 7th order: my guess about the naming

\n\n
Returns
\n\n
    \n
  • str: Name of the initialized polynomial.
    • \n
\n", "signature": "(self, short: bool = False) -> str:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.polynomial_value": {"fullname": "zernpy.zernikepol.ZernPol.polynomial_value", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.polynomial_value", "kind": "function", "doc": "

Calculate Zernike polynomial value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike function performed by exact equations from Ref.[2],\nafter - using the recurrence equations taken from the Ref.[1], using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

Surprisingly, the exact equation for polynomials are just pretty fast to use them directly, without\nany need to use the recurrence equations. It can be used by providing the flag as the input parameter.

\n\n

However, after ~ the 46th radial order due to the high integer values involved in the exact equation\n(factorials) producing ambiguous results (failed simple check that radial polynomial <= 1.0),\nonly iterative equations (which along with increasing order become time-consuming and slow)\ncould be used. The 40th radial order as the limit for usage of the exact equation is selected due to\nfound increasing after this order discrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[2] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n

[3] Andersen T. B. \"Efficient and robust recurrence relations for the Zernike\ncircle polynomials and their derivatives in Cartesian coordinates\" (2018)

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the polynomial is calculated.
    • \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the polynomial is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 40th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Check the Error stack trace for reasons of raising, most probably input parameters aren't acceptable.
    • \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated polynomial values on provided float values / arrays.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\ttheta: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.radial": {"fullname": "zernpy.zernikepol.ZernPol.radial", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.radial", "kind": "function", "doc": "

Calculate R(m, n) - radial Zernike function value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike function performed by exact equations from Ref.[2],\nafter - using the recurrence equations taken from the Ref.[1], using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

Surprisingly, the exact equation for polynomials are just pretty fast to use them directly, without\nany need to use the recurrence equations. It can be used by providing the flag as the input parameter.

\n\n

However, after ~ the 46th radial order due to the high integer values involved in the exact equation\n(factorials) producing ambiguous results (failed simple check that radial polynomial <= 1.0),\nonly iterative equations (which along with increasing order become time-consuming and slow)\ncould be used. The 40th radial order as the limit for usage of the exact equation is selected due to\nfound increasing after this order discrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[2] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n

[3] Andersen T. B. \"Efficient and robust recurrence relations for the Zernike\ncircle polynomials and their derivatives in Cartesian coordinates\" (2018)

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the function is calculated.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 40th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: The probable reasons: radius (radii) doesn't belong to a unit circle, input type isn't acceptable.
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated Zernike radial function value(-s) on provided float values / arrays of radiuses.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.triangular": {"fullname": "zernpy.zernikepol.ZernPol.triangular", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.triangular", "kind": "function", "doc": "

Calculate triangular Zernike function value(-s) within the unit circle.

\n\n
Parameters
\n\n
    \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the polynomial is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Most probably, raised if the conversion to float number is failed.
    • \n
\n\n

It happens when input parameter is not float, numpy.ndarray, list or tuple.

\n\n
    \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated value(-s) of Zernike triangular function on provided angle.
    • \n
\n", "signature": "(self, theta: Union[float, numpy.ndarray]) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.radial_dr": {"fullname": "zernpy.zernikepol.ZernPol.radial_dr", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.radial_dr", "kind": "function", "doc": "

Calculate derivative of radial Zernike polynomial value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike polynomials performed by exact equations,\nafter - using the recurrence equations, using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

The input flag use_exact_eq allows using the exact equation with factorials.\nBut note that after 38th radial order the usage of the exact equation is forbidden, because\nafter ~ the 44th radial order due to the high integer values associated with factorials and power\nvalues produced by derivatives leading to ambiguous results, only iterative equations\n(which along with increasing order become time-consuming and slow) could be used. The 38th radial order\nas the limit for usage of the exact equation is selected due to found increasing after this order\ndiscrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

Same as for the method \"radial\" or \"polynomial value\"

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the polynomial is calculated.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 38th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: The probable reasons: radius (radii) doesn't belong to a unit circle, input type isn't acceptable.
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated derivative of Zernike radial function value(-s) on provided float values / arrays of radiuses.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.triangular_dtheta": {"fullname": "zernpy.zernikepol.ZernPol.triangular_dtheta", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.triangular_dtheta", "kind": "function", "doc": "

Calculate derivative from triangular function on angle theta.

\n\n
Parameters
\n\n
    \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the function is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Most probably, raised if the conversion to float number is failed.
    • \n
\n\n

It happens when input parameter is not float, numpy.ndarray, list or tuple.

\n\n
    \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated derivative value(-s) of Zernike triangular function on provided angle.
    • \n
\n", "signature": "(self, theta: Union[float, numpy.ndarray]) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.normf": {"fullname": "zernpy.zernikepol.ZernPol.normf", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.normf", "kind": "function", "doc": "

Calculate normalization factor (such that Var(Z) = 1) for the associated Zernike polynomial (according to the References below).

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)\n[2] Check also preceding coefficients in the table Zj column: https://en.wikipedia.org/wiki/Zernike_polynomials#Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • float: Normalization factor calculated according to the References.
    • \n
\n", "signature": "(self) -> float:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_osa_index": {"fullname": "zernpy.zernikepol.ZernPol.get_osa_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_osa_index", "kind": "function", "doc": "

Calculate OSA / ANSI index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: OSA index according to [1].
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_noll_index": {"fullname": "zernpy.zernikepol.ZernPol.get_noll_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_noll_index", "kind": "function", "doc": "

Calculate Noll index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: Noll index.
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_fringe_index": {"fullname": "zernpy.zernikepol.ZernPol.get_fringe_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_fringe_index", "kind": "function", "doc": "

Calculate Fringe / University of Arizona index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: Fringe index.
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.index2orders": {"fullname": "zernpy.zernikepol.ZernPol.index2orders", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.index2orders", "kind": "function", "doc": "

Return tuple as (azimuthal, radial) orders for the specified by osa_, noll_ or fringe_index input parameter.

\n\n
Parameters
\n\n
    \n
  • **kwargs (dict):\nRecognizable values: osa_index, noll_index, fringe_index.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: (m, n) - contains azimuthal and radial orders as integers.
    • \n
\n", "signature": "(**kwargs) -> Tuple[int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.osa2noll": {"fullname": "zernpy.zernikepol.ZernPol.osa2noll", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.osa2noll", "kind": "function", "doc": "

Convert the OSA / ANSI index of a Zernike polynomial to the Noll index.

\n\n
Parameters
\n\n
    \n
  • osa_index (int):\nOSA / ANSI index with int type, it must be not less than 0.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 0.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted Noll index.
    • \n
\n", "signature": "(osa_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.noll2osa": {"fullname": "zernpy.zernikepol.ZernPol.noll2osa", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.noll2osa", "kind": "function", "doc": "

Convert the Noll index of a Zernike polynomial to the OSA / ANSI index.

\n\n
Parameters
\n\n
    \n
  • noll_index (int):\nThe Noll index with int type, it must be not less than 1.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 1.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted OSA / ANSI index.
    • \n
\n", "signature": "(noll_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.osa2fringe": {"fullname": "zernpy.zernikepol.ZernPol.osa2fringe", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.osa2fringe", "kind": "function", "doc": "

Convert the OSA / ANSI index of a Zernike polynomial to the Fringe index.

\n\n
Parameters
\n\n
    \n
  • osa_index (int):\nOSA / ANSI index with int type, it must be not less than 0.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 0.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted Fringe index.
    • \n
\n", "signature": "(osa_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.fringe2osa": {"fullname": "zernpy.zernikepol.ZernPol.fringe2osa", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.fringe2osa", "kind": "function", "doc": "

Convert the Fringe / Univ. of Arizona index of a Zernike polynomial to the OSA / ANSI index.

\n\n
Parameters
\n\n
    \n
  • fringe_index (int):\nThe noll index with int type, it must be not less than 1.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 1.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted OSA / ANSI index.
    • \n
\n", "signature": "(fringe_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.sum_zernikes": {"fullname": "zernpy.zernikepol.ZernPol.sum_zernikes", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.sum_zernikes", "kind": "function", "doc": "

Calculate sum of Zernike polynomials with their amplitude coefficients (e.g., for plotting over a unit circle).

\n\n
Parameters
\n\n
    \n
  • coefficients (Sequence[float]):\nCoefficients of Zernike polynomials for calculation of their sum.
    • \n
  • polynomials (Sequence[ZernPol]):\nInitialized polynomials as class instances of ZernPol class specified in this module.
    • \n
  • r (float or numpy.ndarray):\nRadius(Radii) from a unit circle.
    • \n
  • theta (float or numpy.ndarray):\nPolar angle(-s) from a unit circle.
    • \n

  • get_surface (bool, optional):\nIf True, it forces to calculate 2D sum of polynomials based on r and theta (as a mesh of polar coordinates).\nThe default is False.

    \n\n

    Note that if r and theta provided as the numpy ndarrays with different shapes and this flag is False, then\nthe result of this method will raise ValueError (because r and theta shapes will be checked for equality).

    • \n
\n\n
Raises
\n\n
    \n
  • TypeError: If the input parameters aren't iterable (doesn't support len() function), this error will be raised.
    • \n
  • ValueError: If the lengths of lists (tuples, numpy.ndarrays) aren't equal for coefficients and polynomials.
    • \n
\n\n

Or if the list (tuple, numpy.ndarray vector, ...) with Zernike polynomials instances (ZernPol()).

\n\n
Returns
\n\n
    \n
  • Sum of Zernike polynomials (float or numpy.ndarray):\nDepending on the input values and parameter get_surface - can be: float, 1D or 2D numpy.ndarrays.
    • \n
\n", "signature": "(\tcoefficients: Sequence[float],\tpolynomials: Sequence,\tr: Union[float, numpy.ndarray],\ttheta: Union[float, numpy.ndarray],\tget_surface: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_polar_coordinates": {"fullname": "zernpy.zernikepol.ZernPol.gen_polar_coordinates", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_polar_coordinates", "kind": "function", "doc": "

Generate the named tuple \"PolarVectors\" with R and Theta - vectors with polar coordinates for an entire unit circle.

\n\n

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are\ndefined by the specification of r_step and theta_rad_step parameters.

\n\n
Parameters
\n\n
    \n
  • r_step (float, optional):\nStep for generation the vector with radiuses for an entire unit circle. The default is 0.01.
    • \n
  • theta_rad_step (float, optional):\nStep for generation the vector with theta angles for an entire unit circle. The default is (np.pi/240).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the r_step or theta_rad_step provided in the way, that vectors R and Theta cannot be generated.
    • \n
\n\n
Returns
\n\n
    \n
  • polar_vectors: namedtuple(\"PolarVectors\", \"R Theta\"), where R - vector with radiuses values [0.0, r_step, ... 1.0],\nTheta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
    • \n
\n", "signature": "(\tr_step: float = 0.01,\ttheta_rad_step: float = 0.01309) -> zernpy.zernikepol.PolarVectors:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_equal_polar_mesh": {"fullname": "zernpy.zernikepol.ZernPol.gen_equal_polar_mesh", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_equal_polar_mesh", "kind": "function", "doc": "

Generate the named tuple \"PolarVectors\" with R and Theta - vectors with polar coordinates for an entire unit circle.

\n\n

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are\nequal and defined by the parameter n_points.

\n\n
Parameters
\n\n
    \n
  • n_points (int, optional):\nNumber of points between 0.0 ... 1.0 for radii and 0.0 ... 2pi for thetas. The default is 250.
    • \n
\n\n
Returns
\n\n
    \n
  • polar_vectors: namedtuple(\"PolarVectors\", \"R Theta\"), where R - vector with radiuses values [0.0, r_step, ... 1.0],\nTheta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
    • \n
\n", "signature": "(n_points: int = 250) -> zernpy.zernikepol.PolarVectors:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.plot_profile": {"fullname": "zernpy.zernikepol.ZernPol.plot_profile", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.plot_profile", "kind": "function", "doc": "

Plot the provided Zernike polynomial (instance of ZernPol class) on the matplotlib figure.

\n\n

Note that the plotting function plt.show() creates the plot in non-interactive mode.

\n\n
Parameters
\n\n
    \n
  • polynomial (ZernPol):\nInstance of ZernPol class.
    • \n
  • color_map (str, optional):\nColor map of the polar plot, common values for representation: coolwarm, jet, turbo, rainbow.\nAs alternative - perceptually equal color maps: viridis, plasma. The default is \"coolwarm\".\nNote that rainbow, jet, turbo - not perceptually equal color maps.
    • \n
  • show_title (bool, optional):\nToggle for showing the name of polynomial on the plot or not (only works for 2D case).
    • \n
  • use_defaults (bool, optional):\nUse default parameters for polar coordinates generation. The default is True.
    • \n
  • projection (str, optional):\nEither \"2d\" (\"2D\") - for 2D profile plot, or \"3d\" (\"3D\") - for 3D surface plot. The default is \"2d\".
    • \n
  • polar_coordinates (polar_vectors, optional):\nIf the flag 'use_defaults' is False, this named tuple is used for accessing polar coordinates for plotting.\nThe default is ().
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the flag use_defaults is False and polar_coordinates are not provided.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tpolynomial,\tcolor_map: str = 'coolwarm',\tshow_title: bool = True,\tuse_defaults: bool = True,\tprojection: str = '2d',\tpolar_coordinates: zernpy.zernikepol.PolarVectors = ()):", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_zernikes_surface": {"fullname": "zernpy.zernikepol.ZernPol.gen_zernikes_surface", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_zernikes_surface", "kind": "function", "doc": "

Generate surface of provided Zernike polynomials on the generated polar coordinates used steps.

\n\n
Parameters
\n\n
    \n
  • coefficients (Sequence[float]):\nCoefficients of Zernike polynomials for calculation of their sum.
    • \n
  • polynomials (Sequence[ZernPol]):\nInitialized polynomials as class instances of ZernPol class specified in this module.
    • \n

  • r_step (float, optional):\nStep for generation the vector with radiuses for an entire unit circle. The default is 0.01.

    \n\n

    See also the documentation for the method gen_polar_coordinates().

    • \n

  • theta_rad_step (float, optional):\nStep for generation the vector with theta angles for an entire unit circle. The default is (np.pi/180).

    \n\n

    See also the documentation for the method gen_polar_coordinates().

    • \n
  • equal_n_coordinates (bool, optional):\nSwitch between generation polar coordinates based on individual steps or on equal number of points.\nThe default is False.
    • \n
  • n_points (int, optional):\nNumber of points used for generation of equal sized polar coordinates r, theta.
    • \n
\n\n
Returns
\n\n
    \n
  • zernikes_surface: namedtuple(\"ZernikesSurface\", \"ZernSurf R Theta\") - tuple for storing mesh values for polar coordinates.\nZernSurf variable is 2D matrix with the sum of the input polynomials on generated polar coordinates (R, Theta).
    • \n
\n", "signature": "(\tcoefficients: Sequence[float],\tpolynomials: Sequence,\tr_step: float = 0.01,\ttheta_rad_step: float = 0.0174533,\tequal_n_coordinates: bool = False,\tn_points: int = 250) -> zernpy.zernikepol.ZernikesSurface:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.plot_sum_zernikes_on_fig": {"fullname": "zernpy.zernikepol.ZernPol.plot_sum_zernikes_on_fig", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.plot_sum_zernikes_on_fig", "kind": "function", "doc": "

Plot a sum of the specified Zernike polynomials by input lists (see function parameters) on the provided figure.

\n\n

Note that for showing the plotted figure, one needs to call appropriate functions (e.g., matplotlib.pyplot.show()\nor figure.show()) as the method of the input parameter figure.

\n\n
Parameters
\n\n
    \n
  • figure (plt.Figure):\n'Figure' class there the plotting will be done, previous plot will be cleared out.
    • \n
  • use_defaults (bool, optional):\nUse for plotting default values for generation of a mesh of polar coordinates and calculation\nof Zernike polynomials sum or Use for plotting provided calculated beforehand surface. The default is True.
    • \n
  • coefficients (Sequence[float], optional):\nCoefficients of Zernike polynomials for calculation of their sum. The default is ().
    • \n
  • polynomials (Sequence[ZernPol], optional):\nInitialized polynomials as class instances of ZernPol class specified in this module. The default is ().
    • \n
  • zernikes_sum_surface (namedtuple(\"ZernikesSurface\", \"ZernSurf R Theta\") , optional):\nThis tuple should contain the ZernSurf calculated on a mesh of polar coordinates R, Theta.\nThis tuple could be generated by the call of the static method gen_zernikes_surface().\nCheck the method signature for details. The default is ().
    • \n
  • show_range (bool, optional):\nFlag for showing range of provided values as the colorbar on the figure. The default is True.
    • \n
  • color_map (str, optional):\nColor map of the polar plot, common values for representation: coolwarm, jet, turbo, rainbow.\nAs alternative - perceptually equal color maps: viridis, plasma. The default is \"coolwarm\".\nNote that rainbow, jet, turbo - not perceptually equal color maps.
    • \n
  • projection (str, optional):\nEither \"2d\" (\"2D\") - for 2D profile plot, or \"3d\" (\"3D\") - for 3D surface plot. The default is \"2d\".
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Check the signature for details. In general, it will be raised if some input parameters are inconsistent.
    • \n
\n\n
Returns
\n\n
    \n
  • figure (plt.Figure):\nMatplotlib.pyplot Figure class there the Zernike polynomials sum plotted.
    • \n
\n", "signature": "(\tfigure: matplotlib.figure.Figure,\tcoefficients: Sequence[float] = (),\tpolynomials: Sequence = (),\tuse_defaults: bool = True,\tzernikes_sum_surface: zernpy.zernikepol.ZernikesSurface = (),\tshow_range: bool = True,\tcolor_map: str = 'coolwarm',\tprojection: str = '2d') -> matplotlib.figure.Figure:", "funcdef": "def"}, "zernpy.zernikepol.fit_polynomials_vectors": {"fullname": "zernpy.zernikepol.fit_polynomials_vectors", "modulename": "zernpy.zernikepol", "qualname": "fit_polynomials_vectors", "kind": "function", "doc": "

Fit provided Zernike polynomials (instances of ZernPol class) as the input tuple to the provided 1D vectors.

\n\n

1D vectors should contain: phases recorded in the related radii and thetas (polar coordinates). For the example\nof phases and coordinates composing, see the module test_fitting in 'tests' sub-folder of the repository.

\n\n
Parameters
\n\n
    \n
  • polynomials (tuple):\nInitialized tuple with instances of the ZernPol class that effectively represents target set of Zernike polynomials for fitting.
    • \n
  • phases_vector (numpy.ndarray):\nRecorded phases.
    • \n
  • radii_vector (numpy.ndarray):\nRelated radii - 1st polar coordinates for the recorded phases.
    • \n
  • thetas_vector (numpy.ndarray):\nRelated angles (thetas) - 2nd polar coordinates for the recorded phases.
    • \n
  • round_digits (int, optional):\nRound digits for returned polynomials amplitudes (numpy.round(...) function call). The default is 4.
    • \n
\n\n
Raises
\n\n
    \n
  • AttributeError: Any of provided vectors (phases_vector, etc.) isn't proper 1D numpy.ndarray (len(array.shape > 1)).
    • \n
\n\n
Returns
\n\n
    \n
  • zernike_coefficients (numpy.ndarray):\n1D numpy.ndarray with the fitted coefficients of Zernike polynomials.
    • \n
\n", "signature": "(\tpolynomials: tuple,\tphases_vector: numpy.ndarray,\tradii_vector: numpy.ndarray,\tthetas_vector: numpy.ndarray,\tround_digits: int = 4) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernikepol.fit_polynomials": {"fullname": "zernpy.zernikepol.fit_polynomials", "modulename": "zernpy.zernikepol", "qualname": "fit_polynomials", "kind": "function", "doc": "

Fit provided Zernike polynomials (instances of ZernPol class) as the input tuple to the 2D phase image.

\n\n

2D phase image implies that phases recorded depending on cartesian coordinates and circle aperture is cropped\nout from this image for fitting procedure. One can check the result of cropping by plotting return_cropped_image as\nTrue and plotting the second item from the returned tuple.

\n\n
Parameters
\n\n
    \n
  • phases_image (numpy.ndarray):\n2D image with recorded phases which should be approximated by the sum of Zernike polynomials.\nNote that image is assumed as the recorded phases on the cartesian coordinates. The circle\n(aperture) containing phases is cropped from the input image during the fitting procedure.
    • \n
  • polynomials (tuple):\nInitialized tuple with instances of the ZernPol class that effectively represents target set of Zernike polynomials.
    • \n
  • crop_radius (float, optional):\nAllow cropping pixel from range [0.5, 1.0], where 1.0 corresponds to radius of the cropped circle = min image size.\nThe default is 1.0.
    • \n
  • suppress_warnings (bool, optional):\nFlag for suppress warnings about the provided 2D image sizes. The default is False.
    • \n
  • strict_circle_border (bool, optional):\nFlag for controlling how the border pixels (on the circle radius) are treated: strictly or less strict for\nallowing more pixels to be treated as belonged to a cropped circle. The default is False.
    • \n
  • round_digits (int, optional):\nRound digits for returned polynomials amplitudes (numpy.round(...) function call). The default is 4.
    • \n
  • return_cropped_image (bool, optional):\nFlag for calculating and returning cropped image, used for fitting procedure. The default is False.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: Depending on the input parameter (flag) \"return_cropped_image\":\nif it is True, then tuple returned with following variables: zernike_coefficients - 1D numpy.ndarray\nwith the fitted coefficients of Zernike polynomials, and cropped_image - the cropped part from the\ninput image with phases that is used for fitting procedure (useful for debugging purposes);\nif it is False, the following tuple will be returned: zernike_coefficients, None - 1st with the same\nmeaning and type as explained before.
    • \n
\n", "signature": "(\tphases_image: numpy.ndarray,\tpolynomials: tuple,\tcrop_radius: float = 1.0,\tsuppress_warnings: bool = False,\tstrict_circle_border: bool = False,\tround_digits: int = 4,\treturn_cropped_image: bool = False) -> Tuple[numpy.ndarray, Optional[numpy.ndarray]]:", "funcdef": "def"}, "zernpy.zernikepol.generate_phases_image": {"fullname": "zernpy.zernikepol.generate_phases_image", "modulename": "zernpy.zernikepol", "qualname": "generate_phases_image", "kind": "function", "doc": "

Generate phases image (profile) for provided set of polynomials with provided coefficients (amplitudes).

\n\n
Parameters
\n\n
    \n
  • polynomials (tuple, optional):\nInitialized ZernPol instances for generation of phases as the sum of all stored in this tuple polynomials. The default is ().
    • \n
  • polynomials_amplitudes (tuple, optional):\nAmplitudes of polynomials provided in the tuple 'polynomials'. The default is ().
    • \n
  • img_width (int, optional):\nWidth of generated image. The default is 513.
    • \n
  • img_height (int, optional):\nHeight of generated image. The default is 513.
    • \n
\n\n
Returns
\n\n
    \n
  • phases_image (np.ndarray):\n2D image with phases calculated as the sum of provided polynomials.
    • \n
\n", "signature": "(\tpolynomials: tuple = (),\tpolynomials_amplitudes: tuple = (),\timg_width: int = 513,\timg_height: int = 513) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernikepol.generate_random_phases": {"fullname": "zernpy.zernikepol.generate_random_phases", "modulename": "zernpy.zernikepol", "qualname": "generate_random_phases", "kind": "function", "doc": "

Generate phases image (profile) for random set of polynomials with randomly selected amplitudes.

\n\n
Parameters
\n\n
    \n
  • max_order (int, optional):\nMaximum radial order of generated Zernike polynomials. The default is 4.
    • \n
  • img_width (int, optional):\nWidth of generated image. The default is 513.
    • \n
  • img_height (int, optional):\nHeight of generated image. The default is 513.
    • \n
  • round_digits (int, optional):\nRound digits for polynomials amplitudes generation (numpy.round(...) function call). The default is 4.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: Consisting of:\n2D phase profile image with provided width and height;\n1D numpy.ndarray containing randomly selected polynomials amplitudes;\ntuple with generated Zernike polynomials.
    • \n
\n", "signature": "(\tmax_order: int = 4,\timg_width: int = 513,\timg_height: int = 513,\tround_digits: int = 4) -> Tuple[numpy.ndarray, numpy.ndarray, Tuple[zernpy.zernikepol.ZernPol]]:", "funcdef": "def"}, "zernpy.zernikepol.generate_polynomials": {"fullname": "zernpy.zernikepol.generate_polynomials", "modulename": "zernpy.zernikepol", "qualname": "generate_polynomials", "kind": "function", "doc": "

Generate tuple with ZernPol instances (ultimately, representing polynomials) indexed using OSA scheme, starting with Piston(m=0,n=0).

\n\n
Parameters
\n\n
    \n
  • max_order (int, optional):\nMaximum overall radial order (n) for generated Zernike list (pyramid). The default is 10.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Raised if max_order < 1, because it should be not less than 0.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: It composes generated ZernPol instances (Zernike polynomials) ordered using OSA indexing scheme.
    • \n
\n", "signature": "(max_order: int = 10) -> Tuple[zernpy.zernikepol.ZernPol]:", "funcdef": "def"}, "zernpy.zernpsf": {"fullname": "zernpy.zernpsf", "modulename": "zernpy.zernpsf", "kind": "module", "doc": "

PSF class definition based on Zernike polynomial for computation of its kernel for convolution / deconvolution.

\n\n

@author: Sergei Klykov, @year: 2025, @licence: MIT

\n"}, "zernpy.zernpsf.ZernPSF": {"fullname": "zernpy.zernpsf.ZernPSF", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF", "kind": "class", "doc": "

The PSF (2D) class for focal plane of a microscopic system assuming that the phase profile is described by the Zernike polynomial.

\n\n

In other words, the PSF describing the image of point source formed by the microscopic system.

\n\n

Check the set_physical_props() method for the list of expected physical parameters for PSF calculation and calculate_psf_kernel() for\nthe references to the diffraction integral used for calculations.

\n\n
References
\n\n

[1] Principles of Optics, by M. Born and E. Wolf, 4 ed., 1968

\n\n

[2] https://en.wikipedia.org/wiki/Optical_aberration#Zernike_model_of_aberrations

\n\n

[3] https://wp.optics.arizona.edu/jsasian/wp-content/uploads/sites/33/2016/03/ZP-Lecture-12.pdf

\n\n

[4] https://www.researchgate.net/publication/236097143_Imaging_characteristics_of_Zernike_and_annular_polynomial_aberrations

\n\n

[5] https://nijboerzernike.nl/_PDF/JOSA-A-19-849-2002.pdf#[0,{%22name%22:%22Fit%22}]

\n"}, "zernpy.zernpsf.ZernPSF.__init__": {"fullname": "zernpy.zernpsf.ZernPSF.__init__", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.__init__", "kind": "function", "doc": "

Initiate the PSF wrapping class.

\n\n
Parameters
\n\n
    \n
  • zernpol (ZernPol | Sequence[ZernPol]):\nSingle instance of ZernPol() class or Sequence with ZernPol instances.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: 1) If not instance(-s) of ZernPol class provided as the input parameter;
    • \n
\n\n

2) If the provided sequence has zero length;

\n\n

3) If not all members of the provided sequence are instance of the \"ZernPol\" class;

\n\n

4) If the provided sequence contain repeated polynomials.

\n\n
Returns
\n\n
    \n
  • ZernPSF() class instance.
    • \n
\n", "signature": "(\tzernpol: Union[zernpy.zernikepol.ZernPol, Sequence[zernpy.zernikepol.ZernPol]])"}, "zernpy.zernpsf.ZernPSF.kernel": {"fullname": "zernpy.zernpsf.ZernPSF.kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.kernel", "kind": "variable", "doc": "

\n", "annotation": ": numpy.ndarray", "default_value": "array([[1.]])"}, "zernpy.zernpsf.ZernPSF.kernel_size": {"fullname": "zernpy.zernpsf.ZernPSF.kernel_size", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.kernel_size", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "1"}, "zernpy.zernpsf.ZernPSF.NA": {"fullname": "zernpy.zernpsf.ZernPSF.NA", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.NA", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "1.0"}, "zernpy.zernpsf.ZernPSF.wavelength": {"fullname": "zernpy.zernpsf.ZernPSF.wavelength", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.wavelength", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.532"}, "zernpy.zernpsf.ZernPSF.expansion_coeff": {"fullname": "zernpy.zernpsf.ZernPSF.expansion_coeff", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.expansion_coeff", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.5"}, "zernpy.zernpsf.ZernPSF.zernpol": {"fullname": "zernpy.zernpsf.ZernPSF.zernpol", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.zernpol", "kind": "variable", "doc": "

\n", "annotation": ": zernpy.zernikepol.ZernPol", "default_value": "<zernpy.zernikepol.ZernPol object>"}, "zernpy.zernpsf.ZernPSF.polynomials": {"fullname": "zernpy.zernpsf.ZernPSF.polynomials", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.polynomials", "kind": "variable", "doc": "

\n", "default_value": "()"}, "zernpy.zernpsf.ZernPSF.pixel_size_nyquist": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size_nyquist", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size_nyquist", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.133"}, "zernpy.zernpsf.ZernPSF.pixel_size_nyquist_eStr": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size_nyquist_eStr", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size_nyquist_eStr", "kind": "variable", "doc": "

\n", "default_value": "'1.330e-01'"}, "zernpy.zernpsf.ZernPSF.pixel_size": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size", "kind": "variable", "doc": "

\n", "default_value": "0.13034"}, "zernpy.zernpsf.ZernPSF.alpha": {"fullname": "zernpy.zernpsf.ZernPSF.alpha", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.alpha", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.9398496240601504"}, "zernpy.zernpsf.ZernPSF.airy": {"fullname": "zernpy.zernpsf.ZernPSF.airy", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.airy", "kind": "variable", "doc": "

\n", "annotation": ": bool", "default_value": "False"}, "zernpy.zernpsf.ZernPSF.n_int_r_points": {"fullname": "zernpy.zernpsf.ZernPSF.n_int_r_points", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.n_int_r_points", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "320"}, "zernpy.zernpsf.ZernPSF.n_int_phi_points": {"fullname": "zernpy.zernpsf.ZernPSF.n_int_phi_points", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.n_int_phi_points", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "300"}, "zernpy.zernpsf.ZernPSF.k": {"fullname": "zernpy.zernpsf.ZernPSF.k", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.k", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "11.810498697705988"}, "zernpy.zernpsf.ZernPSF.json_file_path": {"fullname": "zernpy.zernpsf.ZernPSF.json_file_path", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.json_file_path", "kind": "variable", "doc": "

\n", "annotation": ": str", "default_value": "''"}, "zernpy.zernpsf.ZernPSF.coefficients": {"fullname": "zernpy.zernpsf.ZernPSF.coefficients", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.coefficients", "kind": "variable", "doc": "

\n", "annotation": ": numpy.ndarray", "default_value": "None"}, "zernpy.zernpsf.ZernPSF.amplitudes": {"fullname": "zernpy.zernpsf.ZernPSF.amplitudes", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.amplitudes", "kind": "variable", "doc": "

\n", "annotation": ": numpy.ndarray", "default_value": "None"}, "zernpy.zernpsf.ZernPSF.set_physical_props": {"fullname": "zernpy.zernpsf.ZernPSF.set_physical_props", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.set_physical_props", "kind": "function", "doc": "

Set parameters in physical units.

\n\n
Parameters
\n\n
    \n
  • NA (float):\nNumerical aperture of an objective, assumed usage of microscopic ones.
    • \n
  • wavelength (float):\nWavelength of monochromatic light (\u03bb) used for imaging in physical units (e.g., as \u00b5m).
    • \n

  • expansion_coeff (float | Sequence[float]):\nAmplitude(-s) or expansion coefficient(-s) of the Zernike polynomial in physical units.\nNote that according to the used equation for PSF calculation it will be adjusted to the units of wavelength:\nalpha = expansion_coeff/wavelength. See the equation in the method \"calculate_psf_kernel\".

    \n\n

    Note that if Airy pattern (PSF for Piston polynomial) is provided, it's required to provide amplitude for it.\nHowever, this amplitude will be ignored in general for calculation because of its properties.

    • \n
  • pixel_physical_size (float):\nPixel size of the formed image in physical units (do not mix up with the physical sensor (camera) pixel size!).\nThe sanity check performed as the comparison with the Abbe resolution limit (see ref. [1] and [2]), provided pixel size\nshould be less than this limit.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If one of the sanity check has been failed, check the Error message for details.
    • \n
\n\n
References
\n\n

[1] https://www.microscopyu.com/techniques/super-resolution/the-diffraction-barrier-in-optical-microscopy

\n\n

[2] https://www.edinst.com/de/blog/the-rayleigh-criterion-for-microscope-resolution/

\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tself,\tNA: float,\twavelength: float,\texpansion_coeff: Union[float, Sequence[float]],\tpixel_physical_size: float):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.set_calculation_props": {"fullname": "zernpy.zernpsf.ZernPSF.set_calculation_props", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.set_calculation_props", "kind": "function", "doc": "

Set calculation properties: kernel size, number of integration points on polar coordinates.

\n\n

Note that it's recommended to set the physical properties by set_physical_props() method for getting estimated\nrequired kernel size.

\n\n
Parameters
\n\n
    \n
  • kernel_size (int):\nSize of PSF kernel (2D matrix used for convolution). Should be odd integer not less than 3.
    • \n
  • n_integration_points_r (int):\nNumber of integration points used for calculation diffraction integral on the radius of the entrance pupil\n(normalized to the range [0.0, 1.0]). Should be integer not less than 20.
    • \n
  • n_integration_points_phi (int):\nNumber of integration points used for calculation diffraction integral on the polar angle phi of the entrance pupil\n(from the range [0.0, 2pi]). Should be integer not less than 36.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If sanity checks fail (if provided parameters less than sanity values).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tself,\tkernel_size: int,\tn_integration_points_r: int,\tn_integration_points_phi: int) -> None:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.calculate_psf_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.calculate_psf_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.calculate_psf_kernel", "kind": "function", "doc": "

Calculate PSF kernel using the specified or default calculation parameters and physical values.

\n\n

Calculation based on the diffraction integral for the circular aperture. The final equation is derived based from the 2 References.

\n\n

Kernel is defined as the image formed on the sensor (camera) by the diffraction-limited, ideal microscopic system.\nThe diffraction integral is calculated numerically on polar coordinates, assuming circular aperture of\nan imaging system (micro-objective).

\n\n

The order of integration and used equations in short:\n1st - integration going on radius p, using trapezoidal rule: p\u2022(alpha\u2022zernike_pol.polynomial_value(p, phi) -\n r\u2022p\u2022cos(phi - theta))\u20221j

\n\n

2nd - integration going on angle phi, using Simpson rule, calling the returned integrals by 1st call for each phi and as the final\noutput, it provides as the np.power(np.abs(integral_sum), 2)\u2022integral_normalization, there integral_normalization =\n1.0/(pi\u2022pi) - the square of the module of the diffraction integral (complex value), i.e. intensity as the PSF value.

\n\n

For details of implementation, explore methods in 'calculations' module, calc_psfs.py file.

\n\n

Note that the Nijboer's approximation for calculation of diffraction integral also has been tested, but the results is not in agreement\nwith the reference [3] due to the large expansion coefficients for Zernike polynomials.

\n\n

Note that for Piston (m=0, n=0) the exact equation is used, that provides Airy pattern as the result.

\n\n
Parameters
\n\n
    \n
  • suppress_warnings (bool, optional):\nFlag to suppress all possible warnings. The default is False.
    • \n
  • normalized (bool, optional):\nFlag to return normalized PSF values to max=1.0. The default is True.
    • \n
  • verbose_info (bool, optional):\nFlag to print out each step completion report and measured elapsed time in ms. The default is False.
    • \n
  • accelerated (bool, optional):\nFlag to accelerate the calculations by using numba library for scripts compilation. Acceleration will be used automatically,\nif None is provided and 'numba' library is installed. The default is None.
    • \n
\n\n
References
\n\n

[1] Principles of Optics, by M. Born and E. Wolf, 4 ed., 1968

\n\n

[2] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf

\n\n

[3] PSF shapes: https://en.wikipedia.org/wiki/Zernike_polynomials#/media/File:ZernikeAiryImage.jpg

\n\n

[4] https://opg.optica.org/ao/abstract.cfm?uri=ao-52-10-2062 (DOI: 10.1364/AO.52.002062)

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: 2D PSF kernel.
    • \n
\n", "signature": "(\tself,\tsuppress_warnings: bool = False,\tnormalized: bool = True,\tverbose_info: bool = False,\taccelerated: bool = None) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.plot_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.plot_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.plot_kernel", "kind": "function", "doc": "

Plot on the external figure (matplotlib.pyplot.figure()) calculated PSF kernel.

\n\n
Parameters
\n\n
    \n
  • id_str (str, optional):\nString with ID for making unique Figure. The default is \"\".
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, id_str: str = ''):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.convolute_img": {"fullname": "zernpy.zernpsf.ZernPSF.convolute_img", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.convolute_img", "kind": "function", "doc": "

Convolute the provided image with PSF kernel as 2D arrays and return the convolved image with the same type as the original one.

\n\n
Parameters
\n\n
    \n
  • image (numpy.ndarray):\nSample image, not colour.
    • \n
  • scale2original (bool):\nConvolution resulting image will be rescaled to the max intensity of the provided image if True. The default is True.
    • \n
\n\n
Returns
\n\n
    \n
  • convolved_image (numpy.ndarray):\nResult of convolution (by using function scipy.ndimage.convolve).
    • \n
\n", "signature": "(self, image: numpy.ndarray, scale2original: bool = True) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.visualize_convolution": {"fullname": "zernpy.zernpsf.ZernPSF.visualize_convolution", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.visualize_convolution", "kind": "function", "doc": "

Plot convolution of the PSF kernel and sample image (even centered disk with blurred edges).

\n\n
Parameters
\n\n
    \n
  • radius (float, optional):\nRadius of the centered disk. The default is 4.0.
    • \n
  • max_intensity (int, optional):\nMaximum intensity of the even disk. The default is 255.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, radius: float = 4.0, max_intensity: int = 255):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.crop_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.crop_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.crop_kernel", "kind": "function", "doc": "

Crop redundant points from kernel.

\n\n

By default, all rows and columns containing any single value that more than 1% of max kernel value, are not cropped.

\n\n

Cropped kernel saved in class variable 'kernel'.

\n\n
Parameters
\n\n
    \n
  • min_part_of_max (float, optional):\nPart of kernel max that is used for checking rows / columns for cropping. The default is 0.01.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If parameter 'min_part_of_max' is not > 0.0 and not < 0.5.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, min_part_of_max: float = 0.01):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.save_json": {"fullname": "zernpy.zernpsf.ZernPSF.save_json", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.save_json", "kind": "function", "doc": "

Save class attributes (PSF kernel, physical properties, etc.) in the JSON file for further reloading and avoiding long computation.

\n\n
Parameters
\n\n
    \n
  • abs_path (str | Path, optional):\nAbsolute path for the file. If None, the file will be saved in the folder \"saved_psfs\" in the root of the package.\nThe default is None.
    • \n
  • overwrite (bool, optional):\nFlag for overwriting the existing file. The default is False.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tself,\tabs_path: Union[str, pathlib.Path] = None,\toverwrite: bool = False):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.read_json": {"fullname": "zernpy.zernpsf.ZernPSF.read_json", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.read_json", "kind": "function", "doc": "

Read the JSON file with the saved attributes and setting it for the class.

\n\n
Parameters
\n\n
    \n
  • abs_path (str | Path, optional):\nAbsolute path to the file. If None is provided, then the stored in the attribute path will be checked. The default is None.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, abs_path: Union[str, pathlib.Path] = None):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.initialize_parallel_workers": {"fullname": "zernpy.zernpsf.ZernPSF.initialize_parallel_workers", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.initialize_parallel_workers", "kind": "function", "doc": "

Initialize 4 Processes() for performing integration.

\n\n

See intmproc.py script (utils module) for implementation details.\nTests showed that this way doesn't provide performance gain.

\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.get_psf_point_r_parallel": {"fullname": "zernpy.zernpsf.ZernPSF.get_psf_point_r_parallel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.get_psf_point_r_parallel", "kind": "function", "doc": "

Parallel implementation of numerical integration.

\n\n
Parameters
\n\n
    \n
  • r (float):\nInput radial polar coordinate.
    • \n
  • theta (float):\nInput angular polar coordinate.
    • \n
\n\n
Returns
\n\n
    \n
  • float: Each point for PSF kernel.
    • \n
\n", "signature": "(self, r: float, theta: float) -> float:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.get_kernel_parallel": {"fullname": "zernpy.zernpsf.ZernPSF.get_kernel_parallel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.get_kernel_parallel", "kind": "function", "doc": "

Parallelized implementation of PSF kernel calculation.

\n\n

Note it's much less effective than common calculate_psf_kernel() method.

\n\n
Parameters
\n\n
    \n
  • normalize_values (bool, optional):\nFlag to normalize values. The default is True.
    • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: PSF kernel.
    • \n
\n", "signature": "(self, normalize_values: bool = True) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.deinitialize_workers": {"fullname": "zernpy.zernpsf.ZernPSF.deinitialize_workers", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.deinitialize_workers", "kind": "function", "doc": "

Release initialized before Processes for performing parallel computation.

\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "zernpy.zernpsf.force_get_psf_compilation": {"fullname": "zernpy.zernpsf.force_get_psf_compilation", "modulename": "zernpy.zernpsf", "qualname": "force_get_psf_compilation", "kind": "function", "doc": "

Force compilation of computing functions for round and ellipse 'precise' shaped objects.

\n\n

verbose_report : bool, optional\n Flag for printing out the elapsed for compilation time. The default is False.

\n\n
Returns
\n\n
    \n
  • None or tuple with 2 used ZernPSF instances depending on 'numba_installed' flag.
    • \n
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{"zernpy.zernikepol.ZernPol.sum_zernikes": {"tf": 1}, "zernpy.zernikepol.ZernPol.gen_zernikes_surface": {"tf": 1}, "zernpy.zernpsf": {"tf": 1}, "zernpy.zernpsf.ZernPSF.calculate_psf_kernel": {"tf": 1.4142135623730951}}, "df": 4}}}, "r": {"docs": {}, "df": 0, "r": {"docs": {}, "df": 0, "i": {"docs": {}, "df": 0, "e": {"docs": {}, "df": 0, "r": {"docs": {"zernpy.zernpsf.ZernPSF.set_physical_props": {"tf": 1}}, "df": 1}}}}}}, "l": {"docs": {}, "df": 0, "u": {"docs": {}, "df": 0, "r": {"docs": {}, "df": 0, "r": {"docs": {}, "df": 0, "e": {"docs": {}, "df": 0, "d": {"docs": {"zernpy.zernpsf.ZernPSF.visualize_convolution": {"tf": 1}}, "df": 1}}}}}}}, "j": {"docs": {}, "df": 0, "u": {"docs": {}, "df": 0, "s": {"docs": {}, "df": 0, "t": {"docs": {"zernpy.zernikepol.ZernPol.polynomial_value": {"tf": 1}, "zernpy.zernikepol.ZernPol.radial": {"tf": 1}}, "df": 2}}}, "e": {"docs": {}, "df": 0, "t": {"docs": {"zernpy.zernikepol.ZernPol.plot_profile": {"tf": 1.4142135623730951}, "zernpy.zernikepol.ZernPol.plot_sum_zernikes_on_fig": {"tf": 1.4142135623730951}}, "df": 2}}, "p": {"docs": {}, "df": 0, "g": {"docs": {"zernpy.zernpsf.ZernPSF.calculate_psf_kernel": {"tf": 1}}, "df": 1}}, "s": {"docs": {}, "df": 0, "o": {"docs": {}, "df": 0, "n": {"docs": {"zernpy.zernpsf.ZernPSF.save_json": {"tf": 1}, "zernpy.zernpsf.ZernPSF.read_json": {"tf": 1}}, "df": 2}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; + /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"zernpy.zernikepol": {"fullname": "zernpy.zernikepol", "modulename": "zernpy.zernikepol", "kind": "module", "doc": "

Main script with the class definition for accessing Zernike polynomial initialization, calculation and plotting.

\n\n

Also, provides a few functions useful for fitting set of Zernike polynomials to an image with phases.

\n\n

@author: Sergei Klykov, @year: 2026, @license: MIT

\n"}, "zernpy.zernikepol.ZernPol": {"fullname": "zernpy.zernikepol.ZernPol", "modulename": "zernpy.zernikepol", "qualname": "ZernPol", "kind": "class", "doc": "

Define the Zernike polynomial class and associated calculation methods.

\n"}, "zernpy.zernikepol.ZernPol.__init__": {"fullname": "zernpy.zernikepol.ZernPol.__init__", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.__init__", "kind": "function", "doc": "

Initialize of the class for Zernike polynomial definition as the object.

\n\n
Parameters
\n\n
    \n

  • **kwargs (orders or index for Zernike polynomial initialization expected as key=value pairs):\nAcceptable variants for key=value pairs arguments:

    \n\n

    1) n=int, m=int with alternatives: \"radial_order\" for n; \"l\", \"azimuthal_order\", \"angular_frequency\" for m;

    \n\n

    2) osa_index=int with alternatives: \"osa\", \"ansi_index\", \"ansi\";

    \n\n

    3) noll_index=int with alternative \"noll\";

    \n\n

    4) fringe_index=int with alternative \"fringe\"

    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Raised if the specified orders (m, n) or index (OSA, Noll...) have inconsistencies like:
    • \n
\n\n

for specified orders:\n1) m < 0 or n < 0; 2) m or n is not int; 3) (self.__n - abs(self.__m)) % 2 == 0;

\n\n

4) if n > 54 - because the polynomials with higher orders are meaningless due to very slow calculations;

\n\n

for indices - see the raised error message.

\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n

[2] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[3] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n
Returns
\n\n
    \n
  • ZernPol class instance.
    • \n
\n", "signature": "(**kwargs)"}, "zernpy.zernikepol.ZernPol.get_indices": {"fullname": "zernpy.zernikepol.ZernPol.get_indices", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_indices", "kind": "function", "doc": "

Return the tuple with following orders: ((m, n), OSA index, Noll index, Fringe index).

\n\n
Returns
\n\n
    \n
  • tuple: with elements: (tuple (azimuthal (m), radial (n)) orders, OSA index, Noll index, Fringe index)
    • \n
\n\n

All indices are integers.

\n", "signature": "(self) -> Tuple[Tuple[int, int], int, int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_mn_orders": {"fullname": "zernpy.zernikepol.ZernPol.get_mn_orders", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_mn_orders", "kind": "function", "doc": "

Return tuple with the (azimuthal, radial) orders, i.e. return (m, n).

\n\n
Returns
\n\n
    \n
  • tuple: with the (azimuthal, radial) orders for the initialized Zernike polynomial.
    • \n
\n", "signature": "(self) -> Tuple[int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_polynomial_name": {"fullname": "zernpy.zernikepol.ZernPol.get_polynomial_name", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_polynomial_name", "kind": "function", "doc": "

Return string with the conventional name (see references for details) of polynomial up to 7th order.

\n\n
Parameters
\n\n
    \n
  • short (bool, optional):\nIf True, this method returns shortened name. The default is False.
    • \n
\n\n
References
\n\n

[1] Up to 4th order: Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n

[2] 5th order names: from the website https://www.telescope-optics.net/monochromatic_eye_aberrations.htm

\n\n

6th order - 7th order: my guess about the naming

\n\n
Returns
\n\n
    \n
  • str: Name of the initialized polynomial.
    • \n
\n", "signature": "(self, short: bool = False) -> str:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.polynomial_value": {"fullname": "zernpy.zernikepol.ZernPol.polynomial_value", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.polynomial_value", "kind": "function", "doc": "

Calculate Zernike polynomial value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike function performed by exact equations from Ref.[2],\nafter - using the recurrence equations taken from the Ref.[1], using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

Surprisingly, the exact equation for polynomials are just pretty fast to use them directly, without\nany need to use the recurrence equations. It can be used by providing the flag as the input parameter.

\n\n

However, after ~ the 46th radial order due to the high integer values involved in the exact equation\n(factorials) producing ambiguous results (failed simple check that radial polynomial <= 1.0),\nonly iterative equations (which along with increasing order become time-consuming and slow)\ncould be used. The 40th radial order as the limit for usage of the exact equation is selected due to\nfound increasing after this order discrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[2] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n

[3] Andersen T. B. \"Efficient and robust recurrence relations for the Zernike\ncircle polynomials and their derivatives in Cartesian coordinates\" (2018)

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the polynomial is calculated.
    • \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the polynomial is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 40th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Check the Error stack trace for reasons of raising, most probably input parameters aren't acceptable.
    • \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated polynomial values on provided float values / arrays.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\ttheta: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.radial": {"fullname": "zernpy.zernikepol.ZernPol.radial", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.radial", "kind": "function", "doc": "

Calculate R(m, n) - radial Zernike function value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike function performed by exact equations from Ref.[2],\nafter - using the recurrence equations taken from the Ref.[1], using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

Surprisingly, the exact equation for polynomials are just pretty fast to use them directly, without\nany need to use the recurrence equations. It can be used by providing the flag as the input parameter.

\n\n

However, after ~ the 46th radial order due to the high integer values involved in the exact equation\n(factorials) producing ambiguous results (failed simple check that radial polynomial <= 1.0),\nonly iterative equations (which along with increasing order become time-consuming and slow)\ncould be used. The 40th radial order as the limit for usage of the exact equation is selected due to\nfound increasing after this order discrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)

\n\n

[2] Lakshminarayanan V., Fleck A. \"Zernike polynomials: a guide\" (2011)

\n\n

[3] Andersen T. B. \"Efficient and robust recurrence relations for the Zernike\ncircle polynomials and their derivatives in Cartesian coordinates\" (2018)

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the function is calculated.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 40th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: The probable reasons: radius (radii) doesn't belong to a unit circle, input type isn't acceptable.
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated Zernike radial function value(-s) on provided float values / arrays of radiuses.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.triangular": {"fullname": "zernpy.zernikepol.ZernPol.triangular", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.triangular", "kind": "function", "doc": "

Calculate triangular Zernike function value(-s) within the unit circle.

\n\n
Parameters
\n\n
    \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the polynomial is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Most probably, raised if the conversion to float number is failed.
    • \n
\n\n

It happens when input parameter is not float, numpy.ndarray, list or tuple.

\n\n
    \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated value(-s) of Zernike triangular function on provided angle.
    • \n
\n", "signature": "(self, theta: Union[float, numpy.ndarray]) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.radial_dr": {"fullname": "zernpy.zernikepol.ZernPol.radial_dr", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.radial_dr", "kind": "function", "doc": "

Calculate derivative of radial Zernike polynomial value(-s) within the unit circle.

\n\n

Calculation up to 10th order of Zernike polynomials performed by exact equations,\nafter - using the recurrence equations, using shortcut of storing\ncoefficients for each power of radius (coefficient*R^n)

\n\n

The input flag use_exact_eq allows using the exact equation with factorials.\nBut note that after 38th radial order the usage of the exact equation is forbidden, because\nafter ~ the 44th radial order due to the high integer values associated with factorials and power\nvalues produced by derivatives leading to ambiguous results, only iterative equations\n(which along with increasing order become time-consuming and slow) could be used. The 38th radial order\nas the limit for usage of the exact equation is selected due to found increasing after this order\ndiscrepancy between results of recursive and factorial formulas.

\n\n
References
\n\n

Same as for the method \"radial\" or \"polynomial value\"

\n\n
Parameters
\n\n
    \n
  • r (float or numpy.ndarray):\nRadius (radii) from unit circle or the range [0.0, 1.0], float / array, for which the polynomial is calculated.
    • \n
  • use_exact_eq (bool, optional):\nFlag for using the exact equation with factorials. The default is False.\nNote about the limit for usage of the exact equation - up to 38th radial order (n).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: The probable reasons: radius (radii) doesn't belong to a unit circle, input type isn't acceptable.
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated derivative of Zernike radial function value(-s) on provided float values / arrays of radiuses.
    • \n
\n", "signature": "(\tself,\tr: Union[float, numpy.ndarray],\tuse_exact_eq: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.triangular_dtheta": {"fullname": "zernpy.zernikepol.ZernPol.triangular_dtheta", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.triangular_dtheta", "kind": "function", "doc": "

Calculate derivative from triangular function on angle theta.

\n\n
Parameters
\n\n
    \n
  • theta (float or numpy.ndarray):\nTheta - angle in radians from the range [0, 2*pi], float or array, for which the function is calculated.\nNote that the theta counting is counterclockwise, as it is default for the matplotlib library.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Most probably, raised if the conversion to float number is failed.
    • \n
\n\n

It happens when input parameter is not float, numpy.ndarray, list or tuple.

\n\n
    \n
  • Warning: If the theta angles lie outside the range [0, 2*pi] (entire period).
    • \n
\n\n
Returns
\n\n
    \n
  • float or numpy.ndarray: Calculated derivative value(-s) of Zernike triangular function on provided angle.
    • \n
\n", "signature": "(self, theta: Union[float, numpy.ndarray]) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.normf": {"fullname": "zernpy.zernikepol.ZernPol.normf", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.normf", "kind": "function", "doc": "

Calculate normalization factor (such that Var(Z) = 1) for the associated Zernike polynomial (according to the References below).

\n\n
References
\n\n

[1] Shakibaei B.H., Paramesran R. \"Recursive formula to compute Zernike radial polynomials\" (2013)\n[2] Check also preceding coefficients in the table Zj column: https://en.wikipedia.org/wiki/Zernike_polynomials#Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • float: Normalization factor calculated according to the References.
    • \n
\n", "signature": "(self) -> float:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_osa_index": {"fullname": "zernpy.zernikepol.ZernPol.get_osa_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_osa_index", "kind": "function", "doc": "

Calculate OSA / ANSI index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: OSA index according to [1].
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_noll_index": {"fullname": "zernpy.zernikepol.ZernPol.get_noll_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_noll_index", "kind": "function", "doc": "

Calculate Noll index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: Noll index.
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.get_fringe_index": {"fullname": "zernpy.zernikepol.ZernPol.get_fringe_index", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.get_fringe_index", "kind": "function", "doc": "

Calculate Fringe / University of Arizona index from the 2 orders of Zernike polynomials.

\n\n
Parameters
\n\n
    \n
  • m (int):\nAzimuthal order (angular frequency).
    • \n
  • n (int):\nRadial order.
    • \n
\n\n
References
\n\n

[1] Wiki article: https://en.wikipedia.org/wiki/Zernike_polynomials

\n\n
Returns
\n\n
    \n
  • int: Fringe index.
    • \n
\n", "signature": "(m: int, n: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.index2orders": {"fullname": "zernpy.zernikepol.ZernPol.index2orders", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.index2orders", "kind": "function", "doc": "

Return tuple as (azimuthal, radial) orders for the specified by osa_, noll_ or fringe_index input parameter.

\n\n
Parameters
\n\n
    \n
  • **kwargs (dict):\nRecognizable values: osa_index, noll_index, fringe_index.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: (m, n) - contains azimuthal and radial orders as integers.
    • \n
\n", "signature": "(**kwargs) -> Tuple[int, int]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.osa2noll": {"fullname": "zernpy.zernikepol.ZernPol.osa2noll", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.osa2noll", "kind": "function", "doc": "

Convert the OSA / ANSI index of a Zernike polynomial to the Noll index.

\n\n
Parameters
\n\n
    \n
  • osa_index (int):\nOSA / ANSI index with int type, it must be not less than 0.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 0.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted Noll index.
    • \n
\n", "signature": "(osa_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.noll2osa": {"fullname": "zernpy.zernikepol.ZernPol.noll2osa", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.noll2osa", "kind": "function", "doc": "

Convert the Noll index of a Zernike polynomial to the OSA / ANSI index.

\n\n
Parameters
\n\n
    \n
  • noll_index (int):\nThe Noll index with int type, it must be not less than 1.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 1.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted OSA / ANSI index.
    • \n
\n", "signature": "(noll_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.osa2fringe": {"fullname": "zernpy.zernikepol.ZernPol.osa2fringe", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.osa2fringe", "kind": "function", "doc": "

Convert the OSA / ANSI index of a Zernike polynomial to the Fringe index.

\n\n
Parameters
\n\n
    \n
  • osa_index (int):\nOSA / ANSI index with int type, it must be not less than 0.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 0.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted Fringe index.
    • \n
\n", "signature": "(osa_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.fringe2osa": {"fullname": "zernpy.zernikepol.ZernPol.fringe2osa", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.fringe2osa", "kind": "function", "doc": "

Convert the Fringe / Univ. of Arizona index of a Zernike polynomial to the OSA / ANSI index.

\n\n
Parameters
\n\n
    \n
  • fringe_index (int):\nThe noll index with int type, it must be not less than 1.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the index provided with not int type or index < 1.
    • \n
\n\n
Returns
\n\n
    \n
  • int: Converted OSA / ANSI index.
    • \n
\n", "signature": "(fringe_index: int) -> int:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.sum_zernikes": {"fullname": "zernpy.zernikepol.ZernPol.sum_zernikes", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.sum_zernikes", "kind": "function", "doc": "

Calculate sum of Zernike polynomials with their amplitude coefficients (e.g., for plotting over a unit circle).

\n\n
Parameters
\n\n
    \n
  • coefficients (Sequence[float]):\nCoefficients of Zernike polynomials for calculation of their sum.
    • \n
  • polynomials (Sequence[ZernPol]):\nInitialized polynomials as class instances of ZernPol class specified in this module.
    • \n
  • r (float or numpy.ndarray):\nRadius(Radii) from a unit circle.
    • \n
  • theta (float or numpy.ndarray):\nPolar angle(-s) from a unit circle.
    • \n

  • get_surface (bool, optional):\nIf True, it forces to calculate 2D sum of polynomials based on r and theta (as a mesh of polar coordinates).\nThe default is False.

    \n\n

    Note that if r and theta provided as the numpy ndarrays with different shapes and this flag is False, then\nthe result of this method will raise ValueError (because r and theta shapes will be checked for equality).

    • \n
\n\n
Raises
\n\n
    \n
  • TypeError: If the input parameters aren't iterable (doesn't support len() function), this error will be raised.
    • \n
  • ValueError: If the lengths of lists (tuples, numpy.ndarrays) aren't equal for coefficients and polynomials.
    • \n
\n\n

Or if the list (tuple, numpy.ndarray vector, ...) with Zernike polynomials instances (ZernPol()).

\n\n
Returns
\n\n
    \n
  • Sum of Zernike polynomials (float or numpy.ndarray):\nDepending on the input values and parameter get_surface - can be: float, 1D or 2D numpy.ndarrays.
    • \n
\n", "signature": "(\tcoefficients: Sequence[float],\tpolynomials: Sequence,\tr: Union[float, numpy.ndarray],\ttheta: Union[float, numpy.ndarray],\tget_surface: bool = False) -> Union[float, numpy.ndarray]:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_polar_coordinates": {"fullname": "zernpy.zernikepol.ZernPol.gen_polar_coordinates", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_polar_coordinates", "kind": "function", "doc": "

Generate the named tuple \"polar_vectors\" with R and Theta - vectors with polar coordinates for an entire unit circle.

\n\n

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are\ndefined by the specification of r_step and theta_rad_step parameters.

\n\n
Parameters
\n\n
    \n
  • r_step (float, optional):\nStep for generation the vector with radiuses for an entire unit circle. The default is 0.01.
    • \n
  • theta_rad_step (float, optional):\nStep for generation the vector with theta angles for an entire unit circle. The default is (np.pi/240).
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the r_step or theta_rad_step provided in the way, that vectors R and Theta cannot be generated.
    • \n
\n\n
Returns
\n\n
    \n
  • polar_vectors: namedtuple(\"polar_vectors\", \"R Theta\"), where R - vector with radiuses values [0.0, r_step, ... 1.0],\nTheta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
    • \n
\n", "signature": "(\tr_step: float = 0.01,\ttheta_rad_step: float = 0.01309) -> zernpy.zernikepol.polar_vectors:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_equal_polar_mesh": {"fullname": "zernpy.zernikepol.ZernPol.gen_equal_polar_mesh", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_equal_polar_mesh", "kind": "function", "doc": "

Generate the named tuple \"polar_vectors\" with R and Theta - vectors with polar coordinates for an entire unit circle.

\n\n

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are\nequal and defined by the parameter n_points.

\n\n
Parameters
\n\n
    \n
  • n_points (int, optional):\nNumber of points between 0.0 ... 1.0 for radii and 0.0 ... 2pi for thetas. The default is 250.
    • \n
\n\n
Returns
\n\n
    \n
  • polar_vectors: namedtuple(\"polar_vectors\", \"R Theta\"), where R - vector with radiuses values [0.0, r_step, ... 1.0],\nTheta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
    • \n
\n", "signature": "(n_points: int = 250) -> zernpy.zernikepol.polar_vectors:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.plot_profile": {"fullname": "zernpy.zernikepol.ZernPol.plot_profile", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.plot_profile", "kind": "function", "doc": "

Plot the provided Zernike polynomial (instance of ZernPol class) on the matplotlib figure.

\n\n

Note that the plotting function plt.show() creates the plot in non-interactive mode.

\n\n
Parameters
\n\n
    \n
  • polynomial (ZernPol):\nInstance of ZernPol class.
    • \n
  • color_map (str, optional):\nColor map of the polar plot, common values for representation: coolwarm, jet, turbo, rainbow.\nAs alternative - perceptually equal color maps: viridis, plasma. The default is \"coolwarm\".\nNote that rainbow, jet, turbo - not perceptually equal color maps.
    • \n
  • show_title (bool, optional):\nToggle for showing the name of polynomial on the plot or not (only works for 2D case).
    • \n
  • use_defaults (bool, optional):\nUse default parameters for polar coordinates generation. The default is True.
    • \n
  • projection (str, optional):\nEither \"2d\" (\"2D\") - for 2D profile plot, or \"3d\" (\"3D\") - for 3D surface plot. The default is \"2d\".
    • \n
  • polar_coordinates (polar_vectors, optional):\nIf the flag 'use_defaults' is False, this named tuple is used for accessing polar coordinates for plotting.\nThe default is None.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If the flag use_defaults is False and polar_coordinates are not provided.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tpolynomial,\tcolor_map: str = 'coolwarm',\tshow_title: bool = True,\tuse_defaults: bool = True,\tprojection: str = '2d',\tpolar_coordinates: Optional[zernpy.zernikepol.polar_vectors] = None):", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.gen_zernikes_surface": {"fullname": "zernpy.zernikepol.ZernPol.gen_zernikes_surface", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.gen_zernikes_surface", "kind": "function", "doc": "

Generate surface of provided Zernike polynomials on the generated polar coordinates used steps.

\n\n
Parameters
\n\n
    \n
  • coefficients (Sequence[float]):\nCoefficients of Zernike polynomials for calculation of their sum.
    • \n
  • polynomials (Sequence[ZernPol]):\nInitialized polynomials as class instances of ZernPol class specified in this module.
    • \n

  • r_step (float, optional):\nStep for generation the vector with radiuses for an entire unit circle. The default is 0.01.

    \n\n

    See also the documentation for the method gen_polar_coordinates().

    • \n

  • theta_rad_step (float, optional):\nStep for generation the vector with theta angles for an entire unit circle. The default is (np.pi/180).

    \n\n

    See also the documentation for the method gen_polar_coordinates().

    • \n
  • equal_n_coordinates (bool, optional):\nSwitch between generation polar coordinates based on individual steps or on equal number of points.\nThe default is False.
    • \n
  • n_points (int, optional):\nNumber of points used for generation of equal sized polar coordinates r, theta.
    • \n
\n\n
Returns
\n\n
    \n
  • zernikes_surface: namedtuple(\"zernikes_surface\", \"ZernSurf R Theta\") - tuple for storing mesh values for polar coordinates.\nZernSurf variable is 2D matrix with the sum of the input polynomials on generated polar coordinates (R, Theta).
    • \n
\n", "signature": "(\tcoefficients: Sequence[float],\tpolynomials: Sequence,\tr_step: float = 0.01,\ttheta_rad_step: float = 0.0174533,\tequal_n_coordinates: bool = False,\tn_points: int = 250) -> zernpy.zernikepol.zernikes_surface:", "funcdef": "def"}, "zernpy.zernikepol.ZernPol.plot_sum_zernikes_on_fig": {"fullname": "zernpy.zernikepol.ZernPol.plot_sum_zernikes_on_fig", "modulename": "zernpy.zernikepol", "qualname": "ZernPol.plot_sum_zernikes_on_fig", "kind": "function", "doc": "

Plot a sum of the specified Zernike polynomials by input lists (see function parameters) on the provided figure.

\n\n

Note that for showing the plotted figure, one needs to call appropriate functions (e.g., matplotlib.pyplot.show()\nor figure.show()) as the method of the input parameter figure.

\n\n
Parameters
\n\n
    \n
  • figure (plt.Figure):\n'Figure' class there the plotting will be done, previous plot will be cleared out.
    • \n
  • use_defaults (bool, optional):\nUse for plotting default values for generation of a mesh of polar coordinates and calculation\nof Zernike polynomials sum or Use for plotting provided calculated beforehand surface. The default is True.
    • \n
  • coefficients (Sequence[float], optional):\nCoefficients of Zernike polynomials for calculation of their sum. The default is ().
    • \n
  • polynomials (Sequence[ZernPol], optional):\nInitialized polynomials as class instances of ZernPol class specified in this module. The default is ().
    • \n
  • zernikes_sum_surface (namedtuple(\"zernikes_surface\", \"ZernSurf R Theta\"), optional):\nThis tuple should contain the ZernSurf calculated on a mesh of polar coordinates R, Theta.\nThis tuple could be generated by the call of the static method gen_zernikes_surface().\nCheck the method signature for details. The default is None.
    • \n
  • show_range (bool, optional):\nFlag for showing range of provided values as the colorbar on the figure. The default is True.
    • \n
  • color_map (str, optional):\nColor map of the polar plot, common values for representation: coolwarm, jet, turbo, rainbow.\nAs alternative - perceptually equal color maps: viridis, plasma. The default is \"coolwarm\".\nNote that rainbow, jet, turbo - not perceptually equal color maps.
    • \n
  • projection (str, optional):\nEither \"2d\" (\"2D\") - for 2D profile plot, or \"3d\" (\"3D\") - for 3D surface plot. The default is \"2d\".
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Check the signature for details. In general, it will be raised if some input parameters are inconsistent.
    • \n
\n\n
Returns
\n\n
    \n
  • figure (plt.Figure):\nMatplotlib.pyplot Figure class there the Zernike polynomials sum plotted.
    • \n
\n", "signature": "(\tfigure: matplotlib.figure.Figure,\tcoefficients: Sequence[float] = (),\tpolynomials: Sequence = (),\tuse_defaults: bool = True,\tzernikes_sum_surface: Optional[zernpy.zernikepol.zernikes_surface] = None,\tshow_range: bool = True,\tcolor_map: str = 'coolwarm',\tprojection: str = '2d') -> matplotlib.figure.Figure:", "funcdef": "def"}, "zernpy.zernikepol.fit_polynomials_vectors": {"fullname": "zernpy.zernikepol.fit_polynomials_vectors", "modulename": "zernpy.zernikepol", "qualname": "fit_polynomials_vectors", "kind": "function", "doc": "

Fit provided Zernike polynomials (instances of ZernPol class) as the input tuple to the provided 1D vectors.

\n\n

1D vectors should contain: phases recorded in the related radii and thetas (polar coordinates). For the example\nof phases and coordinates composing, see the module test_fitting in 'tests' sub-folder of the repository.

\n\n
Parameters
\n\n
    \n
  • polynomials (tuple):\nInitialized tuple with instances of the ZernPol class that effectively represents target set of Zernike polynomials for fitting.
    • \n
  • phases_vector (numpy.ndarray):\nRecorded phases.
    • \n
  • radii_vector (numpy.ndarray):\nRelated radii - 1st polar coordinates for the recorded phases.
    • \n
  • thetas_vector (numpy.ndarray):\nRelated angles (thetas) - 2nd polar coordinates for the recorded phases.
    • \n
  • round_digits (int, optional):\nRound digits for returned polynomials amplitudes (numpy.round(...) function call). The default is 4.
    • \n
\n\n
Raises
\n\n
    \n
  • AttributeError: Any of provided vectors (phases_vector, etc.) isn't proper 1D numpy.ndarray (len(array.shape > 1)).
    • \n
\n\n
Returns
\n\n
    \n
  • zernike_coefficients (numpy.ndarray):\n1D numpy.ndarray with the fitted coefficients of Zernike polynomials.
    • \n
\n", "signature": "(\tpolynomials: tuple,\tphases_vector: numpy.ndarray,\tradii_vector: numpy.ndarray,\tthetas_vector: numpy.ndarray,\tround_digits: int = 4) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernikepol.fit_polynomials": {"fullname": "zernpy.zernikepol.fit_polynomials", "modulename": "zernpy.zernikepol", "qualname": "fit_polynomials", "kind": "function", "doc": "

Fit provided Zernike polynomials (instances of ZernPol class) as the input tuple to the 2D phase image.

\n\n

2D phase image implies that phases recorded depending on cartesian coordinates and circle aperture is cropped\nout from this image for fitting procedure. One can check the result of cropping by plotting return_cropped_image as\nTrue and plotting the second item from the returned tuple.

\n\n
Parameters
\n\n
    \n
  • phases_image (numpy.ndarray):\n2D image with recorded phases which should be approximated by the sum of Zernike polynomials.\nNote that image is assumed as the recorded phases on the cartesian coordinates. The circle\n(aperture) containing phases is cropped from the input image during the fitting procedure.
    • \n
  • polynomials (tuple):\nInitialized tuple with instances of the ZernPol class that effectively represents target set of Zernike polynomials.
    • \n
  • crop_radius (float, optional):\nAllow cropping pixel from range [0.5, 1.0], where 1.0 corresponds to radius of the cropped circle = min image size.\nThe default is 1.0.
    • \n
  • suppress_warnings (bool, optional):\nFlag for suppress warnings about the provided 2D image sizes. The default is False.
    • \n
  • strict_circle_border (bool, optional):\nFlag for controlling how the border pixels (on the circle radius) are treated: strictly or less strict for\nallowing more pixels to be treated as belonged to a cropped circle. The default is False.
    • \n
  • round_digits (int, optional):\nRound digits for returned polynomials amplitudes (numpy.round(...) function call). The default is 4.
    • \n
  • return_cropped_image (bool, optional):\nFlag for calculating and returning cropped image, used for fitting procedure. The default is False.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: Depending on the input parameter (flag) \"return_cropped_image\":\nif it is True, then tuple returned with following variables: zernike_coefficients - 1D numpy.ndarray\nwith the fitted coefficients of Zernike polynomials, and cropped_image - the cropped part from the\ninput image with phases that is used for fitting procedure (useful for debugging purposes);\nif it is False, the following tuple will be returned: zernike_coefficients, None - 1st with the same\nmeaning and type as explained before.
    • \n
\n", "signature": "(\tphases_image: numpy.ndarray,\tpolynomials: tuple,\tcrop_radius: float = 1.0,\tsuppress_warnings: bool = False,\tstrict_circle_border: bool = False,\tround_digits: int = 4,\treturn_cropped_image: bool = False) -> Tuple[numpy.ndarray, Optional[numpy.ndarray]]:", "funcdef": "def"}, "zernpy.zernikepol.generate_phases_image": {"fullname": "zernpy.zernikepol.generate_phases_image", "modulename": "zernpy.zernikepol", "qualname": "generate_phases_image", "kind": "function", "doc": "

Generate phases image (profile) for provided set of polynomials with provided coefficients (amplitudes).

\n\n
Parameters
\n\n
    \n
  • polynomials (tuple, optional):\nInitialized ZernPol instances for generation of phases as the sum of all stored in this tuple polynomials. The default is ().
    • \n
  • polynomials_amplitudes (tuple, optional):\nAmplitudes of polynomials provided in the tuple 'polynomials'. The default is ().
    • \n
  • img_width (int, optional):\nWidth of generated image. The default is 513.
    • \n
  • img_height (int, optional):\nHeight of generated image. The default is 513.
    • \n
\n\n
Returns
\n\n
    \n
  • phases_image (np.ndarray):\n2D image with phases calculated as the sum of provided polynomials.
    • \n
\n", "signature": "(\tpolynomials: tuple = (),\tpolynomials_amplitudes: tuple = (),\timg_width: int = 513,\timg_height: int = 513) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernikepol.generate_random_phases": {"fullname": "zernpy.zernikepol.generate_random_phases", "modulename": "zernpy.zernikepol", "qualname": "generate_random_phases", "kind": "function", "doc": "

Generate phases image (profile) for random set of polynomials with randomly selected amplitudes.

\n\n
Parameters
\n\n
    \n
  • max_order (int, optional):\nMaximum radial order of generated Zernike polynomials. The default is 4.
    • \n
  • img_width (int, optional):\nWidth of generated image. The default is 513.
    • \n
  • img_height (int, optional):\nHeight of generated image. The default is 513.
    • \n
  • round_digits (int, optional):\nRound digits for polynomials amplitudes generation (numpy.round(...) function call). The default is 4.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: Consisting of:\n2D phase profile image with provided width and height;\n1D numpy.ndarray containing randomly selected polynomials amplitudes;\ntuple with generated Zernike polynomials.
    • \n
\n", "signature": "(\tmax_order: int = 4,\timg_width: int = 513,\timg_height: int = 513,\tround_digits: int = 4) -> Tuple[numpy.ndarray, numpy.ndarray, Tuple[zernpy.zernikepol.ZernPol, ...]]:", "funcdef": "def"}, "zernpy.zernikepol.generate_polynomials": {"fullname": "zernpy.zernikepol.generate_polynomials", "modulename": "zernpy.zernikepol", "qualname": "generate_polynomials", "kind": "function", "doc": "

Generate tuple with ZernPol instances (ultimately, representing polynomials) indexed using OSA scheme, starting with Piston(m=0,n=0).

\n\n
Parameters
\n\n
    \n
  • max_order (int, optional):\nMaximum overall radial order (n) for generated Zernike list (pyramid). The default is 10.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: Raised if max_order < 1, because it should be not less than 0.
    • \n
\n\n
Returns
\n\n
    \n
  • tuple: It composes generated ZernPol instances (Zernike polynomials) ordered using OSA indexing scheme.
    • \n
\n", "signature": "(max_order: int = 10) -> Tuple[zernpy.zernikepol.ZernPol, ...]:", "funcdef": "def"}, "zernpy.zernpsf": {"fullname": "zernpy.zernpsf", "modulename": "zernpy.zernpsf", "kind": "module", "doc": "

PSF class definition based on Zernike polynomial for computation of its kernel for convolution / deconvolution.

\n\n

@author: Sergei Klykov, @year: 2025, @license: MIT

\n"}, "zernpy.zernpsf.ZernPSF": {"fullname": "zernpy.zernpsf.ZernPSF", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF", "kind": "class", "doc": "

The PSF (2D) class for focal plane of a microscopic system assuming that the phase profile is described by the Zernike polynomial.

\n\n

In other words, the PSF describing the image of point source formed by the microscopic system.

\n\n

Check the set_physical_props() method for the list of expected physical parameters for PSF calculation and calculate_psf_kernel() for\nthe references to the diffraction integral used for calculations.

\n\n
References
\n\n

[1] Principles of Optics, by M. Born and E. Wolf, 4 ed., 1968

\n\n

[2] https://en.wikipedia.org/wiki/Optical_aberration#Zernike_model_of_aberrations

\n\n

[3] https://wp.optics.arizona.edu/jsasian/wp-content/uploads/sites/33/2016/03/ZP-Lecture-12.pdf

\n\n

[4] https://www.researchgate.net/publication/236097143_Imaging_characteristics_of_Zernike_and_annular_polynomial_aberrations

\n\n

[5] https://nijboerzernike.nl/_PDF/JOSA-A-19-849-2002.pdf#[0,{%22name%22:%22Fit%22}]

\n"}, "zernpy.zernpsf.ZernPSF.__init__": {"fullname": "zernpy.zernpsf.ZernPSF.__init__", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.__init__", "kind": "function", "doc": "

Initiate the PSF wrapping class.

\n\n
Parameters
\n\n
    \n
  • zernpol (ZernPol | Sequence[ZernPol]):\nSingle instance of ZernPol() class or Sequence with ZernPol instances.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: 1) If not instance(-s) of ZernPol class provided as the input parameter;
    • \n
\n\n

2) If the provided sequence has zero length;

\n\n

3) If not all members of the provided sequence are instance of the \"ZernPol\" class;

\n\n

4) If the provided sequence contain repeated polynomials.

\n\n
Returns
\n\n
    \n
  • ZernPSF() class instance.
    • \n
\n", "signature": "(\tzernpol: Union[zernpy.zernikepol.ZernPol, Sequence[zernpy.zernikepol.ZernPol]])"}, "zernpy.zernpsf.ZernPSF.kernel": {"fullname": "zernpy.zernpsf.ZernPSF.kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.kernel", "kind": "variable", "doc": "

\n", "annotation": ": numpy.ndarray", "default_value": "array([[1.]])"}, "zernpy.zernpsf.ZernPSF.kernel_size": {"fullname": "zernpy.zernpsf.ZernPSF.kernel_size", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.kernel_size", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "1"}, "zernpy.zernpsf.ZernPSF.NA": {"fullname": "zernpy.zernpsf.ZernPSF.NA", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.NA", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "1.0"}, "zernpy.zernpsf.ZernPSF.wavelength": {"fullname": "zernpy.zernpsf.ZernPSF.wavelength", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.wavelength", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.532"}, "zernpy.zernpsf.ZernPSF.expansion_coeff": {"fullname": "zernpy.zernpsf.ZernPSF.expansion_coeff", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.expansion_coeff", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.5"}, "zernpy.zernpsf.ZernPSF.zernpol": {"fullname": "zernpy.zernpsf.ZernPSF.zernpol", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.zernpol", "kind": "variable", "doc": "

\n", "annotation": ": Optional[zernpy.zernikepol.ZernPol]", "default_value": "None"}, "zernpy.zernpsf.ZernPSF.polynomials": {"fullname": "zernpy.zernpsf.ZernPSF.polynomials", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.polynomials", "kind": "variable", "doc": "

\n", "annotation": ": tuple", "default_value": "()"}, "zernpy.zernpsf.ZernPSF.pixel_size_nyquist": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size_nyquist", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size_nyquist", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.133"}, "zernpy.zernpsf.ZernPSF.pixel_size_nyquist_eStr": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size_nyquist_eStr", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size_nyquist_eStr", "kind": "variable", "doc": "

\n", "default_value": "'1.330e-01'"}, "zernpy.zernpsf.ZernPSF.pixel_size": {"fullname": "zernpy.zernpsf.ZernPSF.pixel_size", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.pixel_size", "kind": "variable", "doc": "

\n", "default_value": "0.13034"}, "zernpy.zernpsf.ZernPSF.alpha": {"fullname": "zernpy.zernpsf.ZernPSF.alpha", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.alpha", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "0.9398496240601504"}, "zernpy.zernpsf.ZernPSF.airy": {"fullname": "zernpy.zernpsf.ZernPSF.airy", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.airy", "kind": "variable", "doc": "

\n", "annotation": ": bool", "default_value": "False"}, "zernpy.zernpsf.ZernPSF.n_int_r_points": {"fullname": "zernpy.zernpsf.ZernPSF.n_int_r_points", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.n_int_r_points", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "320"}, "zernpy.zernpsf.ZernPSF.n_int_phi_points": {"fullname": "zernpy.zernpsf.ZernPSF.n_int_phi_points", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.n_int_phi_points", "kind": "variable", "doc": "

\n", "annotation": ": int", "default_value": "300"}, "zernpy.zernpsf.ZernPSF.k": {"fullname": "zernpy.zernpsf.ZernPSF.k", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.k", "kind": "variable", "doc": "

\n", "annotation": ": float", "default_value": "11.810498697705988"}, "zernpy.zernpsf.ZernPSF.json_file_path": {"fullname": "zernpy.zernpsf.ZernPSF.json_file_path", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.json_file_path", "kind": "variable", "doc": "

\n", "annotation": ": str", "default_value": "''"}, "zernpy.zernpsf.ZernPSF.coefficients": {"fullname": "zernpy.zernpsf.ZernPSF.coefficients", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.coefficients", "kind": "variable", "doc": "

\n", "annotation": ": Optional[numpy.ndarray]", "default_value": "None"}, "zernpy.zernpsf.ZernPSF.amplitudes": {"fullname": "zernpy.zernpsf.ZernPSF.amplitudes", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.amplitudes", "kind": "variable", "doc": "

\n", "annotation": ": Optional[numpy.ndarray]", "default_value": "None"}, "zernpy.zernpsf.ZernPSF.set_physical_props": {"fullname": "zernpy.zernpsf.ZernPSF.set_physical_props", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.set_physical_props", "kind": "function", "doc": "

Set parameters in physical units.

\n\n
Parameters
\n\n
    \n
  • NA (float):\nNumerical aperture of an objective, assumed usage of microscopic ones.
    • \n
  • wavelength (float):\nWavelength of monochromatic light (\u03bb) used for imaging in physical units (e.g., as \u00b5m).
    • \n

  • expansion_coeff (float | Sequence[float]):\nAmplitude(-s) or expansion coefficient(-s) of the Zernike polynomial in physical units.\nNote that according to the used equation for PSF calculation it will be adjusted to the units of wavelength:\nalpha = expansion_coeff/wavelength. See the equation in the method \"calculate_psf_kernel\".

    \n\n

    Note that if Airy pattern (PSF for Piston polynomial) is provided, it's required to provide amplitude for it.\nHowever, this amplitude will be ignored in general for calculation because of its properties.

    • \n
  • pixel_physical_size (float):\nPixel size of the formed image in physical units (do not mix up with the physical sensor (camera) pixel size!).\nThe sanity check performed as the comparison with the Abbe resolution limit (see ref. [1] and [2]), provided pixel size\nshould be less than this limit.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If one of the sanity check has been failed, check the Error message for details.
    • \n
\n\n
References
\n\n

[1] https://www.microscopyu.com/techniques/super-resolution/the-diffraction-barrier-in-optical-microscopy

\n\n

[2] https://www.edinst.com/de/blog/the-rayleigh-criterion-for-microscope-resolution/

\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tself,\tNA: float,\twavelength: float,\texpansion_coeff: Union[float, Sequence[float]],\tpixel_physical_size: float):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.set_calculation_props": {"fullname": "zernpy.zernpsf.ZernPSF.set_calculation_props", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.set_calculation_props", "kind": "function", "doc": "

Set calculation properties: kernel size, number of integration points on polar coordinates.

\n\n

Note that it's recommended to set the physical properties by set_physical_props() method for getting estimated\nrequired kernel size.

\n\n
Parameters
\n\n
    \n
  • kernel_size (int):\nSize of PSF kernel (2D matrix used for convolution). Should be odd integer not less than 3.
    • \n
  • n_integration_points_r (int):\nNumber of integration points used for calculation diffraction integral on the radius of the entrance pupil\n(normalized to the range [0.0, 1.0]). Should be integer not less than 20.
    • \n
  • n_integration_points_phi (int):\nNumber of integration points used for calculation diffraction integral on the polar angle phi of the entrance pupil\n(from the range [0.0, 2pi]). Should be integer not less than 36.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If sanity checks fail (if provided parameters less than sanity values).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tself,\tkernel_size: int,\tn_integration_points_r: int,\tn_integration_points_phi: int):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.calculate_psf_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.calculate_psf_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.calculate_psf_kernel", "kind": "function", "doc": "

Calculate PSF kernel using the specified or default calculation parameters and physical values.

\n\n

Calculation based on the diffraction integral for the circular aperture. The final equation is derived based from the 2 References.

\n\n

Kernel is defined as the image formed on the sensor (camera) by the diffraction-limited, ideal microscopic system.\nThe diffraction integral is calculated numerically on polar coordinates, assuming circular aperture of\nan imaging system (micro-objective).

\n\n

The order of integration and used equations in short:\n1st - integration going on radius p, using trapezoidal rule: p\u2022(alpha\u2022zernike_pol.polynomial_value(p, phi) -\n r\u2022p\u2022cos(phi - theta))\u20221j

\n\n

2nd - integration going on angle phi, using Simpson rule, calling the returned integrals by 1st call for each phi and as the final\noutput, it provides as the np.power(np.abs(integral_sum), 2)\u2022integral_normalization, there integral_normalization =\n1.0/(pi\u2022pi) - the square of the module of the diffraction integral (complex value), i.e. intensity as the PSF value.

\n\n

For details of implementation, explore methods in 'calculations' module, calc_psfs.py file.

\n\n

Note that the Nijboer's approximation for calculation of diffraction integral also has been tested, but the results is not in agreement\nwith the reference [3] due to the large expansion coefficients for Zernike polynomials.

\n\n

Note that for Piston (m=0, n=0) the exact equation is used, that provides Airy pattern as the result.

\n\n
Parameters
\n\n
    \n
  • suppress_warnings (bool, optional):\nFlag to suppress all possible warnings. The default is False.
    • \n
  • normalized (bool, optional):\nFlag to return normalized PSF values to max=1.0. The default is True.
    • \n
  • verbose_info (bool, optional):\nFlag to print out each step completion report and measured elapsed time in ms. The default is False.
    • \n
  • accelerated (bool, optional):\nFlag to accelerate the calculations by using numba library for scripts compilation. Acceleration will be used automatically,\nif None is provided and 'numba' library is installed. The default is None.
    • \n
\n\n
References
\n\n

[1] Principles of Optics, by M. Born and E. Wolf, 4 ed., 1968

\n\n

[2] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf

\n\n

[3] PSF shapes: https://en.wikipedia.org/wiki/Zernike_polynomials#/media/File:ZernikeAiryImage.jpg

\n\n

[4] https://opg.optica.org/ao/abstract.cfm?uri=ao-52-10-2062 (DOI: 10.1364/AO.52.002062)

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: 2D PSF kernel.
    • \n
\n", "signature": "(\tself,\tsuppress_warnings: bool = False,\tnormalized: bool = True,\tverbose_info: bool = False,\taccelerated: Optional[bool] = None) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.plot_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.plot_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.plot_kernel", "kind": "function", "doc": "

Plot on the external figure (matplotlib.pyplot.figure()) calculated PSF kernel.

\n\n
Parameters
\n\n
    \n
  • id_str (str, optional):\nString with ID for making unique Figure. The default is \"\".
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, id_str: str = ''):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.convolute_img": {"fullname": "zernpy.zernpsf.ZernPSF.convolute_img", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.convolute_img", "kind": "function", "doc": "

Convolute the provided image with PSF kernel as 2D arrays and return the convolved image with the same type as the original one.

\n\n
Parameters
\n\n
    \n
  • image (numpy.ndarray):\nSample gray-scaled (2D array) image.
    • \n
  • scale2original (bool):\nConvolution resulting image will be rescaled to the max intensity of the provided image if True. The default is True.
    • \n
\n\n
Returns
\n\n
    \n
  • convolved_image (numpy.ndarray):\nResult of convolution (by using function scipy.ndimage.convolve).
    • \n
\n", "signature": "(self, image: numpy.ndarray, scale2original: bool = True) -> numpy.ndarray:", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.visualize_convolution": {"fullname": "zernpy.zernpsf.ZernPSF.visualize_convolution", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.visualize_convolution", "kind": "function", "doc": "

Plot convolution of the PSF kernel and sample image (even centered disk with blurred edges).

\n\n
Parameters
\n\n
    \n
  • radius (float, optional):\nRadius of the centered disk. The default is 4.0.
    • \n
  • max_intensity (int, optional):\nMaximum intensity of the even disk. The default is 255.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, radius: float = 4.0, max_intensity: int = 255):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.crop_kernel": {"fullname": "zernpy.zernpsf.ZernPSF.crop_kernel", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.crop_kernel", "kind": "function", "doc": "

Crop redundant points from kernel.

\n\n

By default, all rows and columns containing any single value that more than 1% of max kernel value, are not cropped.

\n\n

Cropped kernel saved in class variable 'kernel'.

\n\n
Parameters
\n\n
    \n
  • min_part_of_max (float, optional):\nPart of kernel max that is used for checking rows / columns for cropping. The default is 0.01.
    • \n
\n\n
Raises
\n\n
    \n
  • ValueError: If parameter 'min_part_of_max' is not > 0.0 and not < 0.5.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, min_part_of_max: float = 0.01):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.save_json": {"fullname": "zernpy.zernpsf.ZernPSF.save_json", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.save_json", "kind": "function", "doc": "

Save class attributes (PSF kernel, physical properties, etc.) in the JSON file for further reloading and avoiding long computation.

\n\n
Parameters
\n\n
    \n
  • abs_path (str | Path, optional):\nAbsolute path for the file. If None, the file will be saved in the folder \"saved_psfs\" in the root of the package.\nThe default is None.
    • \n
  • overwrite (bool, optional):\nFlag for overwriting the existing file. The default is False.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(\tself,\tabs_path: Union[str, pathlib.Path, NoneType] = None,\toverwrite: bool = False):", "funcdef": "def"}, "zernpy.zernpsf.ZernPSF.read_json": {"fullname": "zernpy.zernpsf.ZernPSF.read_json", "modulename": "zernpy.zernpsf", "qualname": "ZernPSF.read_json", "kind": "function", "doc": "

Read the JSON file with the saved attributes and setting it for the class.

\n\n
Parameters
\n\n
    \n
  • abs_path (str | Path, optional):\nAbsolute path to the file. If None is provided, then the stored in the attribute path will be checked. The default is None.
    • \n
\n\n
Returns
\n\n
    \n
  • None.
    • \n
\n", "signature": "(self, abs_path: Union[str, pathlib.Path, NoneType] = None):", "funcdef": "def"}, "zernpy.zernpsf.force_get_psf_compilation": {"fullname": "zernpy.zernpsf.force_get_psf_compilation", "modulename": "zernpy.zernpsf", "qualname": "force_get_psf_compilation", "kind": "function", "doc": "

Force compilation of computing functions for round and ellipse 'precise' shaped objects.

\n\n

verbose_report : bool, optional\n Flag for printing out the elapsed for compilation time. The default is False.

\n\n
Returns
\n\n
    \n
  • None or tuple with 2 used ZernPSF instances depending on 'numba_installed' flag.
    • \n
\n", "signature": "(\tverbose_report: bool = False) -> Optional[Tuple[zernpy.zernpsf.ZernPSF, zernpy.zernpsf.ZernPSF]]:", "funcdef": "def"}, "zernpy.zernpsf.clean_zernpy_cache": {"fullname": "zernpy.zernpsf.clean_zernpy_cache", "modulename": "zernpy.zernpsf", "qualname": "clean_zernpy_cache", "kind": "function", "doc": "

Clean locally cached files created by numba after compilation of computation methods from the 'calc_psfs_numba' module.

\n\n
Returns
\n\n
    \n
  • bool: Flag if local cache is assumed (at least 6 cached files successfully removed) to be cleaned.
    • \n
\n", "signature": "() -> bool:", "funcdef": "def"}}, "docInfo": {"zernpy.zernikepol": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 46}, "zernpy.zernikepol.ZernPol": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 12}, "zernpy.zernikepol.ZernPol.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 251}, "zernpy.zernikepol.ZernPol.get_indices": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 48, "bases": 0, "doc": 51}, "zernpy.zernikepol.ZernPol.get_mn_orders": {"qualname": 4, "fullname": 6, "annotation": 0, "default_value": 0, "signature": 26, "bases": 0, "doc": 38}, "zernpy.zernikepol.ZernPol.get_polynomial_name": {"qualname": 4, "fullname": 6, "annotation": 0, "default_value": 0, "signature": 31, "bases": 0, "doc": 114}, "zernpy.zernikepol.ZernPol.polynomial_value": {"qualname": 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API Documentation

-
zernpy ver. 0.1.0, 2026 Sergei Klykov
+
zernpy ver. 0.1.1, 2026 Sergei Klykov
built with

Also, provides a few functions useful for fitting set of Zernike polynomials to an image with phases.

-

@author: Sergei Klykov, @year: 2026, @licence: MIT

+

@author: Sergei Klykov, @year: 2026, @license: MIT

@@ -917,13 +917,13 @@
Returns
@staticmethod
def - gen_polar_coordinates( r_step: float = 0.01, theta_rad_step: float = 0.01309) -> zernpy.zernikepol.PolarVectors: + gen_polar_coordinates( r_step: float = 0.01, theta_rad_step: float = 0.01309) -> zernpy.zernikepol.polar_vectors: -

Generate the named tuple "PolarVectors" with R and Theta - vectors with polar coordinates for an entire unit circle.

+

Generate the named tuple "polar_vectors" with R and Theta - vectors with polar coordinates for an entire unit circle.

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are defined by the specification of r_step and theta_rad_step parameters.

@@ -946,7 +946,7 @@
Raises
Returns
    -
  • polar_vectors: namedtuple("PolarVectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], +
  • polar_vectors: namedtuple("polar_vectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], Theta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
@@ -958,13 +958,13 @@
Returns
@staticmethod
def - gen_equal_polar_mesh(n_points: int = 250) -> zernpy.zernikepol.PolarVectors: + gen_equal_polar_mesh(n_points: int = 250) -> zernpy.zernikepol.polar_vectors:
-

Generate the named tuple "PolarVectors" with R and Theta - vectors with polar coordinates for an entire unit circle.

+

Generate the named tuple "polar_vectors" with R and Theta - vectors with polar coordinates for an entire unit circle.

Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are equal and defined by the parameter n_points.

@@ -979,7 +979,7 @@
Parameters
Returns
    -
  • polar_vectors: namedtuple("PolarVectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], +
  • polar_vectors: namedtuple("polar_vectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], Theta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi].
@@ -991,7 +991,7 @@
Returns
@staticmethod
def - plot_profile( polynomial, color_map: str = 'coolwarm', show_title: bool = True, use_defaults: bool = True, projection: str = '2d', polar_coordinates: zernpy.zernikepol.PolarVectors = ()): + plot_profile( polynomial, color_map: str = 'coolwarm', show_title: bool = True, use_defaults: bool = True, projection: str = '2d', polar_coordinates: Optional[zernpy.zernikepol.polar_vectors] = None):
@@ -1018,7 +1018,7 @@
Parameters
Either "2d" ("2D") - for 2D profile plot, or "3d" ("3D") - for 3D surface plot. The default is "2d".
  • polar_coordinates (polar_vectors, optional): If the flag 'use_defaults' is False, this named tuple is used for accessing polar coordinates for plotting. -The default is ().
    • +The default is None.
    Raises
    @@ -1041,7 +1041,7 @@
    Returns
    @staticmethod
    def - gen_zernikes_surface( coefficients: Sequence[float], polynomials: Sequence, r_step: float = 0.01, theta_rad_step: float = 0.0174533, equal_n_coordinates: bool = False, n_points: int = 250) -> zernpy.zernikepol.ZernikesSurface: + gen_zernikes_surface( coefficients: Sequence[float], polynomials: Sequence, r_step: float = 0.01, theta_rad_step: float = 0.0174533, equal_n_coordinates: bool = False, n_points: int = 250) -> zernpy.zernikepol.zernikes_surface: @@ -1074,7 +1074,7 @@
    Parameters
    Returns
      -
    • zernikes_surface: namedtuple("ZernikesSurface", "ZernSurf R Theta") - tuple for storing mesh values for polar coordinates. +
    • zernikes_surface: namedtuple("zernikes_surface", "ZernSurf R Theta") - tuple for storing mesh values for polar coordinates. ZernSurf variable is 2D matrix with the sum of the input polynomials on generated polar coordinates (R, Theta).
    @@ -1086,7 +1086,7 @@
    Returns
    @staticmethod
    def - plot_sum_zernikes_on_fig( figure: matplotlib.figure.Figure, coefficients: Sequence[float] = (), polynomials: Sequence = (), use_defaults: bool = True, zernikes_sum_surface: zernpy.zernikepol.ZernikesSurface = (), show_range: bool = True, color_map: str = 'coolwarm', projection: str = '2d') -> matplotlib.figure.Figure: + plot_sum_zernikes_on_fig( figure: matplotlib.figure.Figure, coefficients: Sequence[float] = (), polynomials: Sequence = (), use_defaults: bool = True, zernikes_sum_surface: Optional[zernpy.zernikepol.zernikes_surface] = None, show_range: bool = True, color_map: str = 'coolwarm', projection: str = '2d') -> matplotlib.figure.Figure: @@ -1109,10 +1109,10 @@
    Parameters
    Coefficients of Zernike polynomials for calculation of their sum. The default is ().
  • polynomials (Sequence[ZernPol], optional): Initialized polynomials as class instances of ZernPol class specified in this module. The default is ().
    • -
  • zernikes_sum_surface (namedtuple("ZernikesSurface", "ZernSurf R Theta") , optional): +
  • zernikes_sum_surface (namedtuple("zernikes_surface", "ZernSurf R Theta"), optional): This tuple should contain the ZernSurf calculated on a mesh of polar coordinates R, Theta. This tuple could be generated by the call of the static method gen_zernikes_surface(). -Check the method signature for details. The default is ().
    • +Check the method signature for details. The default is None.
  • show_range (bool, optional): Flag for showing range of provided values as the colorbar on the figure. The default is True.
  • color_map (str, optional): @@ -1278,7 +1278,7 @@
    Returns
    def - generate_random_phases( max_order: int = 4, img_width: int = 513, img_height: int = 513, round_digits: int = 4) -> Tuple[numpy.ndarray, numpy.ndarray, Tuple[ZernPol]]: + generate_random_phases( max_order: int = 4, img_width: int = 513, img_height: int = 513, round_digits: int = 4) -> Tuple[numpy.ndarray, numpy.ndarray, Tuple[ZernPol, ...]]:
    @@ -1315,7 +1315,7 @@
    Returns
    def - generate_polynomials(max_order: int = 10) -> Tuple[ZernPol]: + generate_polynomials(max_order: int = 10) -> Tuple[ZernPol, ...]:
    diff --git a/docs/api/zernpy/zernpsf.html b/docs/api/zernpy/zernpsf.html index 3d38c5f..e4ede15 100644 --- a/docs/api/zernpy/zernpsf.html +++ b/docs/api/zernpy/zernpsf.html @@ -120,28 +120,19 @@

    API Documentation

  • read_json
    • -
  • - initialize_parallel_workers -
    • -
  • - get_psf_point_r_parallel -
    • -
  • - get_kernel_parallel -
    • -
  • - deinitialize_workers -
  • force_get_psf_compilation
    • +
  • + clean_zernpy_cache +
    • -
    zernpy ver. 0.1.0, 2026 Sergei Klykov
    +
    zernpy ver. 0.1.1, 2026 Sergei Klykov
    built with

    PSF class definition based on Zernike polynomial for computation of its kernel for convolution / deconvolution.

    -

    @author: Sergei Klykov, @year: 2025, @licence: MIT

    +

    @author: Sergei Klykov, @year: 2025, @license: MIT

    @@ -296,8 +287,8 @@
    Returns
    - zernpol: zernpy.zernikepol.ZernPol = -<zernpy.zernikepol.ZernPol object> + zernpol: Optional[zernpy.zernikepol.ZernPol] = +None
    @@ -308,7 +299,7 @@
    Returns
    - polynomials = + polynomials: tuple = () @@ -428,7 +419,7 @@
    Returns
    - coefficients: numpy.ndarray = + coefficients: Optional[numpy.ndarray] = None @@ -440,7 +431,7 @@
    Returns
    - amplitudes: numpy.ndarray = + amplitudes: Optional[numpy.ndarray] = None @@ -507,7 +498,7 @@
    Returns
    def - set_calculation_props( self, kernel_size: int, n_integration_points_r: int, n_integration_points_phi: int) -> None: + set_calculation_props( self, kernel_size: int, n_integration_points_r: int, n_integration_points_phi: int):
    @@ -550,7 +541,7 @@
    Returns
    def - calculate_psf_kernel( self, suppress_warnings: bool = False, normalized: bool = True, verbose_info: bool = False, accelerated: bool = None) -> numpy.ndarray: + calculate_psf_kernel( self, suppress_warnings: bool = False, normalized: bool = True, verbose_info: bool = False, accelerated: Optional[bool] = None) -> numpy.ndarray:
    @@ -656,7 +647,7 @@
    Parameters
    • image (numpy.ndarray): -Sample image, not colour.
      • +Sample gray-scaled (2D array) image.
    • scale2original (bool): Convolution resulting image will be rescaled to the max intensity of the provided image if True. The default is True.
    @@ -743,7 +734,7 @@
    Returns
    def - save_json( self, abs_path: Union[str, pathlib.Path] = None, overwrite: bool = False): + save_json( self, abs_path: Union[str, pathlib.Path, NoneType] = None, overwrite: bool = False):
    @@ -774,7 +765,7 @@
    Returns
    def - read_json(self, abs_path: Union[str, pathlib.Path] = None): + read_json(self, abs_path: Union[str, pathlib.Path, NoneType] = None):
    @@ -798,131 +789,47 @@
    Returns
    -
    -
    - - def - initialize_parallel_workers(self): - - -
    - - -

    Initialize 4 Processes() for performing integration.

    - -

    See intmproc.py script (utils module) for implementation details. -Tests showed that this way doesn't provide performance gain.

    - -
    Returns
    - -
      -
    • None.
      • -
    -
    - - -
    -
    -
    - - def - get_psf_point_r_parallel(self, r: float, theta: float) -> float: - - -
    - - -

    Parallel implementation of numerical integration.

    - -
    Parameters
    - -
      -
    • r (float): -Input radial polar coordinate.
      • -
    • theta (float): -Input angular polar coordinate.
      • -
    - -
    Returns
    - -
      -
    • float: Each point for PSF kernel.
      • -
    -
    - - -
    -
    -
    + +
    +
    def - get_kernel_parallel(self, normalize_values: bool = True) -> numpy.ndarray: + force_get_psf_compilation( verbose_report: bool = False) -> Optional[Tuple[ZernPSF, ZernPSF]]:
    - + -

    Parallelized implementation of PSF kernel calculation.

    - -

    Note it's much less effective than common calculate_psf_kernel() method.

    - -
    Parameters
    - -
      -
    • normalize_values (bool, optional): -Flag to normalize values. The default is True.
      • -
    - -
    Returns
    - -
      -
    • numpy.ndarray: PSF kernel.
      • -
    -
    - - -
    -
    -
    - - def - deinitialize_workers(self): +

    Force compilation of computing functions for round and ellipse 'precise' shaped objects.

    - -
    - - -

    Release initialized before Processes for performing parallel computation.

    +

    verbose_report : bool, optional + Flag for printing out the elapsed for compilation time. The default is False.

    Returns
      -
    • None.
      • +
    • None or tuple with 2 used ZernPSF instances depending on 'numba_installed' flag.
    -
    -
    +
    def - force_get_psf_compilation(verbose_report: bool = False) -> Optional[tuple]: + clean_zernpy_cache() -> bool:
    - + -

    Force compilation of computing functions for round and ellipse 'precise' shaped objects.

    - -

    verbose_report : bool, optional - Flag for printing out the elapsed for compilation time. The default is False.

    +

    Clean locally cached files created by numba after compilation of computation methods from the 'calc_psfs_numba' module.

    Returns
      -
    • None or tuple with 2 used ZernPSF instances depending on 'numba_installed' flag.
      • +
    • bool: Flag if local cache is assumed (at least 6 cached files successfully removed) to be cleaned.
    diff --git a/pyproject.toml b/pyproject.toml index b9dc177..bc21129 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -2,26 +2,31 @@ name = "zernpy" dynamic = ["version"] # Discovering of the version by the setuptools (see below: in the 'file' or 'attr') authors = [ - {name = "Sergei Klykov"}, - {email = "sergej.klykow@gmail.com"} + { name = "Sergei Klykov" }, + { email = "sergej.klykow@gmail.com" } ] description = "Calculation of real Zernike polynomials values, associated PSFs, plotting of their profiles in polar coordinates" readme = "README.md" -# license = {file = "LICENSE"} # includes the whole text in METADATA, maybe not so convienient requires-python = ">=3.8" classifiers = [ "Programming Language :: Python :: 3", "Operating System :: OS Independent", ] + dependencies = [ "numpy", "matplotlib", - "scipy", + "scipy", ] +[project.optional-dependencies] +performance = ["numba>=0.57.1"] +dev = ["ruff", "mypy", "pytest"] +all = ["numba>=0.57.1"] + keywords = ["zernike-polynomials", "zernike-psf"] [project.urls] # METADATA in wheel file will represent the data below by using pip show zernpy -v -# But the the links themselves are mapped / parced by the PyPi website +# But the links themselves are mapped / parsed by the PyPi website "Homepage" = "https://pypi.org/project/zernpy/" "Repository" = "https://github.com/sklykov/zernpy/" "Bug Tracker" = "https://github.com/sklykov/zernpy/issues/" @@ -31,14 +36,59 @@ keywords = ["zernike-polynomials", "zernike-psf"] [tool.setuptools.packages.find] # Manifest.in file is only required for adding some package-data where = ["src"] include = ["zernpy*"] -exclude = ["tests"] +exclude = ["zernpy.tests*"] # only packages should be specified, folders - exclude in MANIFEST.in +namespaces = false # forbid treating a folder as a module without explicit __init__.py presence -[tool.setuptools.exclude-package-data] -zernpy = ["*.png"] # should exclude image files from distribution +[tool.setuptools] +include-package-data = false # forbid to make a confusion on the src/zernpy/tests folder presence +# confusion is produced because it is an importable module [tool.setuptools.dynamic] -version = {attr = "zernpy.__version__"} # Variable set in the __init__.py +version = { attr = "zernpy.__version__" } # Variable set in the __init__.py [build-system] requires = ["setuptools>=75.0"] build-backend = "setuptools.build_meta" + +[tool.mypy] +python_version = "3.11" +warn_unused_configs = true # mypy will warn if any of options below not valid +warn_redundant_casts = true # warn about unnecessary cast(): from typing import cast +warn_unused_ignores = true # warn about unused comments '# type: ignore' +show_error_codes = true # enables error code in a report +pretty = true # better formatted report in a console +strict_equality = true # checks proper usage of ==, !=, in +no_implicit_optional = true # throws error on: def f(x: int = None): ... +# Note: flags below introduces too strict type checks +# disallow_untyped_defs = true # all parameters and return types must be fully annotated +check_untyped_defs = true # mypy checks untyped expressions and tries to infer types +# warn_return_any = true # Any couldn't be used as return type +# disallow_any_generics = true # forbid bare generics like list, dict, tuple... -> instead List[float] +exclude = [ + '^tests/', + '^build/', + '^dist/', + '^src/zernpy/tests/' +] +[[tool.mypy.overrides]] # for ignoring warning about not checked imported libraries +module = ["numba", "joblib"] +ignore_missing_imports = true +# [[tool.mypy.overrides]] # ignore any errors in specific test files - retained for ref. +# module = ["zernpy.run_zernpsf_as_main"] +# ignore_errors = true + +[tool.ruff] +line-length = 145 # my own preference +indent-width = 4 +target-version = "py311" +[tool.ruff.lint] +select = ["E4", "E7", "E9", "F", "I", "B", "SIM"] +ignore = ["E702", "E402", # used in the IDE + "SIM108", # many ternany operator replacements in a code + "SIM113", # potentially can break logic in a loop +] +[tool.ruff.format] +quote-style = "double" +indent-style = "space" +line-ending = "auto" +docstring-code-format = true diff --git a/src/zernpy/__init__.py b/src/zernpy/__init__.py index 02f60ba..a537efa 100644 --- a/src/zernpy/__init__.py +++ b/src/zernpy/__init__.py @@ -8,21 +8,11 @@ """ -__version__ = "0.1.0" # Straightforward way of specifying package version and including it to the package attributes +__version__ = "0.1.1" # Straightforward way of specifying package version and including it to the package attributes -if __name__ == "__main__": - # use absolute imports for importing as module - __all__ = ['zernikepol', 'zernpsf'] # for specifying from zernpy import * if package imported from some script -elif __name__ == "zernpy": - pass # do not add module "zernikepol" to __all__ attribute, because it demands to construct explicit path +# Univesal logic for making all main classes and functions available after calling 'from project import *' +from .zernikepol import ZernPol, fit_polynomials, fit_polynomials_vectors, generate_phases_image, generate_polynomials, generate_random_phases +from .zernpsf import ZernPSF, clean_zernpy_cache, force_get_psf_compilation -# Automatically bring the main class and some methods to the name space when one of import command is used commands: -# 1) from zernpy import ZernPol, ... functions; 2) from zernpy import * -if __name__ != "__main__" and __name__ != "__mp_main__": - from .zernikepol import ZernPol # main class auto export on the import call of the package - # functions auto export - when everything imported from the module - from .zernikepol import generate_polynomials, fit_polynomials, generate_random_phases, fit_polynomials_vectors, generate_phases_image - from .zernpsf import ZernPSF # class for ZernPSF auto export on the import call of the package - from .zernpsf import force_get_psf_compilation # function for precompile functions by numba library - __all__ = ["ZernPol", "generate_polynomials", "fit_polynomials", "generate_random_phases", "fit_polynomials_vectors", - "generate_phases_image", "ZernPSF", "force_get_psf_compilation"] +__all__ = ["ZernPol", "generate_polynomials", "fit_polynomials", "generate_random_phases", "fit_polynomials_vectors", + "generate_phases_image", "ZernPSF", "force_get_psf_compilation", "clean_zernpy_cache"] diff --git a/src/zernpy/calculations/calc_psfs.py b/src/zernpy/calculations/calc_psfs.py index 406d067..eb9745b 100644 --- a/src/zernpy/calculations/calc_psfs.py +++ b/src/zernpy/calculations/calc_psfs.py @@ -7,19 +7,18 @@ """ # %% Global imports -import numpy as np -import matplotlib.pyplot as plt -from scipy.special import jv -from pathlib import Path -import warnings -from math import sqrt, pi, e -import time -from scipy.ndimage import convolve import json -from matplotlib.patches import Circle +import time +import warnings from functools import partial -from typing import Union -# import time +from math import e, pi, sqrt +from pathlib import Path +from typing import Optional, Union + +import matplotlib.pyplot as plt +import numpy as np +from scipy.ndimage import convolve +from scipy.special import jv # Testing the parallelization with joblib. Native Pool.map() tested and results transferred to the collection_numCalc repo try: @@ -29,21 +28,17 @@ joblib_installed = False # %% Local (package-scoped) imports -if __name__ == "__main__" or __name__ == Path(__file__).stem or __name__ == "__mp_main__": - from calc_zernike_pol import define_orders -else: - from .calc_zernike_pol import define_orders +from .calc_zernike_pol import define_orders # %% Module parameters __docformat__ = "numpydoc" um_char = "\u00B5" # Unicode char code for micrometers lambda_char = "\u03BB" # Unicode char code for lambda (wavelength) pi_char = "\u03C0" # Unicode char code for pi -# print(um_char, lambda_char, pi_char) # check the codes for characters from above # %% Reference - Airy profile for Z(0, 0) -def airy_ref_pattern(r: float): +def airy_ref_pattern(r: float) -> float: """ Return Airy pattern radial function J1(r)/r. @@ -59,17 +54,15 @@ def airy_ref_pattern(r: float): """ r = round(r, 12) - if r == 0.0: - ratio = jv(1, 1E-11)/1E-11 - else: - ratio = jv(1, r)/r + ratio = jv(1, 1E-11)/1E-11 if r == 0.0 else jv(1, r)/r # NOTE that the values produced by exact equation below is off with the direct computation of diffraction integral # apporoximate coefficient is 0.986711 for a central point. Most likely, the difference because of numerical integration return 4.0*pow(ratio, 2) # %% PSF pixel value calc. -def diffraction_integral_r(zernike_pol, alpha: float, phi: float, p: Union[float, np.ndarray], theta: float, r: float) -> np.array: +def diffraction_integral_r(zernike_pol, alpha: float, phi: float, p: Union[float, np.ndarray], theta: float, + r: float) -> Union[complex, np.ndarray]: """ Diffraction integral function for the formed image point (see the references as the sources of the equation). @@ -263,17 +256,16 @@ def get_psf_point_r_parallel(zernike_pol, r: float, theta: float, alpha: float, # Vectorized or parallelized form of for loop for even and odd phi-s if not joblib_installed or paralleljobs is None: - even_sums = [radial_integral(zernike_pol, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(2, n_int_phi_points-2, 2)] - even_sums = np.asarray(even_sums); even_sum = np.sum(even_sums) - odd_sums = [radial_integral(zernike_pol, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(1, n_int_phi_points-1, 2)] - odd_sums = np.asarray(odd_sums); odd_sum = np.sum(odd_sums) + even_sums = np.asarray([radial_integral(zernike_pol, r, theta, i*h_phi, alpha, n_int_r_points) + for i in range(2, n_int_phi_points-2, 2)]) + odd_sums = np.asarray([radial_integral(zernike_pol, r, theta, i*h_phi, alpha, n_int_r_points) + for i in range(1, n_int_phi_points-1, 2)]) + even_sum = np.sum(even_sums); odd_sum = np.sum(odd_sums) else: if paralleljobs is not None and isinstance(paralleljobs, Parallel): - even_sums = paralleljobs(delayed(radial_integral_fixed_args)(i*h_phi) for i in range(2, n_int_phi_points-2, 2)) - odd_sums = paralleljobs(delayed(radial_integral_fixed_args)(i*h_phi) for i in range(1, n_int_phi_points-1, 2)) - # even_sum = sum(even_sums, start=even_sum); odd_sum = sum(even_sums, start=odd_sum) - even_sums = np.asarray(even_sums); even_sum = np.sum(even_sums); odd_sums = np.asarray(odd_sums); odd_sum = np.sum(odd_sums) - + even_sums = np.asarray(paralleljobs(delayed(radial_integral_fixed_args)(i*h_phi) for i in range(2, n_int_phi_points-2, 2))) + odd_sums = np.asarray(paralleljobs(delayed(radial_integral_fixed_args)(i*h_phi) for i in range(1, n_int_phi_points-1, 2))) + even_sum = np.sum(even_sums); odd_sum = np.sum(odd_sums) # Simpson integration rule implementation yA = radial_integral(zernike_pol, r, theta, 0.0, alpha, n_int_r_points) yB = radial_integral(zernike_pol, r, theta, 2.0*pi, alpha, n_int_r_points) @@ -306,13 +298,13 @@ def get_kernel_size(zernike_pol, len2pixels: float, alpha: float, wavelength: fl Estimated kernel size. """ - (m, n) = define_orders(zernike_pol) # get polynomial orders + m, n = define_orders(zernike_pol) # get polynomial orders size_ext = 0 # additional size depending on some parameters below - if m == 0 and n == 0: # Airy + if m == 0 and n == 0: # Airy profile if 0.25 < NA < 1.0: - multiplier = 5.0*(1.0 - NA) + 1.5 + multiplier = 5.0*(1.0 - NA) + 1.5 + alpha else: - multiplier = 4.5 + 2.5*sqrt(1.0 / NA) + multiplier = 4.5 + 2.5*sqrt(1.0 / NA) + 1.25*alpha else: multiplier = 1.25*sqrt(n) # Enlarge kernel size according to the provided radial order n if abs(m) > 0 and n % 2 != 0: # Enlarge kernel size for the not symmetrical orders @@ -336,7 +328,7 @@ def get_kernel_size(zernike_pol, len2pixels: float, alpha: float, wavelength: fl def get_psf_kernel(zernike_pol, len2pixels: float, alpha: float, wavelength: float, NA: float, n_int_r_points: int = 320, - n_int_phi_points: int = 300, show_kernel: bool = False, fig_title: str = None, normalize_values: bool = False, + n_int_phi_points: int = 300, show_kernel: bool = False, fig_title: Optional[str] = None, normalize_values: bool = False, airy_pattern: bool = False, kernel_size: int = 0, test_parallel: bool = False, fig_id: str = "", test_vectorized: bool = False, suppress_warns: bool = False, verbose: bool = False) -> np.ndarray: """ @@ -386,7 +378,7 @@ def get_psf_kernel(zernike_pol, len2pixels: float, alpha: float, wavelength: flo Matrix with PSF values. """ - (m, n) = define_orders(zernike_pol) # get polynomial orders + m, n = define_orders(zernike_pol) # get polynomial orders # Convert provided absolute value of Zernike expansion coefficient (in um) into fraction of wavelength alpha /= wavelength; k = 2.0*pi/wavelength # Calculate angular frequency (k) # Empirical estimation of the sufficient size for the kernel @@ -410,9 +402,9 @@ def get_psf_kernel(zernike_pol, len2pixels: float, alpha: float, wavelength: flo # Check that the calibration coefficient is sufficient for calculation pixel_size_nyquist = 0.5*0.61*wavelength/NA if len2pixels > pixel_size_nyquist and not suppress_warns: - __warn_message = f"Provided calibration coefficient {len2pixels} {um_char}/pixels isn't sufficient enough" + __warn_message = f"\nProvided calibration coefficient {len2pixels} {um_char}/pixels isn't sufficient enough" __warn_message += f" (defined by the relation between Nyquist freq. and the optical resolution: 0.61{lambda_char}/NA)" - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) # Calculate the PSF kernel for usage in convolution operation # mean_time_integration = 0.0; n = 0 if not joblib_installed or not test_parallel: @@ -475,7 +467,7 @@ def get_psf_kernel(zernike_pol, len2pixels: float, alpha: float, wavelength: flo if kernel_border_max > np.max(kernel)/20.0 and not suppress_warns: __warn_message = (f"\nThe calculated size for PSF ({size}) isn't sufficient for its proper representation, " + "because the maximum value on the kernel border is bigger than 5% of maximum overall kernel") - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) # Plotting the calculated kernel if show_kernel: if airy_pattern: @@ -484,7 +476,7 @@ def get_psf_kernel(zernike_pol, len2pixels: float, alpha: float, wavelength: flo plt.figure(fig_title, figsize=(6, 6)) else: plt.figure(f"{(m, n)} {zernike_pol.get_polynomial_name(True)}: {round(alpha, 2)}*wavelength {fig_id}", figsize=(6, 6)) - plt.imshow(kernel, cmap=plt.cm.viridis, origin='upper'); plt.tight_layout() + plt.imshow(kernel, cmap=plt.colormaps["viridis"], origin='upper'); plt.tight_layout() return kernel @@ -592,10 +584,11 @@ def get_psf_point_r_pols(polynomials, amplitudes: np.ndarray, r: float, theta: f """ h_phi = 2.0*pi/n_int_phi_points; even_sum = 0.0j; odd_sum = 0.0j # Vectorized or parallelized form of for loop for even and odd phi-s - even_sums = [radial_integral_pols(polynomials, amplitudes, r, theta, i*h_phi, n_int_r_points) for i in range(2, n_int_phi_points-2, 2)] - even_sums = np.asarray(even_sums); even_sum = np.sum(even_sums) - odd_sums = [radial_integral_pols(polynomials, amplitudes, r, theta, i*h_phi, n_int_r_points) for i in range(1, n_int_phi_points-1, 2)] - odd_sums = np.asarray(odd_sums); odd_sum = np.sum(odd_sums) + even_sums = np.asarray([radial_integral_pols(polynomials, amplitudes, r, theta, i*h_phi, n_int_r_points) + for i in range(2, n_int_phi_points-2, 2)]) + odd_sums = np.asarray([radial_integral_pols(polynomials, amplitudes, r, theta, i*h_phi, n_int_r_points) + for i in range(1, n_int_phi_points-1, 2)]) + even_sum = np.sum(even_sums); odd_sum = np.sum(odd_sums) # Simpson integration rule implementation yA = radial_integral_pols(polynomials, amplitudes, r, theta, 0.0, n_int_r_points) yB = radial_integral_pols(polynomials, amplitudes, r, theta, 2.0*pi, n_int_r_points) @@ -661,7 +654,7 @@ def get_psf_kernel_zerns(polynomials, amplitudes: np.ndarray, len2pixels: float, if len2pixels > pixel_size_nyquist and not suppress_warns: __warn_message = f"\nProvided calibration coefficient {len2pixels} {um_char}/pixels isn't sufficient enough" __warn_message += f" (defined by the relation between Nyquist freq. and the optical resolution: 0.61{lambda_char}/NA)" - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) # Verbose info preparation if verbose: calculated_points = 0 # for explicit showing of performance @@ -701,7 +694,7 @@ def get_psf_kernel_zerns(polynomials, amplitudes: np.ndarray, len2pixels: float, if kernel_border_max > np.max(kernel)/20.0 and not suppress_warns: __warn_message = (f"\nThe calculated size for PSF ({size}) isn't sufficient for its proper representation, " + "because the maximum value on the kernel border is bigger than 5% of maximum overall kernel") - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) return kernel @@ -723,8 +716,9 @@ def convolute_img_psf(img: np.ndarray, psf_kernel: np.ndarray, scale2original: b Result of convolution (used scipy.ndimage.convolve). """ - img_type = img.dtype; img = np.copy(img) # get the image type and copy its content to a new container - convolved_img = convolve(np.float64(img), psf_kernel, mode='reflect'); conv_coeff = np.sum(psf_kernel) # convolution using scipy + img_type = img.dtype; img = np.copy(img).astype(np.float64) # get the image type and copy its content to a new container + convolved_img: np.ndarray + convolved_img = convolve(img, psf_kernel, mode='reflect'); conv_coeff = np.sum(psf_kernel) # convolution using scipy if conv_coeff > 0.0: convolved_img /= conv_coeff # correct the convolution result by dividing to the kernel sum if scale2original: @@ -736,8 +730,8 @@ def convolute_img_psf(img: np.ndarray, psf_kernel: np.ndarray, scale2original: b # %% Save and read the calculated PSF matrices def save_psf(psf_kernel: np.ndarray, NA: float, wavelength: float, pixel_size: float, expansion_coefficient: Union[float, np.ndarray], - kernel_size: int, n_int_points_r: int, n_int_points_phi: int, zernike_pol, folder_path: str = None, - overwrite: bool = True, additional_file_name: str = None) -> str: + kernel_size: int, n_int_points_r: int, n_int_points_phi: int, zernike_pol, folder_path: Optional[str] = None, + overwrite: bool = True, additional_file_name: Optional[str] = None) -> str: """ Save the calculated PSF kernel along with the used for the calculation parameters. @@ -775,8 +769,10 @@ def save_psf(psf_kernel: np.ndarray, NA: float, wavelength: float, pixel_size: f """ single_pol_used = False; osa_indices = [] # flag for saving different parameters + if isinstance(expansion_coefficient, np.ndarray): + ampls = expansion_coefficient.copy().tolist() if not hasattr(zernike_pol, '__len__'): - (m, n) = define_orders(zernike_pol); single_pol_used = True # get polynomial orders + m, n = define_orders(zernike_pol); single_pol_used = True # get polynomial orders else: for zernpol in zernike_pol: osa_indices.append(zernpol.get_indices()[1]) @@ -794,12 +790,12 @@ def save_psf(psf_kernel: np.ndarray, NA: float, wavelength: float, pixel_size: f if single_pol_used: json_file_path = saved_psfs_folder.joinpath(f"psf_{(m, n)}_{additional_file_name}_{expansion_coefficient}.json") else: - json_file_path = saved_psfs_folder.joinpath(f"psf_{osa_indices}_{additional_file_name}_{expansion_coefficient}.json") + json_file_path = saved_psfs_folder.joinpath(f"psf_{osa_indices}_{additional_file_name}_{ampls}.json") else: if single_pol_used: json_file_path = saved_psfs_folder.joinpath(f"psf_{(m, n)}_{expansion_coefficient}.json") else: - json_file_path = saved_psfs_folder.joinpath(f"psf_{osa_indices}_{expansion_coefficient}.json") + json_file_path = saved_psfs_folder.joinpath(f"psf_{osa_indices}_{ampls}.json") # Data composing for recording data4serialization = {} # python dictionary is similar to the JSON file structure and can be dumped directly there data4serialization['PSF Kernel'] = psf_kernel.tolist(); data4serialization['NA'] = NA; data4serialization['Wavelength'] = wavelength @@ -808,17 +804,18 @@ def save_psf(psf_kernel: np.ndarray, NA: float, wavelength: float, pixel_size: f if single_pol_used: data4serialization["Expansion Coefficient"] = expansion_coefficient; data4serialization["Polynomial"] = zernike_pol.get_indices()[1] else: - data4serialization["Amplitudes"] = expansion_coefficient.tolist(); data4serialization["Polynomials"] = osa_indices + data4serialization["Amplitudes"] = ampls; data4serialization["Polynomials"] = osa_indices # File presence check and recording if json_file_path.exists() and not overwrite: - _warn_message = "The file already exists, the content won't be overwritten."; warnings.warn(_warn_message) + _warn_message = "\nThe file already exists, the content won't be overwritten." + warnings.warn(_warn_message, stacklevel=2) if not json_file_path.exists() or (json_file_path.exists() and overwrite): with open(json_file_path, 'w') as json_write_file: json.dump(data4serialization, json_write_file) return str(json_file_path.absolute()) -def read_psf(file_path: str) -> dict: +def read_psf(file_path: str) -> Optional[dict]: """ Read the saved PSF data from the *json file. @@ -891,87 +888,3 @@ def get_bumped_circle(radius: float, max_intensity: int = 255) -> np.ndarray: # %% Define standard exports from this module __all__ = ['get_psf_kernel', 'save_psf', 'read_psf', 'convolute_img_psf', 'radial_integral_s', 'get_kernel_size', 'radial_integral', 'get_kernel_size', 'um_char', 'lambda_char', 'get_bumped_circle', 'get_psf_kernel_zerns'] - -# %% Tests -if __name__ == '__main__': - from zernpy import ZernPol - plt.ion(); plt.close('all') # close all plots before plotting new ones - # Physical parameters of a system (an objective) - wavelength = 0.55 # in micrometers - NA = 0.95 # objective property, ultimately NA = d/2*f, there d - aperture diameter, f - distance to the object (focal length for an image) - # Note that ideal Airy pattern will be (2*J1(x)/x)^2, there x = k*NA*r, there r - radius in the polar coordinates on the image - resolution = 0.61*wavelength/NA # ultimate theoretical physical resolution of an objective - pixel_size_nyquist = 0.5*resolution # Nyquist's resolution needed for using theoretical physical resolution above - pixel_size = 0.95*pixel_size_nyquist # the relation between um / pixels for calculating the coordinate in physical units for each pixel - - # Flags for performing tests - check_zero_case = True # checking that integral equation is corresponding to the Airy pattern (zero case) - check_sign_coeff = False # checking the same amplitude applied for the same polynomial (trefoil) - check_performance_optimizations = False # checking optimization of calculations - check_various_pols = False # checking the shape of some Zernike polynomials for comparing with the link below - check_warnings = False # flag for checking the warning producing - check_io = False # check save / read kernels - show_convolution_results = False # check result of convolution of several kernel with the disk - - # Definition of some Zernike polynomials for further tests - pol1 = (0, 0); pol2 = (-1, 1); pol3 = (0, 2); pol4 = (-2, 2); pol5 = (-3, 3); pol6 = (2, 2); pol7 = (-1, 3); pol8 = (0, 4) - pol9 = (-4, 4); pol7z = ZernPol(m=pol7[0], n=pol7[1]) - pol1z = ZernPol(m=pol1[0], n=pol1[1]); pol2z = ZernPol(m=pol2[0], n=pol2[1]); pol3z = ZernPol(m=pol3[0], n=pol3[1]) - - if check_zero_case: - kern_zc = get_psf_kernel(pol1z, len2pixels=wavelength/5.5, alpha=-0.4, wavelength=0.55, NA=0.65, - show_kernel=True, normalize_values=True) - kern_zc_ref = get_psf_kernel(pol1z, len2pixels=wavelength/5.5, alpha=-0.4, wavelength=0.55, NA=0.65, airy_pattern=True, - show_kernel=True, normalize_values=True) - diff = kern_zc_ref - kern_zc; plt.figure("Difference Airy and Piston", figsize=(6, 6)) - plt.imshow(diff, cmap=plt.cm.viridis, origin='upper') - - if check_sign_coeff: - kern_sign_n = get_psf_kernel(pol5, len2pixels=pixel_size, alpha=-0.5, wavelength=wavelength, NA=NA, normalize_values=False) - kern_sign_p = get_psf_kernel(pol5, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, NA=NA, normalize_values=False) - - if check_performance_optimizations: - t1 = time.perf_counter() - kern_sign = get_psf_kernel(ZernPol(m=-3, n=3), len2pixels=pixel_size, alpha=0.2, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=False) - print("Calc. time for 'for loops' form ms:", int(round(1000*(time.perf_counter() - t1), 0))) - t1 = time.perf_counter() - kern_sign2 = get_psf_kernel(ZernPol(m=-3, n=3), len2pixels=pixel_size, alpha=0.2, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=False, test_vectorized=True, fig_id="Vector. Form") - print("Calc. time for 'vectorized' form ms:", int(round(1000*(time.perf_counter() - t1), 0))) - t1 = time.perf_counter() - kern_sign3 = get_psf_kernel(ZernPol(m=-3, n=3), len2pixels=pixel_size, alpha=0.2, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=False, test_parallel=True, fig_id="Parallel. Form") - print("Calc. time for 'parallelized' form ms:", int(round(1000*(time.perf_counter() - t1), 0))) - kern_diff1 = np.round(kern_sign - kern_sign2, 9); kern_diff2 = np.round(kern_sign - kern_sign3, 9) - - if check_various_pols: - kern_def = get_psf_kernel(pol3z, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True) - kern_ast = get_psf_kernel(pol6, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True) - kern_coma = get_psf_kernel(pol7, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True) - kern_spher = get_psf_kernel(pol8, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=True) - kern_4foil = get_psf_kernel(pol9, len2pixels=pixel_size, alpha=0.5, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=True) - - if check_warnings: - kern_def = get_psf_kernel(pol3z, len2pixels=1.0, alpha=0.5, wavelength=wavelength, NA=NA, normalize_values=True) - if show_convolution_results: - # Generate the ideal centralized circle with the blurred edges - radius = 4.0; sample = get_bumped_circle(radius); plt.figure("Sample disk"); m_center, n_center = sample.shape - m_center = m_center // 2; n_center = n_center // 2; axes_img = plt.imshow(sample, cmap=plt.cm.viridis, origin='upper') - plt.tight_layout(); axes_img.axes.add_patch(Circle((n_center, m_center), radius, edgecolor='red', facecolor='none')) - # Visualize results of convolution with various PSFs - kern_def = get_psf_kernel(pol3z, len2pixels=pixel_size, alpha=0.7, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=True) - conv_def = convolute_img_psf(img=sample, psf_kernel=kern_def, scale2original=True) - plt.figure("Defocused"); axes_img2 = plt.imshow(conv_def, cmap=plt.cm.viridis, origin='upper'); plt.tight_layout() - axes_img2.axes.add_patch(Circle((n_center, m_center), radius, edgecolor='red', facecolor='none')) - kern_coma = get_psf_kernel(pol7z, len2pixels=pixel_size, alpha=-0.45, wavelength=wavelength, - NA=NA, normalize_values=True, show_kernel=True) - conv_coma = convolute_img_psf(img=sample, psf_kernel=kern_coma, scale2original=True) - plt.figure("*Coma"); axes_img3 = plt.imshow(conv_coma, cmap=plt.cm.viridis, origin='upper'); plt.tight_layout() - axes_img3.axes.add_patch(Circle((n_center, m_center), radius, edgecolor='red', facecolor='none')) diff --git a/src/zernpy/calculations/calc_psfs_check.py b/src/zernpy/calculations/calc_psfs_check.py deleted file mode 100644 index 79f68bb..0000000 --- a/src/zernpy/calculations/calc_psfs_check.py +++ /dev/null @@ -1,707 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Check calculation and plotting of associated with polynomials PSFs. - -@author: Sergei Klykov -@licence: MIT - -""" -# %% Global imports -import numpy as np -import matplotlib.pyplot as plt -from pathlib import Path -from scipy.special import jv -import warnings -from math import cos, pi -from zernpy import ZernPol -import time -import os -from skimage import io -from skimage.util import img_as_ubyte - -# %% Local (package-scoped) imports -if __name__ == "__main__" or __name__ == Path(__file__).stem or __name__ == "__mp_main__": - from calc_zernike_pol import define_orders - from calc_psfs import convolute_img_psf, save_psf, read_psf -else: - from .calc_zernike_pol import define_orders - from .calc_psfs import convolute_img_psf, save_psf, read_psf - -# %% Module parameters -__docformat__ = "numpydoc" -n_phi_points = 300; n_p_points = 320 -# Physical parameters -wavelength = 0.55 # in micrometers -k = 2.0*np.pi/wavelength # angular frequency -NA = 0.95 # microobjective property, ultimately NA = d/2*f, there d - aperture diameter, f - distance to the object (focal length for an image) -# Note that ideal Airy pattern will be (2*J1(x)/x)^2, there x = k*NA*r, there r - radius in the polar coordinates on the image -pixel_size = 0.14 # in micrometers, physical length in pixels (um / pixels) -pixel2um_coeff = k*NA*pixel_size # coefficient used for relate pixels to physical units -pixel2um_coeff_plot = k*NA*(pixel_size/10.0) # coefficient used for better plotting with the reduced pixel size for preventing pixelated - - -# %% Integral Functions - integration by trapezoidal rule first on radius (normalized on the pupil), after - on angle -def diffraction_integral_r(zernike_pol: ZernPol, alpha: float, phi: float, p: np.array, theta: float, r: float) -> np.array: - """ - Diffraction integral function (see the references for the source of the equation). - - Parameters - ---------- - zernike_pol : ZernPol - Zernike polynomial definition. - alpha : float - Amplitude of the polynomial. - phi : float - Angle on the pupil coordinates. - p : np.ndarray - Integration interval on the pupil coordinates. - theta : float - Angle on the image coordinates. - r : float - Radius on the image coordinates. - - References - ---------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - [2] https://opg.optica.org/ao/abstract.cfm?uri=ao-52-10-2062 (DOI: 10.1364/AO.52.002062) - - Returns - ------- - numpy.ndarray - Values of the diffraction integral. - - """ - # Multiplication by phi (in r*p*np.cos(...) only guides to scaling of the resulting PSF - phase_arg = (alpha*zernike_pol.polynomial_value(p, phi) - r*p*np.cos(phi - theta))*1j - return np.exp(phase_arg)*p - - -def radial_integral(zernike_pol: ZernPol, r: float, theta: float, phi: float, alpha: float) -> complex: - """ - Make integration of the diffraction integral on the radius. - - Parameters - ---------- - zernike_pol : ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - phi : float - Angle on the pupil coordinates. - alpha : float - Amplitude of the polynomial. - - Returns - ------- - complex - Complex amplitude of the field as result of integration on the pupil radius coordinate. - - """ - # Integration on the pupil angle. Vectorized form of the trapezoidal rule - h_p = 1.0/n_p_points; p = np.arange(start=h_p, stop=1.0, step=h_p) - fa = diffraction_integral_r(zernike_pol, alpha, phi, 0.0, theta, r); fb = diffraction_integral_r(zernike_pol, alpha, phi, 1.0, theta, r) - ang_int = np.sum(diffraction_integral_r(zernike_pol, alpha, phi, p, theta, r)) + 0.5*(fa + fb) - return h_p*ang_int - - -def get_psf_point_r(zernike_pol, r: float, theta: float, alpha: float = 1.0) -> float: - """ - Get the point for calculation of PSF. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - alpha : float, optional - Amplitude of the polynomial. The default is 1.0. - - Returns - ------- - float - |U|**2 - the module and square of the amplitude, intensity as the PSF value. - - """ - # Check and initialize Zernike polynomial if provided only orders - (m, n) = define_orders(zernike_pol) # get polynomial orders - if not isinstance(zernike_pol, ZernPol): - zernike_pol = ZernPol(m=m, n=n) - # Integration on the pupil radius using Simpson equation - n_integral_points = n_phi_points; h_phi = 2.0*pi/n_integral_points - even_sum = 0.0j; odd_sum = 0.0j - for i in range(2, n_integral_points-2, 2): - phi = i*h_phi; even_sum += radial_integral(zernike_pol, r, theta, phi, alpha) - for i in range(1, n_integral_points-1, 2): - phi = i*h_phi; odd_sum += radial_integral(zernike_pol, r, theta, phi, alpha) - yA = radial_integral(zernike_pol, r, theta, 0.0, alpha); yB = radial_integral(zernike_pol, r, theta, 2.0*pi, alpha) - integral_sum = (h_phi/3.0)*(yA + yB + 2.0*even_sum + 4.0*odd_sum); integral_normalization = 1.0/(pi*pi) - return np.power(np.abs(integral_sum), 2)*integral_normalization - - -# %% Integral Functions - integration on the radial external, angular - internal by the trapezoidal rule -def diffraction_integral_ang(zernike_pol: ZernPol, alpha: float, phi: np.array, p: float, theta: float, r: float) -> np.array: - """ - Diffraction integral function (see the references for the source of the equation). - - Parameters - ---------- - zernike_pol : ZernPol - Zernike polynomial definition. - alpha : float - Amplitude of the polynomial. - phi : float - Integration interval of angles on the pupil coordinates. - p : float - Radius on the pupil coordinates. - theta : float - Angle on the image coordinates. - r : float - Radius on the image coordinates. - - References - ---------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - [2] https://opg.optica.org/ao/abstract.cfm?uri=ao-52-10-2062 (DOI: 10.1364/AO.52.002062) - - Returns - ------- - numpy.ndarray - Values of the diffraction integral. - - """ - phase_arg = (alpha*zernike_pol.polynomial_value(p, phi) - r*p*np.cos(phi - theta))*1j - return np.exp(phase_arg)*p - - -def angular_integral(zernike_pol: ZernPol, r: float, theta: float, p: float, alpha: float) -> complex: - """ - Make integration of the diffraction integral on the angle. - - Parameters - ---------- - zernike_pol : ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - p : float - Radius on the pupil coordinates. - alpha : float - Amplitude of the polynomial. - - Returns - ------- - complex - Complex amplitude of the field as result of integration on the pupil radius coordinate. - - """ - # Integration on the pupil angle. Vectorized form of the trapezoidal rule - h_phi = pi/n_phi_points; phi = np.arange(start=h_phi, stop=2.0*pi, step=h_phi) - fa = diffraction_integral_ang(zernike_pol, alpha, 0.0, p, theta, r); fb = diffraction_integral_ang(zernike_pol, alpha, 2.0*pi, p, theta, r) - ang_int = np.sum(diffraction_integral_ang(zernike_pol, alpha, phi, p, theta, r)) + 0.5*(fa + fb) - return h_phi*ang_int - - -def get_psf_point_ang(zernike_pol, r: float, theta: float, alpha: float = 1.0) -> float: - """ - Get the point for calculation of PSF. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - alpha : float, optional - Amplitude of the polynomial. The default is 1.0. - - Returns - ------- - float - |U|**2 - the module and square of the amplitude, intensity as the PSF value. - - """ - # Check and initialize Zernike polynomial if provided only orders - (m, n) = define_orders(zernike_pol) # get polynomial orders - if not isinstance(zernike_pol, ZernPol): - zernike_pol = ZernPol(m=m, n=n) - # Integration on the pupil radius using Simpson equation - n_integral_points = n_p_points; h_p = 1.0/n_integral_points - even_sum = 0.0j; odd_sum = 0.0j - for i in range(2, n_integral_points-2, 2): - p = i*h_p; even_sum += angular_integral(zernike_pol, r, theta, p, alpha) - for i in range(1, n_integral_points-1, 2): - p = i*h_p; odd_sum += angular_integral(zernike_pol, r, theta, p, alpha) - yA = angular_integral(zernike_pol, r, theta, 0.0, alpha); yB = angular_integral(zernike_pol, r, theta, 1.0, alpha) - integral_sum = (h_p/3.0)*(yA + yB + 2.0*even_sum + 4.0*odd_sum) - return np.power(np.abs(integral_sum), 2)/(4.0*pi*pi) - - -# %% Attempt to speed up calculations by using provided in the Born & Wolf's handbook equation -def diffraction_int_approx_sum(zernike_pol: ZernPol, s: int, alpha: float, theta, r): - m, n = define_orders(zernike_pol) - if s == 0: - c = 2.0 - else: - c = 4.0 - coefficient = c*pow(1j, (m-1)*s)*np.cos(m*s*theta) - h_p = 1.0/n_p_points; p_arr = np.arange(start=h_p, stop=1.0, step=h_p) - eps_zero = 1E-11 # substitution of the exact 0.0 value - if r <= 1E-12: - r = eps_zero - if alpha <= 1E-12: - alpha = 1E-11 - fa = jv(s, alpha*zernike_pol.radial(eps_zero))*jv(m*s, eps_zero*r)*eps_zero # f(0.0) - fb = jv(s, alpha*zernike_pol.radial(1.0))*jv(m*s, r); fAB = 0.5*(fa + fb) - integral_sum = h_p*np.sum(jv(s, alpha*zernike_pol.radial(p_arr))*jv(m*s, r*p_arr)*p_arr) - return coefficient*(fAB + integral_sum) - - -def get_psf_point_bwap(zernike_pol, r: float, theta: float, alpha: float = 1.0) -> float: - m, n = define_orders(zernike_pol) - if not isinstance(zernike_pol, ZernPol): - zernike_pol = ZernPol(m=m, n=n) - s_max = 30; phases_sum = 0.0j - for s_i in range(s_max): - phases_sum += diffraction_int_approx_sum(zernike_pol, s_i, alpha, theta, r) - integral_normalization = 1.0/(pi*pi) - return integral_normalization*np.power(np.abs(phases_sum), 2) - - -# %% Nijboer's Thesis Functions -def radial_func(n: int, r: float) -> float: - """ - Define the radial function Jn(r)/r, there Jn - Bessel function of 1st kind with order n. - - Parameters - ---------- - n : int - Order of the Bessel function. - r : float - Radial parameter r. - - Returns - ------- - float - Evaluated function Jn(r)/r. - - """ - # Defining pure radial function (angular independent) - Jv(r)/r - if isinstance(r, int): # Convert int to float explicitly - r = float(r) - radial = 0.0 # default value - # Calculate value only for input r as the float number - if isinstance(r, float): - if abs(round(r, 12)) == 0.0: # check that the argument provided with 0 value - radial = round(2.0*pow(jv(n, 1E-11)/1E-11, 2), 11) # approximation of the limit for the special condition jv(x)/x, where x -> 0 - else: - radial = round(2.0*pow(jv(n, r)/r, 2), 11) - return radial - - -def radial_ampl_func(n: int, r: np.ndarray) -> np.ndarray: - """ - Calculate the radial amplitude functions used in the Nijboer's thesis as Jv(r)/r. - - Parameters - ---------- - n : int - Radial order of the Zernike polynomial. - r : np.ndarray - Radii on the pupil coordinates. - Note that the array can only start with the special zero point (r[0] = 0.0). - - Reference - --------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - - Returns - ------- - radial_ampl_f : np.ndarray - Jv(r)/r function values. - - """ - # Expanse the calculation for using the numpy array, assuming it starting with 0.0 - radial_ampl_f = None - print(type(r)) - if isinstance(r, np.ndarray): - r = np.round(r, 12) - if r[0] == 0.0: - radial_ampl_f = np.zeros(shape=(r.shape[0])) - r1 = r[1:]; radial_ampl_f[1:] = jv(n, r1)/r1 - radial_ampl_f[0] = jv(n, 1E-11)/1E-11 - return radial_ampl_f - - -def get_aberrated_psf(zernike_pol, r: float, theta: float, alpha: float = 1.0) -> float: - """ - Get the precalculated expansion of diffraction integral based on the Nijboer's thesis. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - alpha : float, optional - Amplitude of the polynomial. The default is 1.0. - - Reference - --------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - - Returns - ------- - float - PSF point as |U|**2. - - """ - (m, n) = define_orders(zernike_pol) # get polynomial orders - # The analytical equation could be found in the Nijboer's thesis - if m == 0 and n == 0: # piston value - x1 = radial_func(1, r) - return x1*x1*(1.0 + alpha*alpha) - # Approximation of the (-1, 1) polynomial (Y tilt). Note that each polynomial should be somehow evaluated or overall equation used - elif m == -1 and n == 1: - alpha = round(alpha, 4) # rounding with extended precision, commonly alpha up to 0.001 useful - x1 = radial_func(1, r); x2 = radial_func(2, r); x3 = radial_func(3, r); x4 = radial_func(4, r) - c1 = -(alpha*alpha)/8.0; c2 = (alpha*alpha)/4.0; c4 = pow(alpha, 3)/24.0; c5 = pow(alpha, 3)/132.0 - u = x1 + alpha*x2*cos(theta) + c1*(x1 - x3) + c2*x3*cos(2.0*theta) + c4*x4*cos(3.0*theta) + c5*(x4 - 2.0*x1) - if alpha > 1.0: - c6 = pow(alpha, 4)/192.0; x5 = radial_func(5, r) - u += c6*(x1 + -1.5*x3 + 0.5*x5 - cos(2.0*theta)*(3.0*x3 - x5) + cos(4.0*theta)*x5) - if alpha > 2.0: - __warn_message = f"For such big aberration amplitude ({alpha}) not precise equation was found, use it with caution!" - warnings.warn(__warn_message) - return u*u - # Approximation of the (-2, 2) polynomial (defocus) - elif m == 0 and n == 2: - x1 = radial_func(1, r); x3 = radial_func(3, r); x5 = radial_func(5, r); x7 = radial_func(7, r) - c1 = -(alpha*alpha)/2.0; c2 = pow(alpha, 3)/6.0 - a = x1 + c1*((4.0/3.0)*x1 - x3 + (2.0/3.0)*x5); b = alpha*x3 + c2*(-7.0*x1 + 4.8*x3 + 2.0*x5 - 0.8*x7) - if alpha < 0.0: - return a*a - b*b - else: - return b*b - a*a - else: - return 0.0 - - -# %% Another attempt to use Nijboer's Thesis Functions -# Tested, this approximation somehow doesn't work (maybe, the amplitudes of polynomial aren't small enough) -def radial_integral_nijboer(zernike_pol: ZernPol, r: float, order: int, power: int) -> float: - """ - Calculate the radial integrals used in the Nijboer's thesis. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - order : int - Of the Bessel function Jv(r). - power : int - Power of the polynomial radial component. - - Reference - --------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - - Returns - ------- - float - Result of integration. - - """ - integral_sum = 0.0; (m, n) = define_orders(zernike_pol) # get polynomial orders - # Integration on the pupil radius. Vectorized form of simple integration equation - h_p = 1.0/1000; p = np.arange(start=h_p, stop=1.0-h_p, step=h_p) - fa = 0.0; fb = np.power(zernike_pol.radial(1.0), power)*jv(order, r) - integral_sum = h_p*(np.sum(p*np.power(zernike_pol.radial(p), power)*jv(order, p*r)) + 0.5*(fa + fb)) - return integral_sum - - -def psf_point_approx_sum(zernike_pol: ZernPol, r: float, theta: float, alpha: float): - """ - Get the point for calculation of PSF as the expansion of the diffraction integral acquired in the Nijboer's thesis. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - r : float - Radius on the image coordinates. - theta : float - Angle on the image coordinates. - alpha : float, optional - Amplitude of the polynomial. The default is 1.0. - - Reference - --------- - [1] https://nijboerzernike.nl/_downloads/Thesis_Nijboer.pdf - - - Returns - ------- - float - |U|**2 - the module and square of the amplitude, intensity as the PSF value. - - """ - (m, n) = define_orders(zernike_pol) # get polynomial orders - if not isinstance(zernike_pol, ZernPol): - zernike_pol = ZernPol(m=m, n=n) - # Integration on the pupil radius. Vectorized form of simple integration equation - r = round(r, 11) - if r == 0.0: - s1 = 2.0*(jv(1, 1E-11)/1E-11); s2 = -2.0*alpha*pow(1j, m+n+1)*np.cos(m*theta)*(jv(n+1, 1E-11)/1E-11) - else: - s1 = 2.0*(jv(1, r)/r); s2 = -2.0*alpha*pow(1j, m+n+1)*np.cos(m*theta)*(jv(n+1, r)/r) - s3_1 = radial_integral_nijboer(zernike_pol, r, order=0, power=2); s3_2 = radial_integral_nijboer(zernike_pol, r, order=2*m, power=2) - s3 = -(pow(alpha, 2)/2.0)*(s3_1 + pow(1j, 2*m)*np.cos(2*m*theta)*s3_2) - s4_1 = radial_integral_nijboer(zernike_pol, r, order=m, power=3); s4_2 = radial_integral_nijboer(zernike_pol, r, order=3*m, power=3) - s4 = (pow(alpha, 3)/12.0)*(3.0*pow(1j, m+1)*np.cos(m*theta)*s4_1 + pow(1j, 3*m+1)*np.cos(3*m*theta)*s4_2) - s5_1 = 3.0*radial_integral_nijboer(zernike_pol, r, order=0, power=4) - s5_2 = 4.0*pow(1j, 2*m)*np.cos(2*m*theta)*radial_integral_nijboer(zernike_pol, r, order=2*m, power=4) - s5_3 = pow(1j, 4*m)*np.cos(4*m*theta)*radial_integral_nijboer(zernike_pol, r, order=4*m, power=4) - s5 = (pow(alpha, 4)/96.0)*(s5_1 + s5_2 + s5_3) - return np.power(np.abs(s1 + s2 + s3 + s4 + s5), 2) - - -# %% Plotting of PSFs -def get_psf_kernel(zernike_pol, calibration_coefficient: float, alpha: float, unified_kernel_size: bool = False) -> np.ndarray: - """ - Calculate centralized matrix with PSF mask. - - Parameters - ---------- - zernike_pol : tuple (m, n) or instance of the ZernPol class. - Required for calculation Zernike polynomial. - - calibration_coefficient : float - Relation between pixels and distance (physical). - - unified_kernel_size : bool - Flag for adjusting or not the kernel size to the provided absolute value of alpha. The default is False. - - Returns - ------- - kernel : numpy.ndarray - Matrix with PSF values. - """ - (m, n) = define_orders(zernike_pol) # get polynomial orders - # Define the kernel size just empirically, based on made experimental plots - if not unified_kernel_size: - if abs(alpha) < 1.0: - multiplier = 20.0 - elif abs(alpha) < 1.5: - multiplier = 24.0 - elif abs(alpha) <= 2.0: - multiplier = 26.0 - else: - multiplier = 30.0 - else: - multiplier = 26.0 - max_size = int(round(multiplier*(1.0/calibration_coefficient), 0)) + 1 # Note that with the amplitude growth, it requires to grow as well - size = max_size # Just use the maximum estimation - # Auto definition of the required PSF size is failed for the different PSFs forms (e.g., vertical coma with different amplitudes) - # Make kernel with odd sizes for precisely centering the kernel - if size % 2 == 0: - size += 1 - kernel = np.zeros(shape=(size, size)) - i_center = size//2; j_center = size//2 - # Calculate the PSF kernel for usage in convolution operation - for i in range(size): - for j in range(size): - pixel_dist = np.sqrt(np.power((i - i_center), 2) + np.power((j - j_center), 2)) - # The PSF also has the angular dependency, not only the radial one - theta = np.arctan2((i - i_center), (j - j_center)) - theta += np.pi # shift angles to the range [0, 2pi] - # The scaling below is not needed because the Zernike polynomial is scaled as the RMS values - kernel[i, j] = get_psf_point_r(zernike_pol, pixel_dist*calibration_coefficient, theta, alpha) - return kernel - - -def show_ideal_psf(zernike_pol, size: int, calibration_coefficient: float, alpha: float, title: str = None, test_alt: bool = False): - """ - Plot the intensity distribution on the image with WxH: (size, size) and using coefficient between pixel and physical distance. - - Note the color map is viridis. - - Parameters - ---------- - size : int - Size of picture for plotting. - calibration_coefficient : float - Relation between distance in pixels and um (see parameters at the start lines of the script). - title : str, optional - Title for the plotted figure. The default is None. - - Returns - ------- - None. - - """ - if size % 2 == 0: - size += 1 # make the image with odd sizes - img = np.zeros((size, size), dtype=float) - i_center = size//2; j_center = size//2 - for i in range(size): - for j in range(size): - pixel_dist = np.sqrt(np.power((i - i_center), 2) + np.power((j - j_center), 2)) - # The PSF also has the angular dependency, not only the radial one - theta = np.arctan2((i - i_center), (j - j_center)) - theta += np.pi # shift angles to the range [0, 2pi] - if not test_alt: - img[i, j] = get_psf_point_r(zernike_pol, pixel_dist*calibration_coefficient, theta, alpha) - else: - # Implementation for testing and comparing with the general equation - theta -= np.pi/2.0 - img[i, j] = get_psf_point_bwap(zernike_pol, pixel_dist*calibration_coefficient, theta, alpha) - if img[0, 0] > np.max(img)/100: - __warn_message = f"The provided size for plotting PSF ({size}) isn't sufficient for proper representation" - warnings.warn(__warn_message) - if title is not None and len(title) > 0: - plt.figure(title, figsize=(6, 6)) - else: - plt.figure(figsize=(6, 6)) - plt.imshow(img, cmap=plt.cm.viridis, origin='upper'); plt.tight_layout() - return img - - -def plot_correlation(zernike_pol, size: int, calibration_coefficient: float, alpha: float, title: str = None, - show_original: bool = True, show_psf: bool = True, R: int = 1): - """ - Plot result of correlation with the object shown as the pixelated circle. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - size : int - Size of the picture with the object. - calibration_coefficient : float - Coefficient between physical values and pixels. - alpha : float - Amplitude of the polynomial. - title : str, optional - Title of plots. The default is None. - show_original : bool, optional - Flag for plotting the original object. The default is True. - show_psf : bool, optional - Flag for plotting the used PSF. The default is True. - R : int, optional - Radius of the circle. The default is 1. - - Returns - ------- - None. - - """ - if size % 2 == 0: - size += 1 # make the image with odd sizes - img = np.zeros((size, size), dtype=float) - i_center = size//2; j_center = size//2; R = 1 - for i in range(size): - for j in range(size): - pixel_dist = np.sqrt(np.power((i - i_center), 2) + np.power((j - j_center), 2))/R - if pixel_dist < 1.0: - img[i, j] = 1.0 - else: - continue - if show_original: - plt.figure("Original object", figsize=(6, 6)); plt.imshow(img, cmap=plt.cm.viridis, extent=(0, size, 0, size)) - plt.tight_layout() - psf_kernel = get_psf_kernel(zernike_pol, calibration_coefficient, alpha) - if show_psf: - plt.figure(f"PSF for {title}", figsize=(6, 6)); plt.imshow(psf_kernel, cmap=plt.cm.viridis) - conv_img = convolute_img_psf(img, psf_kernel, scale2original=True) - plt.figure(f"Convolved with {title} image"); plt.imshow(conv_img, cmap=plt.cm.viridis, extent=(0, size, 0, size)); plt.tight_layout() - - -def plot_correlation_photo(zernike_pol, calibration_coefficient: float, alpha: float, title: str = None, - show_original: bool = True, show_psf: bool = False): - """ - Plot result of convolution of PSF with the sample image. - - Parameters - ---------- - zernike_pol : tuple (m, n) or ZernPol - Zernike polynomial definition. - size : int - Size of the picture with the object. - calibration_coefficient : float - Coefficient between physical values and pixels. - alpha : float - Amplitude of the polynomial. - title : str, optional - Title of plots. The default is None. - show_original : bool, optional - Flag for plotting the original object. The default is True. - show_psf : bool, optional - Flag for plotting the used PSF. The default is True. - - Returns - ------- - None. - - """ - try: - sample = img_as_ubyte(io.imread(os.path.join(os.getcwd(), "nesvizh_grey.jpg"), as_gray=True)) - if show_original: - plt.figure("Original Photo"); plt.imshow(sample, cmap=plt.cm.gray); plt.axis('off'); plt.tight_layout() - psf_kernel = get_psf_kernel(zernike_pol, calibration_coefficient, alpha) - if show_psf: - plt.figure(f"PSF for {title}", figsize=(6, 6)); plt.imshow(psf_kernel, cmap=plt.cm.viridis) - conv_img = convolute_img_psf(sample, psf_kernel, scale2original=True) - plt.figure(f"Convolved with {title} image"); plt.imshow(conv_img, cmap=plt.cm.gray); plt.axis('off'); plt.tight_layout() - except FileNotFoundError: - _warn_message = "The sample photo is ignored in the repository, load it to the folder with this script from repo 'collection_numCalc'" - warnings.warn(_warn_message) - - -# %% Tests -if __name__ == '__main__': - orders1 = (0, 2); orders2 = (0, 0); orders3 = (-1, 1); orders4 = (-3, 3); plot_pure_psfs = True; plot_photo_convolution = False - plot_photo_convolution_row = False; figsizes = (6.5, 6.5); test_write_read_psf = False - - # Plotting - plt.ion(); plt.close('all'); conv_pic_size = 14; detailed_plots_sizes = 22; calibration_coeff = pixel2um_coeff; alpha = 2.0 - if plot_pure_psfs: - t1 = time.time(); p_img = show_ideal_psf(orders2, detailed_plots_sizes-10, calibration_coeff, alpha, "Piston") - print(f"Calculation (steps on phi/p {n_phi_points}/{n_p_points}) of Piston takes s:", round((time.time() - t1), 3)); t1 = time.time() - - # Testing the kernel calculation - v_coma_m = get_psf_kernel((-1, 3), calibration_coeff, -1.0) - plt.figure(figsize=figsizes); plt.imshow(v_coma_m, cmap=plt.cm.viridis); plt.tight_layout() - - # Plot convolution of the sample photo with the various psfs - if plot_photo_convolution: - plot_correlation_photo(orders2, pixel2um_coeff/1.5, 1.0, "Piston", show_psf=True, show_original=True) - plot_correlation_photo(orders3, pixel2um_coeff/1.5, 1.0, "Y Tilt", show_psf=True, show_original=True) - plot_correlation_photo(orders1, pixel2um_coeff/1.5, 1.0, "Defocus", show_psf=True, show_original=True) - plot_correlation_photo(orders4, pixel2um_coeff/1.5, 1.0, "Vertical Trefoil", show_psf=True, show_original=True) - - # Testing of the convolution results with different amplitudes and signs - if plot_photo_convolution_row: - amplitudes = [-2.0, 0.0, 2.0]; vert_coma = (-1, 3) - for amplitude in amplitudes: - plot_correlation_photo(vert_coma, pixel2um_coeff/1.5, amplitude, f"Y Coma {amplitude}", show_psf=False, show_original=False) - - # Testing saving / reading - if test_write_read_psf: - ampl = -1.0; psf_kernel = get_psf_kernel(orders4, calibration_coeff, ampl) - file_path = save_psf("test", psf_kernel, NA, wavelength, calibration_coeff, ampl, orders4) - psf_stored_data = read_psf(file_path) - read_psf_kernel = np.asarray(psf_stored_data['PSF kernel']) - plt.figure(figsize=figsizes); plt.imshow(read_psf_kernel, cmap=plt.cm.viridis); plt.tight_layout() diff --git a/src/zernpy/calculations/calc_psfs_numba.py b/src/zernpy/calculations/calc_psfs_numba.py index c569a67..2e14516 100644 --- a/src/zernpy/calculations/calc_psfs_numba.py +++ b/src/zernpy/calculations/calc_psfs_numba.py @@ -7,17 +7,19 @@ """ # %% Global imports -import numpy as np -import matplotlib.pyplot as plt +import logging +import time import warnings from math import pi -import time -from typing import Union +from typing import Optional, Union + +import matplotlib.pyplot as plt +import numpy as np # %% Checking and import the numba library for speeding up the calculation -methods_compiled = False # flag for storing if the methods compiled try: from numba import njit + logging.getLogger('numba').setLevel(logging.WARNING) # disable many DEBUG level logs caused by numba during compilation except ModuleNotFoundError: pass @@ -34,8 +36,8 @@ # %% Airy profile for Z(0, 0) ('airy_ref_pattern' cannot be compiled, deleted) # %% Exchange ZernPol class call to calculation functions -@njit -def zernpol_value(orders: tuple, r: Union[float, np.ndarray], theta: Union[float, np.ndarray]) -> np.ndarray: +@njit(cache=True) +def zernpol_value(orders: tuple, r: Union[float, np.ndarray], theta: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Provide composed Zernike polynomial value calculation for compilation by numba. @@ -50,8 +52,8 @@ def zernpol_value(orders: tuple, r: Union[float, np.ndarray], theta: Union[float Returns ------- - np.ndarray - Polynomial value(-s). + Union[float, np.ndarray] (float | np.ndarray) + Polynomial value(-s) depending on used only float values for r and therat or arrays as inputs. """ m, n = orders # transfer definition of a polynomial @@ -71,7 +73,7 @@ def zernpol_value(orders: tuple, r: Union[float, np.ndarray], theta: Union[float radial = np.power(r, 0) # 1st order elif ((m == -1) and (n == 1)) or ((m == 1) and (n == 1)): - radial = r + radial = np.power(r, 1) # explicit for avoiding mypy confusing # 2nd order elif ((m == -2) and (n == 2)) or ((m == 2) and (n == 2)): radial = np.power(r, 2) # r^2 @@ -154,13 +156,14 @@ def zernpol_value(orders: tuple, r: Union[float, np.ndarray], theta: Union[float return np.power(r, n) elif n > 10 and abs(m) == n-2: # equation for high order polynomials (orders with abs(m) == n-2) return float(n)*np.power(r, n) - float(n-1)*np.power(r, n-2) - # Polynomial value as the multiplication of calculated above components + # Polynomial value as the multiplication of 3 parts: normalization, radial, triangular return norm*triangular*radial # %% PSF pixel value calc. -@njit -def diffraction_integral_r_comp(orders: tuple, alpha: float, phi: float, p: Union[float, np.ndarray], theta: float, r: float) -> np.ndarray: +@njit(cache=True) +def diffraction_integral_r_comp(orders: tuple, alpha: float, phi: float, p: Union[float, np.ndarray], theta: float, + r: float) -> Union[float, np.ndarray]: """ Diffraction integral function for the formed image point (see the references as the sources of the equation). @@ -186,15 +189,15 @@ def diffraction_integral_r_comp(orders: tuple, alpha: float, phi: float, p: Unio Returns ------- - numpy.ndarray - Values of the diffraction integral. + Union[float, np.ndarray] (float | np.ndarray) + Value(-s) of the diffraction integral. """ phase_arg = (alpha*zernpol_value(orders, p, phi) - r*p*np.cos(phi - theta))*1j return np.exp(phase_arg)*p -@njit +@njit(cache=True) def radial_integral_comp(orders: tuple, r: float, theta: float, phi: float, alpha: float, n_int_r_points: int) -> complex: """ Make integration of the diffraction integral on the radius of the entrance pupil. @@ -229,7 +232,7 @@ def radial_integral_comp(orders: tuple, r: float, theta: float, phi: float, alph # %% Testing various speeding up calculation approaches -@njit +@njit(cache=True) def get_psf_point_r_comp(orders: tuple, r: float, theta: float, alpha: float, n_int_r_points: int, n_int_phi_points: int) -> float: """ Calculate PSF point for the kernel using Parallel class from the joblib library. @@ -258,10 +261,9 @@ def get_psf_point_r_comp(orders: tuple, r: float, theta: float, alpha: float, n_ """ h_phi = 2.0*pi/n_int_phi_points; even_sum = 0.0j; odd_sum = 0.0j - even_sums = [radial_integral_comp(orders, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(2, n_int_phi_points-2, 2)] - even_sums = np.asarray(even_sums); even_sum = np.sum(even_sums) - odd_sums = [radial_integral_comp(orders, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(1, n_int_phi_points-1, 2)] - odd_sums = np.asarray(odd_sums); odd_sum = np.sum(odd_sums) + even_sums = np.asarray([radial_integral_comp(orders, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(2, n_int_phi_points-2, 2)]) + odd_sums = np.asarray([radial_integral_comp(orders, r, theta, i*h_phi, alpha, n_int_r_points) for i in range(1, n_int_phi_points-1, 2)]) + even_sum = np.sum(even_sums); odd_sum = np.sum(odd_sums) # Simpson integration rule implementation yA = radial_integral_comp(orders, r, theta, 0.0, alpha, n_int_r_points) yB = radial_integral_comp(orders, r, theta, 2.0*pi, alpha, n_int_r_points) @@ -271,7 +273,7 @@ def get_psf_point_r_comp(orders: tuple, r: float, theta: float, alpha: float, n_ # %% PSF kernel calc. (accelerated) def get_psf_kernel_comp(zernike_pol, len2pixels: float, alpha: Union[float, np.ndarray], wavelength: float, NA: float, n_int_r_points: int = 320, - n_int_phi_points: int = 300, show_kernel: bool = False, fig_title: str = None, normalize_values: bool = False, + n_int_phi_points: int = 300, show_kernel: bool = False, fig_title: Optional[str] = None, normalize_values: bool = False, kernel_size: int = 3, fig_id: str = "", suppress_warns: bool = False, verbose: bool = False) -> np.ndarray: """ Calculate centralized matrix (kernel) with the PSF mask values. @@ -327,7 +329,7 @@ def get_psf_kernel_comp(zernike_pol, len2pixels: float, alpha: Union[float, np.n # Provide performance tip if the provided kernel size is quite big for calculations if size > 85 and not suppress_warns: __warn_message = f"\nCalculation of provided kernel size ({size}x{size}) may take more than 20 seconds" - warnings.warn(__warn_message); __warn_message = "" + warnings.warn(__warn_message, stacklevel=2); __warn_message = "" kernel = np.zeros(shape=(size, size)); i_center = size//2; j_center = size//2 # Get the orders of polynomial and check if the equation for compilation was implemented single_polynomial_provided = False # flag for using single polynomial functions @@ -339,18 +341,18 @@ def get_psf_kernel_comp(zernike_pol, len2pixels: float, alpha: Union[float, np.n else: if not isinstance(alpha, np.ndarray): alpha = np.asarray(alpha) - polynomials_orders = [] # for checking and providing for further compilation polynomials in a tuple + polynomials_orders_l = [] # for checking and providing for further compilation polynomials in a tuple for pol in zernike_pol: - m, n = pol.get_mn_orders(); polynomials_orders.append((m, n)) + m, n = pol.get_mn_orders(); polynomials_orders_l.append((m, n)) if n > 10 and (abs(m) != n or abs(m) != n-2): raise ValueError(f"The calculation PSF function isn't implemented for these orders: {m, n}") - polynomials_orders = tuple(polynomials_orders) # convert list to tuple + polynomials_orders = tuple(polynomials_orders_l) # convert list to tuple # Check that the calibration coefficient is sufficient for calculation pixel_size_nyquist = 0.5*0.61*wavelength/NA if len2pixels > pixel_size_nyquist and not suppress_warns: __warn_message = f"\nProvided calibration coefficient {len2pixels} {um_char}/pixels isn't sufficient enough" __warn_message += f" (defined by the relation between Nyquist freq. and the optical resolution: 0.61{lambda_char}/NA)" - warnings.warn(__warn_message); __warn_message = "" + warnings.warn(__warn_message, stacklevel=2); __warn_message = "" # Calculate the PSF kernel for usage in convolution operation if verbose: calculated_points = 0 # for explicit showing of performance @@ -391,23 +393,23 @@ def get_psf_kernel_comp(zernike_pol, len2pixels: float, alpha: Union[float, np.n if kernel_border_max > np.max(kernel)/20.0 and not suppress_warns: __warn_message = (f"\nThe calculated size for PSF ({size}) isn't sufficient for its proper representation, " + "because the maximum value on the kernel border is bigger than 5% of maximum overall kernel") - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) # Plotting the calculated kernel if show_kernel: if fig_title is not None and len(fig_title) > 0: plt.figure(fig_title, figsize=(6, 6)) else: if not hasattr(zernike_pol, "__len__"): - plt.figure(f"{zernike_pol.get_mn_orders()} {zernike_pol.get_polynomial_name(True)}: {round(alpha, 2)}*wavelength {fig_id}", + plt.figure(f"{zernike_pol.get_mn_orders()} {zernike_pol.get_polynomial_name(True)}: {np.round(alpha, 2)}*wavelength {fig_id}", figsize=(6, 6)) else: plt.figure(f"Sum of provided #{len(zernike_pol)} of polynomials {fig_id}", figsize=(6, 6)) - plt.imshow(kernel, cmap=plt.cm.viridis, origin='upper'); plt.tight_layout() + plt.imshow(kernel, cmap=plt.colormaps["viridis"], origin='upper'); plt.tight_layout() return kernel # %% PSF calc. for several polynomials -@njit +@njit(cache=True) def pol_sums(polynomials_orders: tuple, amplitudes: np.ndarray, p: float, phi: float) -> float: """ Wrap calculation of polynomials values sum for compilation. @@ -437,9 +439,9 @@ def pol_sums(polynomials_orders: tuple, amplitudes: np.ndarray, p: float, phi: f return sum_pols -@njit +@njit(cache=True) def diffraction_integral_r_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, phi: float, - p: float, theta: float, r: float) -> float: + p: float, theta: float, r: float) -> np.ndarray: """ Diffraction integral function for the formed image point (see the references as the sources of the equation). @@ -473,7 +475,7 @@ def diffraction_integral_r_pols_comp(polynomials_orders: tuple, amplitudes: np.n return np.exp(phase_arg)*p -@njit +@njit(cache=True) def radial_integral_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, r: float, theta: float, phi: float, n_int_r_points: int) -> complex: """ @@ -508,7 +510,7 @@ def radial_integral_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, return h_p*ang_int -@njit +@njit(cache=True) def get_psf_point_r_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, r: float, theta: float, n_int_r_points: int, n_int_phi_points: int) -> float: """ @@ -540,12 +542,11 @@ def get_psf_point_r_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, """ h_phi = 2.0*pi/n_int_phi_points; even_sum = 0.0j; odd_sum = 0.0j - even_sums = [radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, i*h_phi, n_int_r_points) - for i in range(2, n_int_phi_points-2, 2)] - even_sums = np.asarray(even_sums); even_sum = np.sum(even_sums) - odd_sums = [radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, i*h_phi, n_int_r_points) - for i in range(1, n_int_phi_points-1, 2)] - odd_sums = np.asarray(odd_sums); odd_sum = np.sum(odd_sums) + even_sums = np.asarray([radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, i*h_phi, n_int_r_points) + for i in range(2, n_int_phi_points-2, 2)]) + odd_sums = np.asarray([radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, i*h_phi, n_int_r_points) + for i in range(1, n_int_phi_points-1, 2)]) + even_sum = np.sum(even_sums); odd_sum = np.sum(odd_sums) # Simpson integration rule implementation yA = radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, 0.0, n_int_r_points) yB = radial_integral_pols_comp(polynomials_orders, amplitudes, r, theta, 2.0*pi, n_int_r_points) @@ -553,52 +554,5 @@ def get_psf_point_r_pols_comp(polynomials_orders: tuple, amplitudes: np.ndarray, return np.power(np.abs(integral_sum), 2)*integral_normalization -# %% Utility functions -def set_methods_compiled(): - """ - Reset the flag by external call. - - Returns - ------- - None. - - """ - global methods_compiled; methods_compiled = True - - # %% Define standard exports from this module -__all__ = ['get_psf_kernel_comp', 'methods_compiled', 'set_methods_compiled'] - -# %% Tests -if __name__ == '__main__': - from zernpy import ZernPol # for polynomials initialization - plt.ion(); plt.close('all') # close all plots before plotting new ones - # Physical parameters of a system (an objective) - wavelength = 0.55 # in micrometers - NA = 0.95 # objective property, ultimately NA = d/2*f, there d - aperture diameter, f - distance to the object (focal length for an image) - # Note that ideal Airy pattern will be (2*J1(x)/x)^2, there x = k*NA*r, there r - radius in the polar coordinates on the image - resolution = 0.61*wavelength/NA # ultimate theoretical physical resolution of an objective - pixel_size_nyquist = 0.5*resolution # Nyquist's resolution needed for using theoretical physical resolution above - pixel_size = 0.95*pixel_size_nyquist # the relation between um / pixels for calculating the coordinate in physical units for each pixel - - # Flags for testing various scenarios - test_single_polynomial = False; test_few_polynomials = True - - # Testing implemented calculations for single polynomial - if test_single_polynomial: - get_psf_kernel_comp(ZernPol(m=0, n=0), pixel_size*0.7, alpha=1.5, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True, kernel_size=11, verbose=True) - print("*******************************************") - get_psf_kernel_comp(ZernPol(m=0, n=4), pixel_size*0.7, alpha=0.75, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True, kernel_size=21, verbose=True) - # For several (calculated their sum) - if test_few_polynomials: - # First, checking below sequentially all functions to be compilable - # pols = ((-2, 2), (1, 3)); ampls = np.asarray([-0.4, 0.6]) - # diffraction_integral_r_pols_comp(pols, ampls, phi=0.2, p=0.1, theta=0.3, r=0.5) - # radial_integral_pols_comp(pols, ampls, r=0.5, theta=0.3, phi=1.01, n_int_r_points=300) - # get_psf_point_r_pols_comp(pols, ampls, r=0.5, theta=0.3, n_int_r_points=250, n_int_phi_points=320) - # Second, test all at once for calling the function - zp1 = ZernPol(m=-2, n=2); zp2 = ZernPol(m=0, n=2); zp3 = ZernPol(m=2, n=2); pols = (zp1, zp2, zp3); coeffs = (-0.86, 0.4, 0.7) - get_psf_kernel_comp(pols, pixel_size*0.7, alpha=coeffs, wavelength=wavelength, NA=NA, normalize_values=True, - show_kernel=True, kernel_size=24, verbose=True) +__all__ = ['get_psf_kernel_comp'] diff --git a/src/zernpy/calculations/calc_zernike_pol.py b/src/zernpy/calculations/calc_zernike_pol.py index 65f2b67..2db1bb3 100644 --- a/src/zernpy/calculations/calc_zernike_pol.py +++ b/src/zernpy/calculations/calc_zernike_pol.py @@ -7,17 +7,13 @@ """ # %% Global imports -import numpy as np import math import time -from pathlib import Path -# from decimal import Decimal +from typing import List, Union + +import numpy as np -# %% Local (package-scoped) imports -if __name__ == "__main__" or __name__ == Path(__file__).stem or __name__ == "__mp_main__": - from find_pols_coeffs import find_coeffs_orders, find_coeffs_orders_dr -else: - from .find_pols_coeffs import find_coeffs_orders, find_coeffs_orders_dr +from .find_pols_coeffs import find_coeffs_orders, find_coeffs_orders_dr # %% Module parameters __docformat__ = "numpydoc" @@ -47,9 +43,9 @@ def define_orders(zernike_pol) -> tuple: """ # Get azimuthal and radial orders if isinstance(zernike_pol, tuple): - (m, n) = zernike_pol + m, n = zernike_pol else: - (m, n) = zernike_pol.get_mn_orders() + m, n = zernike_pol.get_mn_orders() return m, n @@ -72,7 +68,7 @@ def normalization_factor(zernike_pol) -> float: Normalization factor, depending only on Zernike type. """ - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders # Calculation of the value according to Ref. if m == 0: return np.sqrt(n + 1) @@ -80,7 +76,7 @@ def normalization_factor(zernike_pol) -> float: return np.sqrt(2*(n + 1)) -def radial_polynomial(zernike_pol, r): +def radial_polynomial(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate radial polynomial R(m, n) value for input r lying in the range [0, 1]. @@ -104,7 +100,7 @@ def radial_polynomial(zernike_pol, r): Depending on the type of theta, return float or np.ndarray with calculated values of radial polynomial. """ - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders # Radial polynomials defined as analytical equations for up to 10th order (check tables from [2]) # 0th order if (m == 0) and (n == 0): @@ -205,7 +201,7 @@ def radial_polynomial(zernike_pol, r): - radial_polynomial((m, n-2), r)) # general recurrence formula from [1] -def radial_derivative(zernike_pol, r): +def radial_derivative(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate the derivative of radial polynomial dR(m, n)/dr value for input r lying in the range [0, 1]. @@ -222,7 +218,7 @@ def radial_derivative(zernike_pol, r): Depending on the type of r, return float or np.ndarray with calculated values of radial polynomial derivative. """ - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders # Derivatives of radial polynomials defined as analytical equations for up to 8th order (check function above) # 0th order if (m == 0) and (n == 0): @@ -327,7 +323,7 @@ def radial_derivative(zernike_pol, r): - radial_derivative((m, n-2), r)) -def radial_polynomial_eq(zernike_pol, r): +def radial_polynomial_eq(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate the radial polynomial R(m, n) using exact equation from the Reference below. @@ -348,11 +344,12 @@ def radial_polynomial_eq(zernike_pol, r): Depending on the type of theta, return float or numpy.ndarray with calculated values of radial polynomial. """ + value: Union[float, np.ndarray] # fix for mypy checks if isinstance(r, float): value = 0.0 elif isinstance(r, np.ndarray): value = np.zeros(r.shape) - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders for k in range(0, ((n - abs(m))//2) + 1): a = (n + m)//2; b = (n - m)//2 value += ((-1)**k)*(((math.factorial(n-k))/(math.factorial(k) @@ -362,7 +359,7 @@ def radial_polynomial_eq(zernike_pol, r): return value -def radial_derivative_eq(zernike_pol, r): +def radial_derivative_eq(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate the derivative of radial polynomial R(m, n) on r (eq. dR(m, n)/dr). @@ -379,11 +376,12 @@ def radial_derivative_eq(zernike_pol, r): Depending on the type of theta, return float or numpy.ndarray with calculated values of radial polynomial derivative. """ + value: Union[float, np.ndarray] # fix for mypy checks if isinstance(r, float): value = 0.0 elif isinstance(r, np.ndarray): value = np.zeros(r.shape) - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders if n > 0: for k in range(0, ((n - abs(m))//2) + 1): a = (n + m)//2; b = (n - m)//2 @@ -395,7 +393,7 @@ def radial_derivative_eq(zernike_pol, r): return value -def triangular_function(zernike_pol, theta): +def triangular_function(zernike_pol, theta: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Return triangular component of the Zernike polynomial. @@ -418,7 +416,7 @@ def triangular_function(zernike_pol, theta): Depending on the type of theta, return float or numpy.ndarray with calculated values of triangular function. """ - (m, n) = define_orders(zernike_pol) # get orders + m, n = define_orders(zernike_pol) # get orders # Calculation of the value according to Refs. if m >= 0: return np.cos(m*theta) @@ -426,7 +424,7 @@ def triangular_function(zernike_pol, theta): return -np.sin(m*theta) -def triangular_derivative(zernike_pol, theta): +def triangular_derivative(zernike_pol, theta: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Return derivative of triangular function of the Zernike polynomial. @@ -444,7 +442,7 @@ def triangular_derivative(zernike_pol, theta): Depending on the type of theta, return float or numpy.ndarray with calculated values of derivative of triangular function. """ - (m_order, n) = define_orders(zernike_pol) # get orders + m_order, n = define_orders(zernike_pol) # get orders # Calculation of the value according to the analytical derivative of the equation above m = float(m_order) if m_order >= 0: @@ -453,7 +451,7 @@ def triangular_derivative(zernike_pol, theta): return -m*np.cos(m*theta) -def radial_polynomial_coeffs(zernike_pol, r): +def radial_polynomial_coeffs(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate radial polynomial using recursive finding algorithm of each coefficient for radial component (e.g. R^6). @@ -481,6 +479,7 @@ def radial_polynomial_coeffs(zernike_pol, r): if n <= MAX_RADIAL_ORDER_COEFFS: pols_coeffs = find_coeffs_orders((m, n)) # Initial value for sum calculation + r_sum: Union[float, np.ndarray] if isinstance(r, float): r_sum = 0.0 elif isinstance(r, np.ndarray): @@ -506,7 +505,7 @@ def radial_polynomial_coeffs(zernike_pol, r): return r_sum -def radial_polynomial_coeffs_dr(zernike_pol, r): +def radial_polynomial_coeffs_dr(zernike_pol, r: Union[float, np.ndarray]) -> Union[float, np.ndarray]: """ Calculate radial polynomial derivative using recursive finding algorithm of each coefficient for radial component. @@ -531,6 +530,7 @@ def radial_polynomial_coeffs_dr(zernike_pol, r): if n <= MAX_RADIAL_ORDER_COEFFS_dR: pols_coeffs = find_coeffs_orders_dr((m, n)) # Initial value for sum calculation + r_sum: Union[float, np.ndarray] if isinstance(r, float): r_sum = 0.0 elif isinstance(r, np.ndarray): @@ -582,30 +582,21 @@ def compare_radial_calculations(max_order: int) -> np.ndarray: if not isinstance(max_order, int) and max_order < 2: print("NOTE that max_order by default set to 2") max_order = 2 - # Generating Zernike orders in OSA/ANSI indexing scheme orders_list = [(0, 0)] for order in range(1, max_order): m = -order; n = order orders_list.append((m, n)) - for n_azimuthals in range(0, order): - m += 2 - orders_list.append((m, n)) - - # Generation numpy array with radii - n_points = 21 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 4) + for _ in range(0, order): + m += 2; orders_list.append((m, n)) + n_points = 21; test_r = np.linspace(start=0.0, stop=1.0, num=n_points) # radii points for testing # Testing that exact calculation and implementation of tabular / recursive are the same diff = np.ones(shape=(len(orders_list), n_points)) - for i, order in enumerate(orders_list): - diff[i, :] = radial_polynomial(order, test_r) - radial_polynomial_eq(order, test_r) + for i, orders in enumerate(orders_list): + diff[i, :] = radial_polynomial(orders, test_r) - radial_polynomial_eq(orders, test_r) diff = np.round(diff, 9) - assert np.max(np.abs(diff)) < 1E-9, (f"Order {order} has inconsistency between tabular/recursion" + assert np.max(np.abs(diff)) < 1E-9, ("Computation of Rmn has inconsistency between tabular/recursion" + f" and exact implementations, diff: {np.max(np.abs(diff))}") - print("Difference between analytical and implemented equations for Zernike pol-s is negligible, test passed") return diff @@ -631,30 +622,21 @@ def compare_radial_derivatives(max_order: int) -> np.ndarray: if not isinstance(max_order, int) and max_order < 2: print("NOTE that max_order by default set to 2") max_order = 2 - # Generating Zernike orders in OSA/ANSI indexing scheme orders_list = [(0, 0)] for order in range(1, max_order): m = -order; n = order orders_list.append((m, n)) - for n_azimuthals in range(0, order): - m += 2 - orders_list.append((m, n)) - - # Generation numpy array with radii - n_points = 21 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 4) + for _ in range(0, order): + m += 2; orders_list.append((m, n)) + n_points = 21; test_r = np.linspace(start=0.0, stop=1.0, num=n_points) # radii points for testing # Testing that exact calculation and implementation of tabular / recursive are the same diff = np.ones(shape=(len(orders_list), n_points)) - for i, order in enumerate(orders_list): - diff[i, :] = radial_derivative(order, test_r) - radial_derivative_eq(order, test_r) + for i, orders in enumerate(orders_list): + diff[i, :] = radial_derivative(orders, test_r) - radial_derivative_eq(orders, test_r) diff = np.round(diff, 9) - assert np.max(np.abs(diff)) < 1E-9, (f"Order {order} has inconsistency between tabular/recursion" + assert np.max(np.abs(diff)) < 1E-9, ("Computation of dRmn/dr has inconsistency between tabular/recursion" + f" and exact implementations, diff: {np.max(np.abs(diff))}") - print("Difference between analytical and implemented equations for derivatives of Zernike pol-s is negligible, test passed") return diff @@ -677,27 +659,16 @@ def compare_recursive_coeffs_radials() -> np.ndarray: for order in range(15, MAX_RADIAL_ORDER_COEFFS+2): m = -order; n = order orders_list.append((m, n)) - for n_azimuthals in range(0, order): - m += 2 - orders_list.append((m, n)) - # Generation numpy array with radii - n_points = 101 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 4) + for _ in range(0, order): + m += 2; orders_list.append((m, n)) + n_points = 101; test_r = np.linspace(start=0.0, stop=1.0, num=n_points) # radii points for testing # Testing that exact calculation and implementation of tabular / recursive are the same diff = np.ones(shape=(len(orders_list), n_points)) - for i, order in enumerate(orders_list): - diff[i, :] = radial_polynomial_eq(order, test_r) - radial_polynomial_coeffs(order, test_r) - # diff[i, :] = radial_polynomial_coeffs(order, test_r) - # diff[i, :] = radial_polynomial_eq(order, test_r) - # if np.max(np.abs(diff)) > 1.0: - # print(order, np.max(np.abs(diff))) + for i, orders in enumerate(orders_list): + diff[i, :] = radial_polynomial_eq(orders, test_r) - radial_polynomial_coeffs(orders, test_r) diff = np.round(diff, 9) - assert np.max(np.abs(diff)) < 2E-2, (f"Order {order} has inconsistency between tabular/recursion" + assert np.max(np.abs(diff)) < 2E-2, ("Computation of Rmn has inconsistency between tabular/recursion" + f" and exact implementations, diff: {np.max(np.abs(diff))}") - print("Difference between exact equation and pols. coeffs. finding algorithm is negligible, test passed") return diff @@ -720,25 +691,16 @@ def compare_recursive_coeffs_radials_dr() -> np.ndarray: for order in range(15, MAX_RADIAL_ORDER_COEFFS_dR+2): m = -order; n = order orders_list.append((m, n)) - for n_azimuthals in range(0, order): - m += 2 - orders_list.append((m, n)) - # Generation numpy array with radii - n_points = 101 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 4) + for _ in range(0, order): + m += 2; orders_list.append((m, n)) + n_points = 101; test_r = np.linspace(start=0.0, stop=1.0, num=n_points) # radii points for testing # Testing that exact calculation and implementation of tabular / recursive are the same diff = np.ones(shape=(len(orders_list), n_points)) - for i, order in enumerate(orders_list): - diff[i, :] = radial_derivative_eq(order, test_r) - radial_polynomial_coeffs_dr(order, test_r) - # if np.max(np.abs(diff)) > 1.0: - # print(order, np.max(np.abs(diff))) + for i, orders in enumerate(orders_list): + diff[i, :] = radial_derivative_eq(orders, test_r) - radial_polynomial_coeffs_dr(orders, test_r) diff = np.round(diff, 9) - assert np.max(np.abs(diff)) < 5E-2, (f"Order {order} has inconsistency between tabular/recursion" + assert np.max(np.abs(diff)) < 5E-2, ("Computation of Rmn has inconsistency between tabular/recursion" + f" and exact implementations, diff: {np.max(np.abs(diff))}") - print("Difference between exact equation and pols. coeffs. finding algorithm is negligible, test passed") return diff @@ -757,22 +719,15 @@ def check_high_orders_recursion() -> np.ndarray: for order in range(MAX_RADIAL_ORDER_COEFFS+1, MAX_RADIAL_ORDER_COEFFS+6): m = -order; n = order orders_list.append((m, n)) - for n_azimuthals in range(0, order): - m += 2 - orders_list.append((m, n)) - # Generation numpy array with radii - n_points = 51 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 4) + for _ in range(0, order): + m += 2; orders_list.append((m, n)) + n_points = 51; test_r = np.linspace(start=0.0, stop=1.0, num=n_points) # radii points for testing # Testing that exact calculation and implementation of tabular / recursive are the same diff = np.ones(shape=(len(orders_list), n_points)) - for i, order in enumerate(orders_list): - diff[i, :] = radial_polynomial_coeffs(order, test_r) + for i, orders in enumerate(orders_list): + diff[i, :] = radial_polynomial_coeffs(orders, test_r) diff = np.round(diff, 6) - assert np.max(np.abs(diff)) <= 1.0, f"Order {order} has inconsistency in max abs value: {np.max(np.abs(diff))}" - print("Abs max in calculated recursively radial polynomials <= 1.0, test passed") + assert np.max(np.abs(diff)) <= 1.0, f"Rmn has inconsistency in max abs value (should be <= 1.0): {np.max(np.abs(diff))}" return diff @@ -785,7 +740,7 @@ def time_radial_pols(): None. """ - calc_times_ms = [] # for storing calculation times + calc_times_ms: List[float] = [] # for storing calculation times zp1 = (2, 16); zp2 = (0, 18); zp3 = (-2, 20); zp4 = (6, 22); zp5 = (-4, 24); r = 0.425 zpols = [zp1, zp2, zp3, zp4, zp5] for zp in zpols: @@ -826,19 +781,3 @@ def time_radial_pols(): calc_times_ms.append(round(1000*(t2-t1), 3)) print("Timed calc. using exact equation rad. pol.", zpols, ":", calc_times_ms) - -# %% Tests -if __name__ == '__main__': - R = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]; R = np.asarray(R) - Theta = [i*np.pi/3 for i in range(6)]; Theta = np.asarray(Theta) - orders = (-2, 2); r = 0.5 - ZR = radial_polynomial(orders, R); ZR1 = radial_polynomial(orders, r) - TR = triangular_function(orders, Theta) - diff = compare_radial_calculations(max_order=20) - diff_deriv = compare_radial_derivatives(max_order=18) - # Test specific implementations - orders = (-8, 52); r = 0.95; val = radial_polynomial_coeffs(orders, r) - time_radial_pols() # initial estimation of performance of calculations - diff_coeffs = compare_recursive_coeffs_radials() - diff_deriv_coeffs = compare_recursive_coeffs_radials_dr() - high_R = check_high_orders_recursion() diff --git a/src/zernpy/calculations/find_pols_coeffs.py b/src/zernpy/calculations/find_pols_coeffs.py index 02f7753..1b10f0c 100644 --- a/src/zernpy/calculations/find_pols_coeffs.py +++ b/src/zernpy/calculations/find_pols_coeffs.py @@ -44,7 +44,7 @@ def make_orders_coeffs(defined_coeff: dict, max_order: int, minus: bool = False) # Setting provided already defined coefficients to the initialized dictionary if len(defined_coeff.keys()) > 0: for key, value in defined_coeff.items(): - if key in coefficients.keys(): + if key in coefficients: if not minus: coefficients[key] = value else: @@ -185,7 +185,7 @@ def check_special_orders(orders: tuple) -> dict: Polynomials coefficients with radial order: value pairs. """ - special_coefficients = None + special_coefficients = {} m, n = orders if abs(m) == n: special_coefficients = make_orders_coeffs({n: 1}, n) @@ -209,7 +209,7 @@ def check_special_orders_dr(orders: tuple) -> dict: Derivatives of polynomials coefficients with radial order: value pairs. """ - special_coefficients = None + special_coefficients = {} m, n = orders if abs(m) == n: special_coefficients = make_orders_coeffs({n-1: n}, n-1) @@ -248,16 +248,16 @@ def find_coeffs_orders(orders: tuple, use_test_dict: bool = False) -> dict: initial_coefficients = initial_coefficients_test else: initial_coefficients = precalculated_initial_coeffs - if orders in initial_coefficients.keys(): + if orders in initial_coefficients: # print("Found in initial dict.: ", initial_coefficients[orders]) return initial_coefficients[orders] # return stored in the dictionary value - elif check_special_orders(orders) is not None: + elif check_special_orders(orders): # Cashing already calculated coefficients in global dictionary specified above if not use_test_dict: - if orders not in precalculated_initial_coeffs.keys(): + if orders not in precalculated_initial_coeffs: precalculated_initial_coeffs[orders] = check_special_orders(orders) else: - if orders not in initial_coefficients_test.keys(): + if orders not in initial_coefficients_test: initial_coefficients_test[orders] = check_special_orders(orders) return check_special_orders(orders) # some special shorthanded cases for polynomials values calculation else: @@ -269,14 +269,14 @@ def find_coeffs_orders(orders: tuple, use_test_dict: bool = False) -> dict: max_order=n-2, minus=True)) # Cashing already calculated coefficients in global dictionary specified above if not use_test_dict: - if (abs(m-1), n-1) not in precalculated_initial_coeffs.keys(): + if (abs(m-1), n-1) not in precalculated_initial_coeffs: precalculated_initial_coeffs[(abs(m-1), n-1)] = polm1n1 - if (m+1, n-1) not in precalculated_initial_coeffs.keys(): + if (m+1, n-1) not in precalculated_initial_coeffs: precalculated_initial_coeffs[(m+1, n-1)] = polmP1n1 else: - if (abs(m-1), n-1) not in initial_coefficients_test.keys(): + if (abs(m-1), n-1) not in initial_coefficients_test: initial_coefficients_test[(abs(m-1), n-1)] = polm1n1 - if (m+1, n-1) not in initial_coefficients_test.keys(): + if (m+1, n-1) not in initial_coefficients_test: initial_coefficients_test[(m+1, n-1)] = polmP1n1 return sum_dict_coeffs @@ -311,16 +311,16 @@ def find_coeffs_orders_dr(orders: tuple, use_test_dict: bool = False) -> dict: initial_coefficients_dr = initial_coefficients_test_dr else: initial_coefficients_dr = precalculated_initial_coeffs_dr - if orders in initial_coefficients_dr.keys(): + if orders in initial_coefficients_dr: # print("Found in initial dict.: ", initial_coefficients[orders]) return initial_coefficients_dr[orders] # return stored in the dictionary value - elif check_special_orders_dr(orders) is not None: + elif check_special_orders_dr(orders): # Cashing already calculated coefficients in global dictionary specified above if not use_test_dict: - if orders not in precalculated_initial_coeffs_dr.keys(): + if orders not in precalculated_initial_coeffs_dr: precalculated_initial_coeffs_dr[orders] = check_special_orders_dr(orders) else: - if orders not in initial_coefficients_test_dr.keys(): + if orders not in initial_coefficients_test_dr: initial_coefficients_test_dr[orders] = check_special_orders_dr(orders) return check_special_orders_dr(orders) # some special shorthanded cases for derivatives values calculation else: @@ -335,22 +335,22 @@ def find_coeffs_orders_dr(orders: tuple, use_test_dict: bool = False) -> dict: max_order=n-2, minus=True)) # Cashing already calculated coefficients in global dictionary specified above if not use_test_dict: - if (abs(m-1), n-1) not in precalculated_initial_coeffs.keys(): + if (abs(m-1), n-1) not in precalculated_initial_coeffs: precalculated_initial_coeffs[(abs(m-1), n-1)] = polm1n1 - if (m+1, n-1) not in precalculated_initial_coeffs.keys(): + if (m+1, n-1) not in precalculated_initial_coeffs: precalculated_initial_coeffs[(m+1, n-1)] = polmP1n1 - if (abs(m-1), n-1) not in precalculated_initial_coeffs_dr.keys(): + if (abs(m-1), n-1) not in precalculated_initial_coeffs_dr: precalculated_initial_coeffs_dr[(abs(m-1), n-1)] = polm1n1_dr - if (m+1, n-1) not in precalculated_initial_coeffs_dr.keys(): + if (m+1, n-1) not in precalculated_initial_coeffs_dr: precalculated_initial_coeffs_dr[(m+1, n-1)] = polmP1n1_dr else: - if (abs(m-1), n-1) not in initial_coefficients_test.keys(): + if (abs(m-1), n-1) not in initial_coefficients_test: initial_coefficients_test[(abs(m-1), n-1)] = polm1n1 - if (m+1, n-1) not in initial_coefficients_test.keys(): + if (m+1, n-1) not in initial_coefficients_test: initial_coefficients_test[(m+1, n-1)] = polmP1n1 - if (abs(m-1), n-1) not in initial_coefficients_test_dr.keys(): + if (abs(m-1), n-1) not in initial_coefficients_test_dr: initial_coefficients_test_dr[(abs(m-1), n-1)] = polm1n1_dr - if (m+1, n-1) not in initial_coefficients_test_dr.keys(): + if (m+1, n-1) not in initial_coefficients_test_dr: initial_coefficients_test_dr[(m+1, n-1)] = polmP1n1_dr return sum_dict_coeffs diff --git a/src/zernpy/calculations/fit_zernike_pols.py b/src/zernpy/calculations/fit_zernike_pols.py index 77144a7..8dfe7ef 100644 --- a/src/zernpy/calculations/fit_zernike_pols.py +++ b/src/zernpy/calculations/fit_zernike_pols.py @@ -7,11 +7,9 @@ """ # %% Global imports -import numpy as np import warnings -# %% Local imports - +import numpy as np # %% Module parameters __docformat__ = "numpydoc" @@ -73,17 +71,17 @@ def crop_phases_img(phases_image: np.ndarray, crop_radius: float = 1.0, suppress cropped_radii_vector = np.zeros(shape=(rows*cols,)); cropped_thetas_vector = np.zeros(shape=(rows*cols,)) # Check input image shape if rows != cols: - __warn_message = "Phases image isn't square, results of fitting could be ambiguous" + __warn_message = "\nPhase profile (image) isn't square, results of fitting could be ambiguous" img_min_size = min(rows, cols); img_max_size = max(rows, cols) if not suppress_warns: - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) else: img_min_size = rows; img_max_size = rows if rows % 2 == 0 or cols % 2 == 0: - __warn_message = ("Phases image provided with even rows or columns, " + __warn_message = ("\nPhase profile (image) provided with even rows or columns, " + "it's error prone to define exact image center") if not suppress_warns: - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) if img_min_size < 3: raise ValueError("Provided image is too small (min size < 3) for producing any meaningful result") # Calculate center of the input image - depending on its sizes @@ -114,7 +112,7 @@ def crop_phases_img(phases_image: np.ndarray, crop_radius: float = 1.0, suppress + " or with 1 pixel difference between them. \n" + "Note that additional border pixels are included to crop.") if not suppress_warns: - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) # Calculate polar coordinates of pixels recalibrate_radii = False; recalibration_coeff = 1.0; vector_index = 0 # Cropping phases, collecting data on cropping process @@ -185,7 +183,7 @@ def fit_zernikes(phases_coordinates_vectors: tuple, polynomials: tuple) -> np.nd # Calculate polynomials values in the unit circle defined by polar coordinates zernike_values = np.zeros(shape=(vector_length, len(polynomials))) # Checking that all polynomials are unique - if not len(polynomials) == 0: + if len(polynomials) != 0: provided_orders = [] for polynomial in polynomials: provided_orders.append(polynomial.get_mn_orders()) @@ -212,28 +210,3 @@ def fit_zernikes(phases_coordinates_vectors: tuple, polynomials: tuple) -> np.nd else: raise ValueError("There isn't any polynomials provided") return zernike_coefficients - - -# %% Basic tests -if __name__ == "__main__": - phases_sample = 4*np.ones(shape=(3, 4), dtype="uint8") - crop_deforms1, polar_coordinates1 = crop_phases_img(phases_sample) - phases_sample = np.ones(shape=(4, 4), dtype="int16") - crop_deforms2, polar_coordinates2 = crop_phases_img(phases_sample) - crop_deforms2a, polar_coordinates2a = crop_phases_img(phases_sample, strict_border=True) - phases_sample = np.ones(shape=(6, 6)) - crop_deforms3, polar_coordinates = crop_phases_img(phases_sample) - phases_sample = np.ones(shape=(3, 3)) - crop_deforms4, polar_coordinates = crop_phases_img(phases_sample) - phases_sample = np.ones(shape=(5, 5)) - crop_deforms5, polar_coordinates = crop_phases_img(phases_sample) - phases_sample = np.ones(shape=(4, 6)) - crop_deforms6, polar_coordinates6 = crop_phases_img(phases_sample) - crop_deforms6a, polar_coordinates6a = crop_phases_img(phases_sample, strict_border=True) - phases_sample = np.ones(shape=(7, 6)) - crop_deforms7, polar_coordinates7 = crop_phases_img(phases_sample) - crop_deforms7a, polar_coordinates7a = crop_phases_img(phases_sample, strict_border=True) - phases_sample = np.ones(shape=(5, 5)) - crop_deforms81, polar_coordinates = crop_phases_img(phases_sample) - crop_deforms82, polar_coordinates = crop_phases_img(phases_sample, crop_radius=0.5) - thetas_grads = polar_coordinates[1]*(180.0/np.pi) diff --git a/src/zernpy/examples/define_pv_values.py b/src/zernpy/examples/define_pv_values.py index 31d1a70..b25fd3f 100644 --- a/src/zernpy/examples/define_pv_values.py +++ b/src/zernpy/examples/define_pv_values.py @@ -7,6 +7,7 @@ """ # %% Global imports import numpy as np + try: from zernpy import generate_polynomials zernpy_installed = True diff --git a/src/zernpy/plotting/plot_zerns.py b/src/zernpy/plotting/plot_zerns.py index 01183b4..d681948 100644 --- a/src/zernpy/plotting/plot_zerns.py +++ b/src/zernpy/plotting/plot_zerns.py @@ -7,8 +7,8 @@ """ # %% Global imports -import numpy as np import matplotlib.pyplot as plt +import numpy as np # %% Module parameters __docformat__ = "numpydoc" diff --git a/src/zernpy/tests/test_calc_psf.py b/src/zernpy/tests/test_calc_psf.py index 4864b87..969db34 100644 --- a/src/zernpy/tests/test_calc_psf.py +++ b/src/zernpy/tests/test_calc_psf.py @@ -9,21 +9,26 @@ @licence: MIT """ -import numpy as np -from pathlib import Path import os +from pathlib import Path + +import numpy as np -# Importing the written in the modules test functions for letting pytest library their automatic exploration -if __name__ != "__main__": - from ..calculations.calc_psfs import (get_psf_kernel) - from ..zernpsf import ZernPSF, force_get_psf_compilation - from ..zernikepol import ZernPol -else: - from zernpy import ZernPol +# Relative import from the modules - designed to be used only by pytest runs +from ..calculations.calc_psfs import get_psf_kernel +from ..zernikepol import ZernPol +from ..zernpsf import ZernPSF, clean_zernpy_cache, force_get_psf_compilation # Testing functions def test_psf_kernel_calc(): + """ + Test common calculation of PSF kernel + comparison with the result of exact equation - Airy pattern. + + Returns + ------- + None + """ NA = 0.35; wavelength = 0.55; pixel_size = wavelength / 3.05; ampl = -0.28 # Common physical properties # Basic test - calculating kernel by numerical integration and by Airy pattern exact equation and compare them piston = ZernPol(m=0, n=0) @@ -52,6 +57,13 @@ def test_psf_kernel_calc(): def test_zernpsf_usage(): + """ + Test wrong initialization parameters for ZernPSF, at the end - normal one. + + Returns + ------- + None + """ NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 5.0; ampl = 0.55 # Common physical properties zp1 = ZernPol(m=0, n=2) # defocus test_init = True # flag, if set to False, the test failed (e.g., expected Error not caught) @@ -101,6 +113,13 @@ def test_zernpsf_usage(): def test_save_load_zernpsf(): + """ + Test saving and loading of PSF kernel stored in a json file. + + Returns + ------- + None + """ zp2 = ZernPol(m=1, n=3); zpsf2 = ZernPSF(zp2) # horizontal coma zp3 = ZernPol(osa=21); zpsf3 = ZernPSF(zp3) # additional classes for testing reading and reassigning values NA = 0.4; wavelength = 0.4; pixel_size = wavelength / 3.0; ampl = 0.11 # Common physical properties @@ -118,7 +137,14 @@ def test_save_load_zernpsf(): def test_numba_compilation(): - force_get_psf_compilation() # force compilation of computation methods + """ + Test compilation by numba of the calculation functions. + + Returns + ------- + None + """ + force_get_psf_compilation() # force compilational of computation methods # Test the difference between accelerated and not accelerated calculation methods NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 4.25; ampl = -0.12 zp6 = ZernPol(m=0, n=2); zpsf6 = ZernPSF(zp6); zpsf7 = ZernPSF(zp6) # defocus @@ -126,4 +152,5 @@ def test_numba_compilation(): zpsf7.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) kernel_acc = zpsf6.calculate_psf_kernel(normalized=True, accelerated=True) # accelerated by numba compilation kernel_norm = zpsf7.calculate_psf_kernel(normalized=True) # normal calculation - assert np.max(np.abs(kernel_acc - kernel_norm) < 1E-6), "Accelerated and not one calculation of kernel methods have significant differences" + assert np.max(np.abs(kernel_acc - kernel_norm) < 1E-6), "Accelerated and not computational of a kernel methods have significant differences" + assert clean_zernpy_cache(), "Local cache with compiled files not cleaned" diff --git a/src/zernpy/tests/test_calculations.py b/src/zernpy/tests/test_calculations.py index a8d76c6..78b1d26 100644 --- a/src/zernpy/tests/test_calculations.py +++ b/src/zernpy/tests/test_calculations.py @@ -1,6 +1,6 @@ # -*- coding: utf-8 -*- """ -Test the implemented calculation functions for module calc_zernike_pol and ZernPol static methods by using pytest library. +Test the implemented calculation functions for the module 'calc_zernike_pol' and the static methods from 'ZernPol' by using pytest library. The pytest library available on: https://docs.pytest.org/en/latest/contents.html For running collected here tests, it's enough to run the command "pytest" from the repository location in the command line. @@ -10,45 +10,75 @@ """ import math + import numpy as np -# Importing the written in the modules test functions for letting pytest library their automatic exploration -if __name__ != "__main__": - from ..calculations.calc_zernike_pol import (compare_radial_calculations, compare_radial_derivatives, - compare_recursive_coeffs_radials, compare_recursive_coeffs_radials_dr, - check_high_orders_recursion) - from ..zernikepol import ZernPol +from ..calculations.calc_zernike_pol import ( + check_high_orders_recursion, + compare_radial_calculations, + compare_radial_derivatives, + compare_recursive_coeffs_radials, + compare_recursive_coeffs_radials_dr, +) +from ..zernikepol import ZernPol -# Testing implemented equations for tabular R(m, n) from References by comparing with the exact ones (with factorials) +# %% Func-s to be run by pytest def test_tabular_orders(): - compare_radial_calculations(max_order=10) + """ + # Test implemented equations for tabular R(m, n) from the References by comparing with the exact ones (with factorials usage). + + Returns + ------- + None + """ + compare_radial_calculations(max_order=17) -# Testing implemented tabular and recursive equations for R(m, n) by comparing with the exact ones (with factorials) -# Also, testing implemented recursive scheme for finding the polynomials coefficients for each order and comparison -# with the exact equations (with factorials) def test_recursive_orders(): - compare_radial_calculations(max_order=17) + """ + Test implemented recursive scheme for finding the polynomials coefficients for each order and comparison with the exact equations. + + Exact equations are based on factorials usage for coefficients calculation. + + Returns + ------- + None + """ compare_recursive_coeffs_radials() check_high_orders_recursion() -# Testing derived equations for derivatives dR(m, n)/dr by comparing with the exact ones (with factorials) def test_tabular_derivatives(): - compare_radial_derivatives(max_order=10) + """ + Test derived equations for derivatives dR(m, n)/dr by comparing with the exact ones (with factorials). + + Returns + ------- + None + """ + compare_radial_derivatives(max_order=17) -# Testing recursive and derived equations for derivatives dR(m, n)/dr by comparing with the exact ones (with factorials) -# Also, testing implemented recursive scheme for finding the polynomials coefficients for each order and comparison -# with the exact equations (with factorials) - derivative cases def test_recursive_derivatives(): - compare_radial_derivatives(max_order=17) + """ + Test implemented recursive scheme for finding derivatives dR(m, n)/dr for each order and comparison with the exact equations. + + Returns + ------- + None + """ compare_recursive_coeffs_radials_dr() -# Testing sum of Zernike polynomials def test_sum_zernikes(): + """ + Test summing of several Zernike polynomials, generation of phase profile and plotting method. + + Returns + ------- + None + """ zp1 = ZernPol(osa_index=1); zp2 = ZernPol(noll_index=2); ampls = [-0.5, 0.5]; theta = math.pi/3; r = 1.0 sum_pols = ZernPol.sum_zernikes(coefficients=ampls, polynomials=[zp1, zp2], r=r, theta=theta) sum_pols_manual = math.cos(theta) - math.sin(theta) # manual calculation of specified above sum @@ -59,14 +89,6 @@ def test_sum_zernikes(): assert isinstance(zern_surface, tuple) and isinstance(zern_surface.ZernSurf, np.ndarray), ("Check gen_zernikes_surface()" + " method output (tuple len=3)") assert len(zern_surface.ZernSurf.shape) == 2, "Check gen_zernikes_surface() method for output matrix shape" - try: - from matplotlib.figure import Figure - fig = Figure() - plotted_fig = ZernPol.plot_sum_zernikes_on_fig(coefficients=ampls, polynomials=[zp1, zp2], - figure=fig, zernikes_sum_surface=zern_surface) - assert isinstance(plotted_fig, Figure) and plotted_fig.tight_layout, "Something wrong with the plotting function" - except ModuleNotFoundError: - assert False, "Install matplotlib for passing the test" # Test difference between direct (naive) implementation and using meshgrids implementation of sum of Zernikes pols = [ZernPol(osa=2), ZernPol(osa=4), ZernPol(osa=7), ZernPol(osa=10), ZernPol(osa=15)] ampls = [-0.85, 0.85, 0.24, -0.37, 1.0]; radii = np.arange(start=0.0, stop=1.0 + 0.05, step=0.05) @@ -79,8 +101,14 @@ def test_sum_zernikes(): + f" and have abs(min) = {abs(np.min(sum_pols_d - sum_pols))}") -# Testing the calculation of polynomial values for edge cases def test_pol_values_edge_cases(): + """ + Test edge cases for proper denial / reporting. + + Returns + ------- + None + """ zp = ZernPol(osa=8) # test polynomial, could be any # Combination list + float r = [0, 0.1, 0.2, 0.5]; theta = 0.2; values = zp.polynomial_value(r, theta) diff --git a/src/zernpy/tests/test_fitting.py b/src/zernpy/tests/test_fitting.py index 4fef08a..15c6be5 100644 --- a/src/zernpy/tests/test_fitting.py +++ b/src/zernpy/tests/test_fitting.py @@ -10,12 +10,11 @@ """ # %% Global imports -import numpy as np import random -# %% Imports from modules -if __name__ != "__main__": - from ..zernikepol import generate_random_phases, fit_polynomials, ZernPol, fit_polynomials_vectors, generate_phases_image +import numpy as np + +from ..zernikepol import ZernPol, fit_polynomials, fit_polynomials_vectors, generate_phases_image, generate_random_phases # %% Test functions @@ -62,7 +61,7 @@ def test_random_fitting(): assert rmse_percentage <= (mdp//2) + 1, ("RMSE between fitted and randomly generated polynomials:" + f" {rmse_percentage} > assumed value {(mdp//2) + 1}") # Test the sign of fitted and randomly generated amplitudes - for i in range(2): # run tests + for _ in range(2): # run tests random_phases_image, random_amplitudes, polynomials_tuple = generate_random_phases(img_height=101, img_width=101) fitted_amplitudes, _ = fit_polynomials(random_phases_image, polynomials_tuple) max_fit_ampl = np.max(fitted_amplitudes); max_src_ampl = np.max(random_amplitudes) @@ -73,9 +72,7 @@ def test_random_fitting(): else: src_ampl = max_src_ampl; fit_ampl = max_fit_ampl same_sign = False - if src_ampl < 0.0 and fit_ampl < 0.0: - same_sign = True - elif src_ampl > 0.0 and fit_ampl > 0.0: + if src_ampl < 0.0 and fit_ampl < 0.0 or src_ampl > 0.0 and fit_ampl > 0.0: same_sign = True assert same_sign, ("\n Fitted and source amplitudes have abs. maximum values with different" + f" signs: source ampl.: {src_ampl}, fitted ampl.: {fit_ampl}") diff --git a/src/zernpy/tests/test_polynomials_initialization.py b/src/zernpy/tests/test_polynomials_initialization.py index 9dd12c6..0b3685a 100644 --- a/src/zernpy/tests/test_polynomials_initialization.py +++ b/src/zernpy/tests/test_polynomials_initialization.py @@ -11,18 +11,95 @@ """ import math -# Importing the written in the modules test functions for letting pytest library their automatic exploration -if __name__ != "__main__": - from ..zernikepol import check_conformity, ZernPol +import numpy as np + +from ..zernikepol import ZernPol -# Testing initialization of Zernike polynomials, for details, see the zernikepol module def test_polynomials_initialization(): - check_conformity() + """ + Test various initialization ways of Zernike polynomials, for details, see the imported function. + + Returns + ------- + None + """ + zp = ZernPol(m=-2, n=2) # Initialization with orders + (m1, n1), osa_i, noll_i, fringe_i = zp.get_indices() + assert (osa_i == 3 and noll_i == 5 and fringe_i == 6), (f"Check consistency of Z{(m1, n1)} indices: " + + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") + zp = ZernPol(l=-3, n=5) + (m2, n2), osa_i, noll_i, fringe_i = zp.get_indices() + assert (osa_i == 16 and noll_i == 19 and fringe_i == 20), (f"Check consistency of Z{(m2, n2)} indices: " + + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") + assert len(zp.get_polynomial_name(short=True)) > 0, f"Short name for Z{(m2, n2)} is zero length" + zp = ZernPol(azimuthal_order=-1, radial_order=5) + (m3, n3), osa_i, noll_i, fringe_i = zp.get_indices() + assert (osa_i == 17 and noll_i == 17 and fringe_i == 15), (f"Check consistency of Z{(m3, n3)} indices: " + + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") + assert len(zp.get_polynomial_name()) > 0, f"Name for Z{(m3, n3)} is zero length" + m4, n4 = zp.get_mn_orders() + assert m4 == m3 and n3 == n4, f"Check method get_mn_orders() for Z{(m3, n3)}" + print(f"Initialization of polynomials Z{(m1, n1)}, Z{(m2, n2)}, Z{(m3, n3)} tested") + osa_i = 12; zp = ZernPol(osa_index=osa_i) # Initialization with OSA index + m, n = zp.get_mn_orders() + assert (m == 0 and n == 4), f"Check consistency of Z[OSA index = {osa_i}] orders {m, n}" + assert zp.get_fringe_index(m, n) == 9, f"Check consistency of Z[OSA index = {osa_i}] Fringe index" + assert zp.get_noll_index(m, n) == 11, f"Check consistency of Z[OSA index = {osa_i}] Noll index" + print(f"Initialization of polynomial Z[OSA index = {osa_i}] tested") + noll_i = 10 # Testing static methods + assert ZernPol.noll2osa(noll_i) == 9, f"Check consistency of Noll index {noll_i} conversion to OSA index" + assert ZernPol.osa2fringe(ZernPol.noll2osa(noll_i)) == 10, ("Check consistency of Noll " + + f"index {noll_i} conversion to OSA index") + print(f"Conversion of Noll index {noll_i} to OSA and Fringe indices tested") + # Test for not proper initialization + try: + m_f = 2; n_f = -2 + zp = ZernPol(m=m_f, n=n_f) + asserting_value = False + except ValueError: + print(f"Polynomial Z{(m_f, n_f)} haven't been initialized, test passed") + asserting_value = True + assert asserting_value, f"Polynomial Z{(m_f, n_f)} initialized with wrong orders assignment" + # Testing input parameters for calculation + zp = ZernPol(m=0, n=2); r = 0.0; theta = math.pi + assert abs(zp.polynomial_value(r, theta) + math.sqrt(3)) < 1E-6, f"Check value of Z[{m}, {n}]({r}, {theta})" + zp = ZernPol(m=-1, n=1); r = 0.5; theta = math.pi/2 + assert abs(zp.polynomial_value(r, theta) - 1.0) < 1E-6, f"Check value of Z[{m}, {n}]({r}, {theta})" + print("Simple values of Zernike polynomials tested successfully") + try: + r = 'd'; theta = [1, 2] + zp.polynomial_value(r, theta) + asserting_value = False + except ValueError: + print("Input as string is not allowed for calculation of polynomial value, tested successfully") + asserting_value = True + assert asserting_value, "Wrong parameter passed (string) for calculation of polynomial value" + try: + r = [0.1, 0.2, 1.0+1E-9]; theta = math.pi + zp.polynomial_value(r, theta) + asserting_value = False + except ValueError: + print("Radius more than 1.0 is not allowed, tested successfully") + asserting_value = True + assert asserting_value, "Wrong parameter passed (r > 1.0) for calculation of polynomial value" + # Compare two implementations of Zernike pol-s sum calculation: direct and using meshgrid + pols = [ZernPol(osa=2), ZernPol(osa=4), ZernPol(osa=7), ZernPol(osa=10), ZernPol(osa=15), + ZernPol(osa=3), ZernPol(osa=9), ZernPol(osa=12), ZernPol(osa=16), ZernPol(osa=19)] + ampls = [-0.85, 0.85, 0.24, -0.37, 1.0, 0.1, -1.0, -0.05, 1.1, 0.41] + radii = np.arange(start=0.0, stop=1.0 + 0.001, step=0.001); thetas = np.arange(start=0.0, stop=2.0*np.pi + np.pi/180, step=np.pi/180) + ZernPol.sum_zernikes(ampls, pols, radii, thetas, get_surface=True) + ZernPol._sum_zernikes_meshgrid(ampls, pols, radii, thetas) -# Explicit testing initialization of Zernike polynomials def test_explicit_initialization(): + """ + Test particular initialization scenarios of Zernike polynomials. + + Returns + ------- + None + """ # Testing the ordinary, normal initialization of polynomials m = 0; n = 2; zp = ZernPol(l=m, n=n) assert abs(zp.radial_dr(0.25) - 1.0) < 1E-9, f"Radial derivative calculated with error for Z{(m, n)}" @@ -167,7 +244,7 @@ def test_explicit_initialization(): assert zp1 == zp2, "Implemented method '==' isn't correct" zp1 = ZernPol(fringe=21); zp2 = ZernPol(noll=8) - assert not zp1 == zp2, "Implemented method '==' isn't correct" + assert zp1 != zp2, "Implemented method '==' isn't correct" zp1 = ZernPol(fringe=17); zp2 = ZernPol(osa=14) assert zp1 == zp2, "Implemented method '==' isn't correct" diff --git a/src/zernpy/utils/intmproc.py b/src/zernpy/utils/intmproc.py index 84107fe..7d62963 100644 --- a/src/zernpy/utils/intmproc.py +++ b/src/zernpy/utils/intmproc.py @@ -7,11 +7,13 @@ """ # %% Global imports -from multiprocessing import Process, Event, Queue import os -import warnings import time -from typing import Callable, Any, Union # Callable[..., Any] - should check for any callable instance accepting / returning any types +import warnings +from multiprocessing import Event, Process, Queue +from typing import Any, Callable, List, Optional, Union + +# Callable[..., Any] - providing any callable instance accepting / returning any types # from collections.abc import Sequence # for more broad typing check - Sequence[Any] | np.ndarray - accept list, set, tuple, str or np.ndarray @@ -19,11 +21,13 @@ class DispenserManager(): """Manager for the distributing calculation job on several Processes.""" - __MAX_WORKERS: int = os.cpu_count(); workers_number: int = __MAX_WORKERS // 2; __warn_message: str = "" - __workers_pool: list = []; __results: list = []; __triggers: list = []; __initialized: bool = False - __global_live_trigger: Event = None; __queues: list = []; __parameters_vector: list = [] + __cpu_count = os.cpu_count() + __MAX_WORKERS: int = __cpu_count if __cpu_count is not None else 1 + workers_number: int = __MAX_WORKERS // 2; __warn_message: str = "" + __workers_pool: list = []; __results: list = []; __triggers: List[Any] = []; __initialized: bool = False + __global_live_trigger: Any = None; __queues: list = []; __parameters_vector: list = [] - def __init__(self, compute_func: Callable[..., Any], params_list: list, n_workers: int = None, verbose_info: bool = False): + def __init__(self, compute_func: Callable[..., Any], params_list: list, n_workers: Optional[int] = None, verbose_info: bool = False): """ Initialize main handling class along with provided (automatically calculated) number of workers. @@ -61,13 +65,13 @@ def __init__(self, compute_func: Callable[..., Any], params_list: list, n_worker if n_workers > self.__MAX_WORKERS: self.__warn_message = (f"Provided more workers than available detected by os.cpu_count() method: {self.__MAX_WORKERS}. " + f"By default, number of workers is set to: {self.workers_number}") - warnings.warn(self.__warn_message) + warnings.warn(self.__warn_message, stacklevel=2) else: self.workers_number = n_workers elif n_workers is not None and n_workers < 2: self.__warn_message = ("Provided number of workers is meaningless for spreading jobs on workers. " + f"Default number of workers will be used: {self.workers_number}") - warnings.warn(self.__warn_message) + warnings.warn(self.__warn_message, stacklevel=2) # Checking input parameters - compute function / method if not callable(compute_func): raise TypeError("Provided computing function isn't callable (not callable(compute_func) - True)") @@ -81,8 +85,8 @@ def __init__(self, compute_func: Callable[..., Any], params_list: list, n_worker # Initializing the pool with Processes self.__global_live_trigger = Event(); self.__global_live_trigger.set(); time.sleep(0.01) # print(f"Initializing {self.workers_number} Processes") - for i in range(self.workers_number): - trigger_event = Event(); queue = Queue(); self.__triggers.append(trigger_event) + for _ in range(self.workers_number): + trigger_event = Event(); queue: Queue = Queue(); self.__triggers.append(trigger_event) worker = IndiWorker(keep_run_trigger=self.__global_live_trigger, trigger=trigger_event, data_queue=queue, compute_func=compute_func) worker.start(); received_confirmation = False # for waiting of initializaton of the Process while not received_confirmation: @@ -92,7 +96,7 @@ def __init__(self, compute_func: Callable[..., Any], params_list: list, n_worker received_confirmation = True; break else: self.__warn_message = f"Not recognized confirmation message '{confirmation}', contact the developer" - warnings.warn(self.__warn_message); break + warnings.warn(self.__warn_message, stacklevel=2); break else: time.sleep(0.005) self.__workers_pool.append(worker); self.__queues.append(queue) @@ -125,8 +129,9 @@ def compute(self): """ if self.__initialized: computed_tasks = 0; init_step = True; indices2process = [i for i in range(len(self.__parameters_vector))] - processing_indices = [None]*len(self.__workers_pool); task_assigned = [False]*len(self.__workers_pool); self.done_jobs_percentage = 0 - while computed_tasks < len(self.__results): + processing_indices = [0]*len(self.__workers_pool); task_assigned = [False]*len(self.__workers_pool) + self.done_jobs_percentage = 0 + while computed_tasks < len(self.__results): # noqa: SIM113 if init_step: current_param_index = 0 for proc_i in range(len(self.__workers_pool)): @@ -166,8 +171,8 @@ def compute(self): self.done_jobs_percentage = done_jobs_percent return self.__results else: - self.__warn_message = ("All workers have been released, no computation has been performed") - warnings.warn(self.__warn_message); return None + self.__warn_message = ("\nAll workers have been released, no computation has been performed") + warnings.warn(self.__warn_message, stacklevel=2); return None def close(self): """ @@ -236,9 +241,9 @@ def update_params(self, params_list: list): class IndiWorker(Process): """Individual Worker based on Process() class for performing computations using provided function.""" - __keep_event: Event = None; __trigger: Event; __data_queue: Queue + __keep_event: Any = None; __trigger: Any; __data_queue: Any - def __init__(self, keep_run_trigger: Event, trigger: Event, data_queue: Queue, compute_func): + def __init__(self, keep_run_trigger: Any, trigger: Any, data_queue: Any, compute_func: Callable[..., Any]): """ Process from multiprocessing based class. @@ -275,11 +280,6 @@ def run(self): while self.__keep_event.is_set(): self.__trigger.wait() # wait that the parameter is transferred if self.__trigger.is_set() and self.__keep_event.is_set(): - # attempts = 0 - # if not self.__data_queue.empty() and attempts < 11: - # parameter = self.__data_queue.get_nowait() - # else: - # time.sleep(0.001); attempts += 1 parameter = self.__data_queue.get() # print(f"Start computing for parameter {parameter}", flush=True) result = self.computation(parameter) # computation work @@ -335,7 +335,7 @@ def test_minus(x: Union[float, int]) -> Union[float, int]: if __name__ == "__main__": params = [10*(i+1) for i in range(177)] # ... computation points # Direct computation - for loop for performance check - t1 = time.perf_counter(); results_for = [None]*len(params) + t1 = time.perf_counter(); results_for = [0.0]*len(params) for i, par in enumerate(params): results_for[i] = test_plus(par) elapsed_ms = int(round(1000.0*(time.perf_counter() - t1), 0)) diff --git a/src/zernpy/zernikepol.py b/src/zernpy/zernikepol.py index f436eac..5931df8 100644 --- a/src/zernpy/zernikepol.py +++ b/src/zernpy/zernikepol.py @@ -4,40 +4,40 @@ Also, provides a few functions useful for fitting set of Zernike polynomials to an image with phases. -@author: Sergei Klykov, @year: 2026, @licence: MIT \n +@author: Sergei Klykov, @year: 2026, @license: MIT \n """ # %% Global imports -import numpy as np -from pathlib import Path +import random import warnings -import math from collections import namedtuple +from typing import Optional, Sequence, Tuple, Union + import matplotlib.pyplot as plt -import random -import time -from typing import Union, Sequence, Tuple +import numpy as np # %% Local (package-scoped) imports -if __name__ == "__main__" or __name__ == Path(__file__).stem or __name__ == "__mp_main__": - from calculations.calc_zernike_pol import (normalization_factor, radial_polynomial, triangular_function, triangular_derivative, - radial_derivative, radial_polynomial_eq, radial_derivative_eq, radial_polynomial_coeffs, - radial_polynomial_coeffs_dr, MAX_RADIAL_ORDER_COEFFS, MAX_RADIAL_ORDER_COEFFS_dR) - from plotting.plot_zerns import plot_sum_fig, subplot_sum_on_fig, plot_sum_fig_3d, subplot_sum_on_fig_3d - from calculations.fit_zernike_pols import crop_phases_img, fit_zernikes - from props.properties import polynomial_names, short_polynomial_names, warn_mess_r_long, warn_mess_dr_long, warn_mess_slow_calc -else: - from .calculations.calc_zernike_pol import (normalization_factor, radial_polynomial, triangular_function, triangular_derivative, - radial_derivative, radial_polynomial_eq, radial_derivative_eq, radial_polynomial_coeffs, - radial_polynomial_coeffs_dr, MAX_RADIAL_ORDER_COEFFS, MAX_RADIAL_ORDER_COEFFS_dR) - from .plotting.plot_zerns import plot_sum_fig, subplot_sum_on_fig, plot_sum_fig_3d, subplot_sum_on_fig_3d - from .calculations.fit_zernike_pols import crop_phases_img, fit_zernikes - from .props.properties import polynomial_names, short_polynomial_names, warn_mess_r_long, warn_mess_dr_long, warn_mess_slow_calc +from .calculations.calc_zernike_pol import ( + MAX_RADIAL_ORDER_COEFFS, + MAX_RADIAL_ORDER_COEFFS_dR, + normalization_factor, + radial_derivative, + radial_derivative_eq, + radial_polynomial, + radial_polynomial_coeffs, + radial_polynomial_coeffs_dr, + radial_polynomial_eq, + triangular_derivative, + triangular_function, +) +from .calculations.fit_zernike_pols import crop_phases_img, fit_zernikes +from .plotting.plot_zerns import plot_sum_fig, plot_sum_fig_3d, subplot_sum_on_fig, subplot_sum_on_fig_3d +from .props.properties import polynomial_names, short_polynomial_names, warn_mess_dr_long, warn_mess_r_long, warn_mess_slow_calc # %% Module parameters __docformat__ = "numpydoc" -polar_vectors = namedtuple("PolarVectors", "R Theta") # re-used below as the return type from the method -zernikes_surface = namedtuple("ZernikesSurface", "ZernSurf R Theta") # used as the input type +polar_vectors = namedtuple("polar_vectors", "R Theta") # re-used below as the return type from the method +zernikes_surface = namedtuple("zernikes_surface", "ZernSurf R Theta") # used as the input type # %% Zernike Pol. class @@ -86,30 +86,29 @@ def __init__(self, **kwargs): key = "" # Zernike polynomial specified with key arguments m, n - check firstly for these parameters if len(kwargs.keys()) == 2: - if "n" in kwargs.keys() or "radial_order" in kwargs.keys(): + if "n" in kwargs or "radial_order" in kwargs: if self.__initialized: raise ValueError("The polynomial has been already initialized, but radial_order/n/m parsed") else: # get the actual name of the key for radial order - if "n" in kwargs.keys(): + if "n" in kwargs: key = "n" else: key = "radial_order" if isinstance(kwargs.get(key), int): - self.__n = kwargs.get(key) # radial order acknowledged + self.__n = int(kwargs[key]) # radial order acknowledged # Below each time key arguments are checked in the list of keys - if ("m" in kwargs.keys() or "l" in kwargs.keys() or "azimuthal_order" in kwargs.keys() - or "angular_frequency" in kwargs.keys()): - if "m" in kwargs.keys(): + if ("m" in kwargs or "l" in kwargs or "azimuthal_order" in kwargs or "angular_frequency" in kwargs): + if "m" in kwargs: key = "m" - elif "l" in kwargs.keys(): + elif "l" in kwargs: key = "l" - elif "azimuthal_order" in kwargs.keys(): + elif "azimuthal_order" in kwargs: key = "azimuthal_order" else: key = "angular_frequency" if isinstance(kwargs.get(key), int): - self.__m = kwargs.get(key) # azimuthal order acknowledged + self.__m = int(kwargs[key]) # azimuthal order acknowledged # Checking that the provided orders are reasonable if not (self.__n - abs(self.__m)) % 2 == 0: # see [1] raise ValueError("Failed sanity check: n - |m| == even number") @@ -120,7 +119,7 @@ def __init__(self, **kwargs): elif self.__n < 0: raise ValueError("Failed sanity check: order n less than 0") elif self.__n > 54: - raise ValueError("Initialization of Zernike with radial order higher than 54" + raise ValueError("\nInitialization of Zernike with radial order higher than 54" + " is meaningless because of very slow calculation performance") # m and n specified correctly, calculate other properties - various indices else: @@ -138,25 +137,24 @@ def __init__(self, **kwargs): raise ValueError("Radial order n provided not as an integer") elif len(kwargs.keys()) == 1: # OSA / ANSI index used for Zernike polynomial initialization - if ("osa_index" in kwargs.keys() or "osa" in kwargs.keys() or "ansi_index" in kwargs.keys() - or "ansi" in kwargs.keys()): + if ("osa_index" in kwargs or "osa" in kwargs or "ansi_index" in kwargs or "ansi" in kwargs): if self.__initialized: raise ValueError("The polynomial has been already initialized, but osa_index/osa... parsed") else: - if "osa_index" in kwargs.keys(): + if "osa_index" in kwargs: key = "osa_index" - elif "osa" in kwargs.keys(): + elif "osa" in kwargs: key = "osa" - elif "ansi_index" in kwargs.keys(): + elif "ansi_index" in kwargs: key = "ansi_index" - elif "ansi" in kwargs.keys(): + elif "ansi" in kwargs: key = "ansi" if isinstance(kwargs.get(key), int): - osa_i = kwargs.get(key) + osa_i = int(kwargs[key]) if osa_i < 0: raise ValueError("OSA / ANSI index should be non-negative integer") elif osa_i > 1539: - ValueError("Initialization of Zernike with OSA index higher than 1539" + ValueError("\nInitialization of Zernike with OSA index higher than 1539" + " is meaningless because of very slow calculation performance") else: self.__osa_index = osa_i; self.__initialized = True @@ -166,20 +164,20 @@ def __init__(self, **kwargs): else: raise ValueError("OSA / ANSI index provided not as an integer") # Noll index used for Zernike polynomial initialization - elif "noll_index" in kwargs.keys() or "noll" in kwargs.keys(): + elif "noll_index" in kwargs or "noll" in kwargs: if self.__initialized: raise ValueError("The polynomial has been already initialized, but noll_index/noll parsed") else: - if "noll_index" in kwargs.keys(): + if "noll_index" in kwargs: key = "noll_index" - elif "noll" in kwargs.keys(): + elif "noll" in kwargs: key = "noll" if isinstance(kwargs.get(key), int): - noll_i = kwargs.get(key) + noll_i = int(kwargs[key]) if noll_i < 1: raise ValueError("Noll index should be not less than 1 integer") elif noll_i > 1540: - ValueError("Initialization of Zernike with Noll index higher than 1540" + ValueError("\nInitialization of Zernike with Noll index higher than 1540" + " is meaningless because of very slow calculation performance") else: self.__noll_index = noll_i; self.__initialized = True @@ -189,23 +187,23 @@ def __init__(self, **kwargs): else: raise ValueError("Noll index provided not as an integer") # Fringe / Univ. of Arizona index used for Zernike polynomial initialization - elif "fringe_index" in kwargs.keys() or "fringe" in kwargs.keys(): + elif "fringe_index" in kwargs or "fringe" in kwargs: if self.__initialized: raise ValueError("The polynomial has been already initialized, but fringe_index/fringe parsed") else: - if "fringe_index" in kwargs.keys(): + if "fringe_index" in kwargs: key = "fringe_index" - elif "fringe" in kwargs.keys(): + elif "fringe" in kwargs: key = "fringe" if isinstance(kwargs.get(key), int): - fringe_i = kwargs.get(key) + fringe_i = int(kwargs[key]) if fringe_i < 1: raise ValueError("Fringe index should be not less than 1 integer") else: self.__fringe_index = fringe_i; self.__initialized = True self.__m, self.__n = ZernPol.index2orders(fringe_index=self.__fringe_index) if self.__n > 54: - raise ValueError("Initialization of Zernike with radial order higher than 54" + raise ValueError("\nInitialization of Zernike with radial order higher than 54" + " is meaningless because of very slow calculation performance") self.__osa_index = ZernPol.get_osa_index(self.__m, self.__n) self.__noll_index = ZernPol.get_noll_index(self.__m, self.__n) @@ -218,11 +216,11 @@ def __init__(self, **kwargs): raise ValueError("The initialization parameters for Zernike polynomial hasn't been parsed / recognized") # Generate warning messages for possible re-usage if self.__n > MAX_RADIAL_ORDER_COEFFS: - self.__warn_mes_r = f"Call for radial order {self.__n} is higher than {MAX_RADIAL_ORDER_COEFFS}" + self.__warn_mes_r = f"\nCall for radial order {self.__n} is higher than {MAX_RADIAL_ORDER_COEFFS}" else: self.warn_mes_r = "" if self.__n > MAX_RADIAL_ORDER_COEFFS_dR: - self.__warn_mes_dr = f"Call for derivative of radial order {self.__n} is > than {MAX_RADIAL_ORDER_COEFFS_dR}" + self.__warn_mes_dr = f"\nCall for derivative of radial order {self.__n} is > than {MAX_RADIAL_ORDER_COEFFS_dR}" else: self.warn_mes_dr = "" @@ -273,10 +271,10 @@ def get_polynomial_name(self, short: bool = False) -> str: """ name = "" if short: - if (self.__m, self.__n) in short_polynomial_names.keys(): + if (self.__m, self.__n) in short_polynomial_names: name = short_polynomial_names[(self.__m, self.__n)] else: - if (self.__m, self.__n) in polynomial_names.keys(): + if (self.__m, self.__n) in polynomial_names: name = polynomial_names[(self.__m, self.__n)] return name @@ -400,9 +398,8 @@ def polynomial_value(self, r: Union[float, np.ndarray], theta: Union[float, np.n r = ZernPol._check_radii(r) # Check radii type and that they are not lying outside range [0.0, 1.0] - unit circle theta = ZernPol._check_angles(theta) # Checking that angles lie in the range [0, 2*pi] and their type # Checking coincidence of shapes if theta and r are arrays - if isinstance(r, type(np.zeros(1))) and isinstance(theta, type(np.zeros(1))): - if r.shape != theta.shape: - raise ValueError("Shape of input arrays r and theta is not equal") + if isinstance(r, type(np.zeros(1))) and isinstance(theta, type(np.zeros(1))) and r.shape != theta.shape: + raise ValueError("Shape of input arrays r and theta is not equal") # Calculation using imported function from submodule depending on radial order, use different eq. nTr = normalization_factor(self)*triangular_function(self, theta) if not use_exact_eq: @@ -411,14 +408,14 @@ def polynomial_value(self, r: Union[float, np.ndarray], theta: Union[float, np.n else: # Raise warning about slow calculations for orders more than 50, only once if self.__n > 50 and not self.__show_slow_calc_warn: - warn_mess = f"ZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc - warnings.warn(warn_mess) + warn_mess = f"\nZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc + warnings.warn(warn_mess, stacklevel=2) self.__show_slow_calc_warn = True # Returning values using recursive scheme for finding the coefficients for all radial orders (e.g. R^6) return nTr*radial_polynomial_coeffs(self, r) else: if self.__n > MAX_RADIAL_ORDER_COEFFS: - warnings.warn(self.__warn_mes_r + warn_mess_r_long) + warnings.warn(self.__warn_mes_r + warn_mess_r_long, stacklevel=2) if isinstance(r, float): return 0.0 elif isinstance(r, np.ndarray): @@ -478,14 +475,14 @@ def radial(self, r: Union[float, np.ndarray], use_exact_eq: bool = False) -> Uni else: # Raise warning about slow calculations for orders more than 50, only once if self.__n > 50 and not self.__show_slow_calc_warn: - warn_mess = f"ZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc - warnings.warn(warn_mess) + warn_mess = f"\nZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc + warnings.warn(warn_mess, stacklevel=2) self.__show_slow_calc_warn = True # Returning values using recursive scheme for finding the coefficients for all radial orders (e.g. R^6) return radial_polynomial_coeffs(self, r) else: if self.__n > MAX_RADIAL_ORDER_COEFFS: - warnings.warn(self.__warn_mes_r + warn_mess_r_long) + warnings.warn(self.__warn_mes_r + warn_mess_r_long, stacklevel=2) if isinstance(r, float): return 0.0 elif isinstance(r, np.ndarray): @@ -561,8 +558,7 @@ def radial_dr(self, r: Union[float, np.ndarray], use_exact_eq: bool = False) -> Calculated derivative of Zernike radial function value(-s) on provided float values / arrays of radiuses. """ - # Checking input parameters for avoiding errors and unexpectable values - r = ZernPol._check_radii(r) + r = ZernPol._check_radii(r) # Checking input parameters for avoiding errors and unexpectable values # Calculation using imported function from submodule depending on radial order, use different eq. if not use_exact_eq: if self.__n <= 12: # condition to switch from direct recurrence equation to finding of coeffs. algorithm @@ -570,14 +566,14 @@ def radial_dr(self, r: Union[float, np.ndarray], use_exact_eq: bool = False) -> else: # Raise warning about slow calculations for orders more than 50, only once if self.__n > 48 and not self.__show_slow_calc_warn: - warn_mess = f"ZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc - warnings.warn(warn_mess) + warn_mess = f"\nZernPol(m={self.__m}, n={self.__n})" + warn_mess_slow_calc + warnings.warn(warn_mess, stacklevel=2) self.__show_slow_calc_warn = True # Returning values using recursive scheme for finding the coefficients for all radial orders (e.g. R^6) return radial_polynomial_coeffs_dr(self, r) else: if self.__n > MAX_RADIAL_ORDER_COEFFS_dR: - warnings.warn(self.__warn_mes_dr + warn_mess_dr_long) + warnings.warn(self.__warn_mes_dr + warn_mess_dr_long, stacklevel=2) if isinstance(r, float): return 0.0 elif isinstance(r, np.ndarray): @@ -680,15 +676,10 @@ def get_noll_index(m: int, n: int) -> int: """ add_n = 1 if m > 0: - if (n % 4) == 0: - add_n = 0 - elif ((n - 1) % 4) == 0: - add_n = 0 - elif m < 0: - if ((n - 2) % 4) == 0: - add_n = 0 - elif ((n - 3) % 4) == 0: + if (n % 4) == 0 or ((n - 1) % 4) == 0: add_n = 0 + elif m < 0 and (((n - 2) % 4) == 0 or ((n - 3) % 4) == 0): + add_n = 0 return (n*(n + 1))//2 + abs(m) + add_n @staticmethod @@ -731,30 +722,29 @@ def index2orders(**kwargs) -> Tuple[int, int]: (m, n) - contains azimuthal and radial orders as integers. """ - osa_index = -1; noll_index = -1; fringe_index = -1; m = -1; n = -1 + osa_index: int = -1; noll_index: int = -1; fringe_index: int = -1; m: int = -1; n: int = -1 highest_order = 56 # default value, limited by the allowed maximal radial order + 2 - if "osa_index" in kwargs.keys(): - osa_index = kwargs.get("osa_index") - elif "noll_index" in kwargs.keys(): - noll_index = kwargs.get("noll_index") - elif "fringe_index" in kwargs.keys(): - fringe_index = kwargs.get("fringe_index") + if "osa_index" in kwargs: + osa_index = int(kwargs["osa_index"]) + elif "noll_index" in kwargs: + noll_index = int(kwargs["noll_index"]) + elif "fringe_index" in kwargs: + fringe_index = int(kwargs["fringe_index"]) highest_order = 250 # to guarantee that right Fringe index found # Define m, n orders up to the specified above highest order (radial) stop_search = False for order in range(0, highest_order): m = -order # azimuthal order n = order # radial order - for polynomial in range(0, order+1): + for _ in range(0, order+1): if osa_index >= 0: if osa_index == ZernPol.get_osa_index(m, n): stop_search = True; break elif noll_index >= 0: if noll_index == ZernPol.get_noll_index(m, n): stop_search = True; break - elif fringe_index >= 0: - if fringe_index == ZernPol.get_fringe_index(m, n): - stop_search = True; break + elif fringe_index >= 0 and fringe_index == ZernPol.get_fringe_index(m, n): + stop_search = True; break m += 2 if stop_search: break @@ -905,9 +895,9 @@ def _sum_zernikes_meshgrid(coefficients: Sequence[float], polynomials: Sequence, raise ValueError("Lengths of coefficients and polynomials aren't equal") else: if not isinstance(r, np.ndarray) or not isinstance(theta, np.ndarray): - warnings.warn("Requested calculation of surface (mesh) values with" + warnings.warn("\nRequested calculation of surface (mesh) values with" + " provided r or theta as not numpy.ndarray.\n" - + "The surface will be generated automatically.") + + "The surface will be generated automatically.", stacklevel=2) else: r_size = np.size(r, 0); theta_size = np.size(theta, 0) theta_grid, r_grid = np.meshgrid(theta, r); S = np.zeros(shape=(r_size, theta_size)) @@ -954,7 +944,7 @@ def sum_zernikes(coefficients: Sequence[float], polynomials: Sequence, r: Union[ Depending on the input values and parameter get_surface - can be: float, 1D or 2D numpy.ndarrays. """ - S = 0.0 # default value - sum + S: Union[float, np.ndarray] if len(coefficients) != len(polynomials): raise ValueError("Lengths of lists with polynomials and their amplitudes aren't equal") elif len(coefficients) == 0: @@ -971,12 +961,10 @@ def sum_zernikes(coefficients: Sequence[float], polynomials: Sequence, r: Union[ S += coefficient*polynomials[i].polynomial_value(r, theta) elif get_surface: if not isinstance(r, np.ndarray) or not isinstance(theta, np.ndarray): - warnings.warn("Requested calculation of surface (mesh) values with" - + " provided r or theta as not numpy.ndarray.\n" - + "The surface will be generated automatically.") + warnings.warn("\nRequested calculation of surface (mesh) values with provided r or theta as not numpy.ndarray.\n" + + "The surface will be generated automatically.", stacklevel=2) else: - r_size = np.size(r, 0); theta_size = np.size(theta, 0) - S = np.zeros(shape=(r_size, theta_size)) + r_size = np.size(r, 0); theta_size = np.size(theta, 0); S = np.zeros(shape=(r_size, theta_size)) for i, coefficient in enumerate(coefficients): if not isinstance(polynomials[i], ZernPol): raise ValueError(f"Variable {polynomials[i]} isn't an instance of ZernPol class") @@ -992,7 +980,7 @@ def sum_zernikes(coefficients: Sequence[float], polynomials: Sequence, r: Union[ @staticmethod def gen_polar_coordinates(r_step: float = 0.01, theta_rad_step: float = round(np.pi/240, 7)) -> polar_vectors: """ - Generate the named tuple "PolarVectors" with R and Theta - vectors with polar coordinates for an entire unit circle. + Generate the named tuple "polar_vectors" with R and Theta - vectors with polar coordinates for an entire unit circle. Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are defined by the specification of r_step and theta_rad_step parameters. @@ -1012,7 +1000,7 @@ def gen_polar_coordinates(r_step: float = 0.01, theta_rad_step: float = round(np Returns ------- polar_vectors - namedtuple("PolarVectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], + namedtuple("polar_vectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], Theta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi]. """ @@ -1031,7 +1019,7 @@ def gen_polar_coordinates(r_step: float = 0.01, theta_rad_step: float = round(np @staticmethod def gen_equal_polar_mesh(n_points: int = 250) -> polar_vectors: """ - Generate the named tuple "PolarVectors" with R and Theta - vectors with polar coordinates for an entire unit circle. + Generate the named tuple "polar_vectors" with R and Theta - vectors with polar coordinates for an entire unit circle. Note that R and Theta are generated as the numpy.ndarrays vectors (shape like (n elements, )). Their shapes are equal and defined by the parameter n_points. @@ -1044,7 +1032,7 @@ def gen_equal_polar_mesh(n_points: int = 250) -> polar_vectors: Returns ------- polar_vectors - namedtuple("PolarVectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], + namedtuple("polar_vectors", "R Theta"), where R - vector with radiuses values [0.0, r_step, ... 1.0], Theta - vector with theta angles values [0.0, theta_rad_step, ... 2*pi]. """ @@ -1055,7 +1043,7 @@ def gen_equal_polar_mesh(n_points: int = 250) -> polar_vectors: @staticmethod def plot_profile(polynomial, color_map: str = "coolwarm", show_title: bool = True, use_defaults: bool = True, - projection: str = "2d", polar_coordinates: polar_vectors = ()): + projection: str = "2d", polar_coordinates: Optional[polar_vectors] = None): """ Plot the provided Zernike polynomial (instance of ZernPol class) on the matplotlib figure. @@ -1077,7 +1065,7 @@ def plot_profile(polynomial, color_map: str = "coolwarm", show_title: bool = Tru Either "2d" ("2D") - for 2D profile plot, or "3d" ("3D") - for 3D surface plot. The default is "2d". polar_coordinates : polar_vectors, optional If the flag 'use_defaults' is False, this named tuple is used for accessing polar coordinates for plotting. - The default is (). + The default is None. Raises ------ @@ -1090,8 +1078,8 @@ def plot_profile(polynomial, color_map: str = "coolwarm", show_title: bool = Tru """ if isinstance(polynomial, ZernPol): - if not use_defaults and len(polar_coordinates) != 2: - raise ValueError("Polar coordinates isn't provided as a tuple with values R, Theta") + if not use_defaults and polar_coordinates is None: + raise ValueError("\nPolar coordinates isn't provided as a tuple with values R, Theta") # Get polar coordinates if use_defaults: if projection == "3d" or projection == "3D": @@ -1099,10 +1087,13 @@ def plot_profile(polynomial, color_map: str = "coolwarm", show_title: bool = Tru else: r, theta = ZernPol.gen_polar_coordinates() else: - r, theta = polar_coordinates.R, polar_coordinates.Theta + if polar_coordinates is not None: + r, theta = polar_coordinates.R, polar_coordinates.Theta + else: + raise ValueError("\nPolar coordinates isn't provided as a tuple with values R, Theta") # Get profile or surface to plot amplitudes = [1.0]; zernikes = [polynomial] # for reusing the sum function of polynomials - zern_surface = ZernPol.sum_zernikes(amplitudes, zernikes, r, theta, get_surface=True) + zern_surface = np.asarray(ZernPol.sum_zernikes(amplitudes, zernikes, r, theta, get_surface=True)) # Select plotting function between 2D and 3D plotting functions if projection == "3d" or projection == "3D": plot_sum_fig_3d(zern_surface, r, theta, color_map) @@ -1115,8 +1106,8 @@ def plot_profile(polynomial, color_map: str = "coolwarm", show_title: bool = Tru @staticmethod def gen_zernikes_surface(coefficients: Sequence[float], polynomials: Sequence, r_step: float = 0.01, - theta_rad_step: float = round(np.pi/180, 7), - equal_n_coordinates: bool = False, n_points: int = 250) -> zernikes_surface: + theta_rad_step: float = round(np.pi/180, 7), equal_n_coordinates: bool = False, + n_points: int = 250) -> zernikes_surface: """ Generate surface of provided Zernike polynomials on the generated polar coordinates used steps. @@ -1141,7 +1132,7 @@ def gen_zernikes_surface(coefficients: Sequence[float], polynomials: Sequence, r Returns ------- zernikes_surface - namedtuple("ZernikesSurface", "ZernSurf R Theta") - tuple for storing mesh values for polar coordinates. + namedtuple("zernikes_surface", "ZernSurf R Theta") - tuple for storing mesh values for polar coordinates. ZernSurf variable is 2D matrix with the sum of the input polynomials on generated polar coordinates (R, Theta). """ @@ -1149,14 +1140,13 @@ def gen_zernikes_surface(coefficients: Sequence[float], polynomials: Sequence, r polar_vectors = ZernPol.gen_polar_coordinates(r_step, theta_rad_step) else: polar_vectors = ZernPol.gen_equal_polar_mesh(n_points) - zernikes_sum = ZernPol.sum_zernikes(coefficients, polynomials, polar_vectors.R, - polar_vectors.Theta, get_surface=True) + zernikes_sum = ZernPol.sum_zernikes(coefficients, polynomials, polar_vectors.R, polar_vectors.Theta, get_surface=True) return zernikes_surface(zernikes_sum, polar_vectors.R, polar_vectors.Theta) @staticmethod def plot_sum_zernikes_on_fig(figure: plt.Figure, coefficients: Sequence[float] = (), polynomials: Sequence = (), use_defaults: bool = True, - zernikes_sum_surface: zernikes_surface = (), show_range: bool = True, color_map: str = "coolwarm", - projection: str = "2d") -> plt.Figure: + zernikes_sum_surface: Optional[zernikes_surface] = None, + show_range: bool = True, color_map: str = "coolwarm", projection: str = "2d") -> plt.Figure: """ Plot a sum of the specified Zernike polynomials by input lists (see function parameters) on the provided figure. @@ -1174,10 +1164,10 @@ def plot_sum_zernikes_on_fig(figure: plt.Figure, coefficients: Sequence[float] = Coefficients of Zernike polynomials for calculation of their sum. The default is (). polynomials : Sequence[ZernPol], optional Initialized polynomials as class instances of ZernPol class specified in this module. The default is (). - zernikes_sum_surface : namedtuple("ZernikesSurface", "ZernSurf R Theta") , optional + zernikes_sum_surface : namedtuple("zernikes_surface", "ZernSurf R Theta"), optional This tuple should contain the ZernSurf calculated on a mesh of polar coordinates R, Theta. This tuple could be generated by the call of the static method gen_zernikes_surface(). - Check the method signature for details. The default is (). + Check the method signature for details. The default is None. show_range : bool, optional Flag for showing range of provided values as the colorbar on the figure. The default is True. color_map : str, optional @@ -1199,16 +1189,15 @@ def plot_sum_zernikes_on_fig(figure: plt.Figure, coefficients: Sequence[float] = """ if use_defaults and len(coefficients) == 0 and len(polynomials) == 0: - raise ValueError("Input Sequence with coefficients or with polynomials is empty along with the flag 'use_defaults' - True") - if not use_defaults and len(zernikes_sum_surface) != 3: - raise ValueError("Zernike surface isn't provided as a tuple with values Sum surface, R, Theta") + raise ValueError("\nInput Sequence with coefficients or with polynomials is empty along with the flag 'use_defaults' - True") + if not use_defaults and zernikes_sum_surface is None: + raise ValueError("\nZernike surface isn't provided as a tuple with values Sum surface, R, Theta") if use_defaults: if projection == "3d" or projection == "3D": polar_vectors = ZernPol.gen_equal_polar_mesh() else: polar_vectors = ZernPol.gen_polar_coordinates() - zernikes_sum = ZernPol.sum_zernikes(coefficients, polynomials, polar_vectors.R, - polar_vectors.Theta, get_surface=True) + zernikes_sum = np.asarray(ZernPol.sum_zernikes(coefficients, polynomials, polar_vectors.R, polar_vectors.Theta, get_surface=True)) if projection == "3d" or projection == "3D": figure = subplot_sum_on_fig_3d(figure, zernikes_sum, polar_vectors.R, polar_vectors.Theta, show_range_colorbar=show_range, color_map=color_map) @@ -1216,20 +1205,21 @@ def plot_sum_zernikes_on_fig(figure: plt.Figure, coefficients: Sequence[float] = figure = subplot_sum_on_fig(figure, zernikes_sum, polar_vectors.R, polar_vectors.Theta, show_range_colorbar=show_range, color_map=color_map) else: - if projection == "3d" or projection == "3D": - figure = subplot_sum_on_fig_3d(figure, zernikes_sum_surface.ZernSurf, zernikes_sum_surface.R, - zernikes_sum_surface.Theta, show_range_colorbar=show_range, - color_map=color_map) + if zernikes_sum_surface is not None: + if projection == "3d" or projection == "3D": + figure = subplot_sum_on_fig_3d(figure, zernikes_sum_surface.ZernSurf, zernikes_sum_surface.R, + zernikes_sum_surface.Theta, show_range_colorbar=show_range, color_map=color_map) + else: + figure = subplot_sum_on_fig(figure, zernikes_sum_surface.ZernSurf, zernikes_sum_surface.R, + zernikes_sum_surface.Theta, show_range_colorbar=show_range, color_map=color_map) else: - figure = subplot_sum_on_fig(figure, zernikes_sum_surface.ZernSurf, zernikes_sum_surface.R, - zernikes_sum_surface.Theta, show_range_colorbar=show_range, - color_map=color_map) + raise ValueError("\nZernike surface isn't provided as a tuple with values Sum surface, R, Theta") return figure @staticmethod def _plot_zernikes_half_pyramid(): """ - Generate halb-pyramid with Zernikes polynomials. + Generate half-pyramid with Zernikes polynomials. Returns ------- @@ -1244,10 +1234,8 @@ def _plot_zernikes_half_pyramid(): for j in range(len(axes[0])): axes[i, j].grid(False) # demanded by pcolormesh function, if not called - deprecation warning if j > ignored_column-1: - zps = [ZernPol(osa=k)] - zernike_surface, r, theta = ZernPol.gen_zernikes_surface(coefficients=ampls, polynomials=zps) - axes[i, j].pcolormesh(theta, r, zernike_surface, cmap=plt.cm.coolwarm, shading='nearest') - k += 1 + zps = [ZernPol(osa=k)]; zernike_surface, r, theta = ZernPol.gen_zernikes_surface(coefficients=ampls, polynomials=zps) + axes[i, j].pcolormesh(theta, r, zernike_surface, cmap=plt.colormaps['coolwarm'], shading='nearest'); k += 1 axes[i, j].axis('off') # off polar coordinate axes ignored_column -= 1 fig.subplots_adjust(left=0, bottom=0, right=1, top=1); fig.tight_layout() @@ -1276,17 +1264,16 @@ def _check_radii(radii: Union[list, tuple, float, int, np.ndarray]) -> Union[flo """ # Trying to convert known (list, tuple) data types into numpy, if they provided as input if not isinstance(radii, np.ndarray) and not isinstance(radii, float): - if isinstance(radii, list) or isinstance(radii, tuple) or isinstance(radii, set): + if isinstance(radii, (list, tuple, set)): radii = np.asarray(radii) # convert list or tuple to np.array else: radii = float(radii) # attempt to convert r to float number, will raise ValueError if it's impossible # Checking that radii or radius lie in the range [0.0, 1.0] if isinstance(radii, np.ndarray): if np.min(radii) < 0.0 or np.max(radii) > 1.0: - raise ValueError("Minimal or maximal value of radii laying outside unit circle [0.0, 1.0]") - elif isinstance(radii, float): - if radii > 1.0 or radii < 0.0: - raise ValueError("Radius laying outside unit circle [0.0, 1.0]") + raise ValueError("\nMinimal or maximal value of radii laying outside unit circle [0.0, 1.0]") + elif isinstance(radii, float) and (radii > 1.0 or radii < 0.0): + raise ValueError("Radius laying outside unit circle [0.0, 1.0]") return radii @staticmethod @@ -1315,27 +1302,26 @@ def _check_angles(angles: Union[list, tuple, float, int, np.ndarray]) -> Union[f """ # Check input parameter type and attempt to convert to acceptable types if not isinstance(angles, np.ndarray) and not isinstance(angles, float): - if isinstance(angles, list) or isinstance(angles, tuple) or isinstance(angles, set): + if isinstance(angles, (list, tuple, set)): angles = np.asarray(angles) # convert list or tuple to np.array else: angles = float(angles) # attempt to convert to float number, will raise ValueError if it's impossible # Checking that angles lie in the range [0, 2*pi] if isinstance(angles, np.ndarray): if np.max(angles) - np.min(angles) > 2.0*np.pi: - _warn_message_ = "Theta angles defined in range outside of interval [0.0, 2.0*pi]" - warnings.warn(_warn_message_) + _warn_message_ = "\nTheta angles defined in range outside of interval [0.0, 2.0*pi]" + warnings.warn(_warn_message_, stacklevel=2) elif np.max(angles) > 2.0*np.pi or np.min(angles) < 0.0: - _warn_message_ = "Max or min of theta angles lies outside of interval [0.0, 2.0*pi]" - warnings.warn(_warn_message_) - elif isinstance(angles, float): - if angles < 0.0 or angles > 2.0*np.pi: - _warn_message_ = "Max or min of theta angles lies outside of interval [0.0, 2.0*pi]" - warnings.warn(_warn_message_) + _warn_message_ = "\nMax or min of theta angles lies outside of interval [0.0, 2.0*pi]" + warnings.warn(_warn_message_, stacklevel=2) + elif isinstance(angles, float) and angles < 0.0 or angles > 2.0*np.pi: + _warn_message_ = "\nMax or min of theta angles lies outside of interval [0.0, 2.0*pi]" + warnings.warn(_warn_message_, stacklevel=2) return angles # %% Independent functions defs. -def generate_polynomials(max_order: int = 10) -> Tuple[ZernPol]: +def generate_polynomials(max_order: int = 10) -> Tuple[ZernPol, ...]: """ Generate tuple with ZernPol instances (ultimately, representing polynomials) indexed using OSA scheme, starting with Piston(m=0,n=0). @@ -1357,14 +1343,14 @@ def generate_polynomials(max_order: int = 10) -> Tuple[ZernPol]: """ # Sanity check of max_order parameter if not isinstance(max_order, int): - __warning_mess = "The parameter max_order provided not as integer, there will be attempt to convert it to int" - warnings.warn(__warning_mess) + __warning_mess = "\nThe parameter max_order provided not as integer, there will be attempt to convert it to int" + warnings.warn(__warning_mess, stacklevel=2) max_order = int(max_order) if max_order < 0: raise ValueError("The maximum order should be not less than 0") if max_order > 30: - __warning_mess = "Calculation polynomial values with orders higher than 30 is really slow" - warnings.warn(__warning_mess) + __warning_mess = "\nCalculation polynomial values with orders higher than 30 is really slow" + warnings.warn(__warning_mess, stacklevel=2) polynomials_list = [ZernPol(m=0, n=0)] # list starting with piston for order in range(1, max_order + 1): # going through all specified orders m = -order # azimuthal order @@ -1376,7 +1362,7 @@ def generate_polynomials(max_order: int = 10) -> Tuple[ZernPol]: def generate_random_phases(max_order: int = 4, img_width: int = 513, img_height: int = 513, - round_digits: int = 4) -> Tuple[np.ndarray, np.ndarray, Tuple[ZernPol]]: + round_digits: int = 4) -> Tuple[np.ndarray, np.ndarray, Tuple[ZernPol, ...]]: """ Generate phases image (profile) for random set of polynomials with randomly selected amplitudes. @@ -1437,8 +1423,7 @@ def generate_random_phases(max_order: int = 4, img_width: int = 513, img_height: for j in range(img_width): euclidean_dist = np.linalg.norm(center - np.asarray([i, j])) if euclidean_dist <= img_radius: - r[j] = euclidean_dist / img_radius - theta[j] = np.arctan2(row_center - i, j - cols_center) + r[j] = euclidean_dist / img_radius; theta[j] = np.arctan2(row_center - i, j - cols_center) if theta[j] < 0.0: theta[j] += 2.0*np.pi # Speed up calculations by using vectors (r, theta) as the input parameters @@ -1449,13 +1434,11 @@ def generate_random_phases(max_order: int = 4, img_width: int = 513, img_height: euclidean_dist = np.linalg.norm(center - np.asarray([i, j])) if euclidean_dist > img_radius: phases_image[i, j] = 0.0 - # Final conversion - polynomials_list = tuple(polynomials_list) - return phases_image, polynomials_amplitudes, polynomials_list + return phases_image, polynomials_amplitudes, tuple(polynomials_list) -def generate_phases_image(polynomials: tuple = (), polynomials_amplitudes: tuple = (), - img_width: int = 513, img_height: int = 513) -> np.ndarray: +def generate_phases_image(polynomials: tuple = (), polynomials_amplitudes: tuple = (), img_width: int = 513, + img_height: int = 513) -> np.ndarray: """ Generate phases image (profile) for provided set of polynomials with provided coefficients (amplitudes). @@ -1488,8 +1471,7 @@ def generate_phases_image(polynomials: tuple = (), polynomials_amplitudes: tuple for j in range(img_width): euclidean_dist = np.linalg.norm(center - np.asarray([i, j])) if euclidean_dist <= img_radius: - r[j] = euclidean_dist / img_radius - theta[j] = np.arctan2(row_center - i, j - cols_center) + r[j] = euclidean_dist / img_radius; theta[j] = np.arctan2(row_center - i, j - cols_center) if theta[j] < 0.0: theta[j] += 2.0*np.pi phases_image[i, :] = ZernPol.sum_zernikes(coefficients=list(polynomials_amplitudes), polynomials=list(polynomials), r=r, theta=theta) @@ -1542,16 +1524,13 @@ def fit_polynomials(phases_image: np.ndarray, polynomials: tuple, crop_radius: f if it is False, the following tuple will be returned: zernike_coefficients, None - 1st with the same meaning and type as explained before. """ - zernike_coefficients = np.zeros(shape=(len(polynomials), )) + zernike_coefficients = np.zeros(shape=(len(polynomials), )); cropped_image = None logic_mask, cropped_phases_coordinates = crop_phases_img(phases_image, crop_radius, suppress_warnings, strict_circle_border) if return_cropped_image: cropped_image = logic_mask*phases_image # for debugging zernike_coefficients = fit_zernikes(cropped_phases_coordinates, polynomials) zernike_coefficients = np.round(zernike_coefficients, round_digits) - if return_cropped_image: - return zernike_coefficients, cropped_image - else: - return zernike_coefficients, None + return zernike_coefficients, cropped_image def fit_polynomials_vectors(polynomials: tuple, phases_vector: np.ndarray, radii_vector: np.ndarray, @@ -1589,260 +1568,10 @@ def fit_polynomials_vectors(polynomials: tuple, phases_vector: np.ndarray, radii # Checking input data consistency if len(phases_vector.shape) > 1 or len(radii_vector.shape) > 1 or len(thetas_vector.shape) > 1: raise TypeError("Some of provided vector is not 1D, check the call len(...shape)") - # Call to fitting procedure zernike_coefficients = fit_zernikes((phases_vector, radii_vector, thetas_vector), polynomials) zernike_coefficients = np.round(zernike_coefficients, round_digits) return zernike_coefficients -def compare_performances(min_order: int, max_order: int) -> Tuple[int, int, str]: - """ - Compare performances of radial polynomials calculation by using recursive and exact equations. - - Comparison achieved by simple measuring of time in msec needed for calculation of all radial - polynomials from minimal radial order up to maximum radial order returned as tuple. - - Parameters - ---------- - min_order : int - Minimum radial order of used polynomials (n). - max_order : int - Maximum radial order of used polynomials (n). - - Returns - ------- - tuple - Composed by time for recursive calculation and time for exact calculation. - - """ - # Generation of orders in OSA/ANSI indexing scheme for initializing Zernike polynomials - zernpols = [] - for order in range(min_order, max_order+1): - m = -order; n = order - zernpols.append(ZernPol(m=m, n=n)) - for n_azimuthals in range(0, order): - m += 2 - zernpols.append(ZernPol(m=m, n=n)) - # Generation numpy array with radii - n_points = 251 - test_r = np.zeros(shape=(n_points, )) - for i in range(n_points): - test_r[i] = i/(n_points-1) - test_r = np.round(test_r, 6) - # Measuring performance of radial polynomials calculations using recursive implementation - t1 = time.perf_counter() - for i, polynomial in enumerate(zernpols): - polynomial.radial(test_r) # calculate radial polynomials over vector of radii - t2 = time.perf_counter() - t_recursive_ms = round(1000*(t2-t1), 3) - # Measuring performance of radial polynomials calculations using exact implementation - t1 = time.perf_counter() - for i, polynomial in enumerate(zernpols): - polynomial.radial(test_r, use_exact_eq=True) # calculate radial polynomials over vector of radii - t2 = time.perf_counter() - t_exact_ms = round(1000*(t2-t1), 3) - return t_recursive_ms, t_exact_ms, f"Used polynomials: {i}", f"Radii: {n_points}" - - -def _estimate_high_order_calc_times(): - """ - Estimate slowing down of radial polynomial calculation with increasing of radial order. - - Returns - ------- - None. - - """ - r = 0.55 - high_order_pols = [ZernPol(m=-2, n=46), ZernPol(m=1, n=47), ZernPol(m=2, n=48), ZernPol(m=-1, n=49), - ZernPol(m=2, n=50), ZernPol(m=1, n=51), ZernPol(m=-2, n=52)] - times = [] - # Single polynomials values - for pol in high_order_pols: - # calculate radial polynomials over vector of radii - t1 = time.perf_counter(); pol.radial(r); t2 = time.perf_counter() - times.append(f"{pol.get_mn_orders()}: {int(round(1000*(t2-t1), 0))} ms") - # Delete polynomials with too high orders for derivatives calculates - high_order_pols.pop(len(high_order_pols)-1); high_order_pols.pop(len(high_order_pols)-1) - high_order_pols.pop(len(high_order_pols)-1) - print(times); times = [] - # Single derivative polynomials values - for pol in high_order_pols: - # calculate derivatives of radial polynomials over vector of radii - t1 = time.perf_counter(); pol.radial_dr(r); t2 = time.perf_counter() - times.append(f"Deriv. {pol.get_mn_orders()}: {int(round(1000*(t2-t1), 0))} ms") - print(times) - - -# %% Test functions for the external call -def check_conformity(): - """ - Test initialization parameters and transform between indices consistency. - - Returns - ------- - None. - - """ - zp = ZernPol(m=-2, n=2) # Initialization with orders - (m1, n1), osa_i, noll_i, fringe_i = zp.get_indices() - assert (osa_i == 3 and noll_i == 5 and fringe_i == 6), (f"Check consistency of Z{(m1, n1)} indices: " - + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") - zp = ZernPol(l=-3, n=5) - (m2, n2), osa_i, noll_i, fringe_i = zp.get_indices() - assert (osa_i == 16 and noll_i == 19 and fringe_i == 20), (f"Check consistency of Z{(m2, n2)} indices: " - + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") - assert len(zp.get_polynomial_name(short=True)) > 0, f"Short name for Z{(m2, n2)} is zero length" - zp = ZernPol(azimuthal_order=-1, radial_order=5) - (m3, n3), osa_i, noll_i, fringe_i = zp.get_indices() - assert (osa_i == 17 and noll_i == 17 and fringe_i == 15), (f"Check consistency of Z{(m3, n3)} indices: " - + f"OSA: {osa_i}, Noll: {noll_i}, Fringe: {fringe_i}") - assert len(zp.get_polynomial_name()) > 0, f"Name for Z{(m3, n3)} is zero length" - m4, n4 = zp.get_mn_orders() - assert m4 == m3 and n3 == n4, f"Check method get_mn_orders() for Z{(m3, n3)}" - print(f"Initialization of polynomials Z{(m1, n1)}, Z{(m2, n2)}, Z{(m3, n3)} tested") - osa_i = 12; zp = ZernPol(osa_index=osa_i) # Initialization with OSA index - m, n = zp.get_mn_orders() - assert (m == 0 and n == 4), f"Check consistency of Z[OSA index = {osa_i}] orders {m, n}" - assert zp.get_fringe_index(m, n) == 9, f"Check consistency of Z[OSA index = {osa_i}] Fringe index" - assert zp.get_noll_index(m, n) == 11, f"Check consistency of Z[OSA index = {osa_i}] Noll index" - print(f"Initialization of polynomial Z[OSA index = {osa_i}] tested") - noll_i = 10 # Testing static methods - assert ZernPol.noll2osa(noll_i) == 9, f"Check consistency of Noll index {noll_i} conversion to OSA index" - assert ZernPol.osa2fringe(ZernPol.noll2osa(noll_i)) == 10, ("Check consistency of Noll " - + f"index {noll_i} conversion to OSA index") - print(f"Conversion of Noll index {noll_i} to OSA and Fringe indices tested") - # Test for not proper initialization - try: - m_f = 2; n_f = -2 - zp = ZernPol(m=m_f, n=n_f) - asserting_value = False - except ValueError: - print(f"Polynomial Z{(m_f, n_f)} haven't been initialized, test passed") - asserting_value = True - assert asserting_value, f"Polynomial Z{(m_f, n_f)} initialized with wrong orders assignment" - # Testing input parameters for calculation - zp = ZernPol(m=0, n=2); r = 0.0; theta = math.pi - assert abs(zp.polynomial_value(r, theta) + math.sqrt(3)) < 1E-6, f"Check value of Z[{m}, {n}]({r}, {theta})" - zp = ZernPol(m=-1, n=1); r = 0.5; theta = math.pi/2 - assert abs(zp.polynomial_value(r, theta) - 1.0) < 1E-6, f"Check value of Z[{m}, {n}]({r}, {theta})" - print("Simple values of Zernike polynomials tested successfully") - try: - r = 'd'; theta = [1, 2] - zp.polynomial_value(r, theta) - asserting_value = False - except ValueError: - print("Input as string is not allowed for calculation of polynomial value, tested successfully") - asserting_value = True - assert asserting_value, "Wrong parameter passed (string) for calculation of polynomial value" - try: - r = [0.1, 0.2, 1.0+1E-9]; theta = math.pi - zp.polynomial_value(r, theta) - asserting_value = False - except ValueError: - print("Radius more than 1.0 is not allowed, tested successfully") - asserting_value = True - assert asserting_value, "Wrong parameter passed (r > 1.0) for calculation of polynomial value" - # Compare two implementations of Zernike pol-s sum calculation: direct and using meshgrid - pols = [ZernPol(osa=2), ZernPol(osa=4), ZernPol(osa=7), ZernPol(osa=10), ZernPol(osa=15), - ZernPol(osa=3), ZernPol(osa=9), ZernPol(osa=12), ZernPol(osa=16), ZernPol(osa=19)] - ampls = [-0.85, 0.85, 0.24, -0.37, 1.0, 0.1, -1.0, -0.05, 1.1, 0.41] - radii = np.arange(start=0.0, stop=1.0 + 0.001, step=0.001) - thetas = np.arange(start=0.0, stop=2.0*np.pi + np.pi/180, step=np.pi/180) - t1 = time.perf_counter(); ZernPol.sum_zernikes(ampls, pols, radii, thetas, get_surface=True) - t_direct = int(round(1000*(time.perf_counter() - t1), 0)); t1 = time.perf_counter() - ZernPol._sum_zernikes_meshgrid(ampls, pols, radii, thetas); t_meshgr = int(round(1000*(time.perf_counter() - t1), 0)) - print(f"Diff. calc. time b/t direct ({t_direct} ms) and meshgrid ({t_meshgr} ms) sums: {t_direct - t_meshgr} ms") - print("ALL TEST PASSED") - - -# %% Define default export classes and methods used with import * statement (import * from zernikepol) -__all__ = ['ZernPol', 'fit_polynomials_vectors', 'fit_polynomials', 'generate_phases_image', - 'generate_random_phases', 'generate_polynomials'] - -# %% Tests -if __name__ == "__main__": - _test_plots = False # regulates testing of plotting various plots - _test_calculations = False # regulates tests below concerning calculations - check_conformity() # testing initialization - - # Testing plotting, the plots will be opened in the additional pop-up windows - if _test_plots: - plt.close("all") # close all previously opened plots - t1 = time.perf_counter(); zp = ZernPol(m=0, n=2); ZernPol.plot_profile(zp, color_map="jet", show_title=True) # basic plot - t2 = time.perf_counter(); print("Plotting of 1 non-zero polynomial takes ms: ", int(round(1000*(t2-t1), 0))) - coordinates = ZernPol.gen_polar_coordinates(r_step=0.005) - zp = ZernPol(m=-10, n=30); ZernPol.plot_profile(zp, color_map="jet", show_title=False, polar_coordinates=coordinates) # high order plot - zp = ZernPol(m=0, n=0); ZernPol.plot_profile(zp, color_map="turbo", show_title=True) # plot of piston polynomial - - # Testing 3D surface plotting - ZernPol.plot_profile(ZernPol(m=0, n=2), color_map="viridis", projection="3d") - - # Testing 3D figure plotting on the externally initialized Figure class - fig3d = plt.figure(figsize=(6.8, 6.8)) - zern_surface = ZernPol.gen_zernikes_surface([1.0], [ZernPol(m=0, n=2)], equal_n_coordinates=True, n_points=400) - ZernPol.plot_sum_zernikes_on_fig(figure=fig3d, use_defaults=False, zernikes_sum_surface=zern_surface, - show_range=True, color_map="magma", projection="3D") - fig3d2 = plt.figure(figsize=(5.8, 5.8)) - ZernPol.plot_sum_zernikes_on_fig(figure=fig3d2, coefficients=[1.0], polynomials=[ZernPol(m=0, n=2)], - show_range=True, color_map="bwr", projection="3D") - - # Testing accelerated plotting / sum calculation - fig3 = plt.figure(figsize=(3, 3)) - t1 = time.perf_counter(); n_pols = 31; polynomials = []; coefficients = [0.0]*n_pols - for i in range(n_pols): - polynomials.append(ZernPol(osa=58+i)) - coefficients[0] = 1.0 # only 1st polynomial will be plotted - fig3 = ZernPol.plot_sum_zernikes_on_fig(figure=fig3, coefficients=coefficients, polynomials=polynomials, - show_range=False, color_map="turbo") - fig3.subplots_adjust(0, 0, 1, 1) - t2 = time.perf_counter(); print("Plotting of 1 non-zero and 30 zero pol-s takes ms: ", int(round(1000*(t2-t1), 0))) - - # Tests with generation / restoring Zernike profiles (phases images) - phases_image, polynomials_ampls, polynomials = generate_random_phases(img_height=301, img_width=321) - plt.figure(); plt.axis("off"); plt.imshow(phases_image, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) - polynomials_amplitudes, cropped_img = fit_polynomials(phases_image, polynomials, return_cropped_image=True, - strict_circle_border=False, crop_radius=1.0) - plt.figure(); plt.axis("off"); plt.imshow(cropped_img, cmap="jet") - plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) - - # Updated test of fitting including piston polynomial - height = 500; width = 481; crop_r = 1.0; strict_border = True; pols_coeffs = [-0.75, 0.86, 0.41]; fig4 = plt.figure(figsize=(4, 4)) - polynomials = [ZernPol(osa=0), ZernPol(m=0, n=2), ZernPol(m=-3, n=3)]; rs, angles = ZernPol.gen_polar_coordinates() - phase_profile = ZernPol.sum_zernikes(coefficients=pols_coeffs, polynomials=polynomials, r=rs, theta=angles, get_surface=True) - # Below - plotting specified polynomials on the polar coordinates - ZernPol.plot_sum_zernikes_on_fig(figure=fig4, use_defaults=False, zernikes_sum_surface=zernikes_surface(phase_profile, rs, angles), - color_map="jet") - # Below - generate phases image with the cartesian coordinates - phases_image2 = generate_phases_image(polynomials=tuple(polynomials), polynomials_amplitudes=tuple(pols_coeffs), - img_height=height, img_width=width) - plt.figure(); plt.axis("off"); im = plt.imshow(phases_image2, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) - plt.colorbar(mappable=im) - # Below - fitting procedure on the provided phases image - polynomials_amplitudes2, cropped_img2 = fit_polynomials(phases_image2, polynomials, return_cropped_image=True, - strict_circle_border=strict_border, crop_radius=crop_r) - print("Difference between used amplitudes and fitted ones:", np.asarray(pols_coeffs) - polynomials_amplitudes2) - plt.figure(); plt.axis("off"); im = plt.imshow(cropped_img2, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) - plt.colorbar(mappable=im) - - plt.show() # show all images created by plt.figure() calls - - # Testing calculations and their performance comparison - if _test_calculations: - # Simple test of two concepts of calculations - exact and recursive equations - z = ZernPol(n=30, m=-2); print("Diff. between recursive and exact equations:", - round(z.radial(0.85) - z.radial(0.85, use_exact_eq=True), 9)) - z = ZernPol(n=32, l=0); print("Diff. between recursive and exact equations:", - round(z.radial(0.35) - z.radial(0.35, use_exact_eq=True), 9)) - r = 0.955; theta = np.pi/8; z = ZernPol(osa=55) - print("Diff. between recursive and exact equations:", - round(z.polynomial_value(r, theta) - z.polynomial_value(r, theta, use_exact_eq=True), 9)) - z = ZernPol(n=35, l=-1); print("Diff. between recursive & exact eq-s for derivatives:", - round(z.radial_dr(0.78) - z.radial_dr(0.78, use_exact_eq=True), 9)) - z = ZernPol(n=38, m=-2); print("Diff. between recursive & exact eq-s for derivatives:", - round(z.radial_dr(0.9) - z.radial_dr(0.9, use_exact_eq=True), 9)) - # Compare performances - print("Tabular (10th order) / exact calc. times:", compare_performances(1, 10)) - print("Recursive / exact calc. times for high orders:", compare_performances(12, 40)) - # Statement below producing expected warnings, it's used for performance estimation - _estimate_high_order_calc_times() +# %% Define exported class and functions +__all__ = ['ZernPol', 'fit_polynomials_vectors', 'fit_polynomials', 'generate_phases_image', 'generate_random_phases', 'generate_polynomials'] diff --git a/src/zernpy/zernpsf.py b/src/zernpy/zernpsf.py index d6b5071..b557d76 100644 --- a/src/zernpy/zernpsf.py +++ b/src/zernpy/zernpsf.py @@ -2,18 +2,19 @@ """ PSF class definition based on Zernike polynomial for computation of its kernel for convolution / deconvolution. -@author: Sergei Klykov, @year: 2025, @licence: MIT \n +@author: Sergei Klykov, @year: 2025, @license: MIT \n """ # %% Global imports -import numpy as np -from pathlib import Path -import warnings -import matplotlib.pyplot as plt -from math import pi import time -from typing import Union, Sequence +import warnings from importlib.metadata import version +from math import pi +from pathlib import Path +from typing import Optional, Sequence, Tuple, Union + +import matplotlib.pyplot as plt +import numpy as np # Check if numba library installed for importing compilable methods numba_installed = False # default value for checking if 'numba' library is installed @@ -25,26 +26,23 @@ pass # %% Local (package-scoped) imports -if __name__ == "__main__" or __name__ == Path(__file__).stem or __name__ == "__mp_main__": - from calculations.calc_psfs import (get_psf_kernel, lambda_char, radial_integral_s, radial_integral, get_kernel_size, - convolute_img_psf, get_bumped_circle, save_psf, read_psf, get_psf_kernel_zerns) - from zernikepol import ZernPol - from utils.intmproc import DispenserManager - if numba_installed: - from calculations.calc_psfs_numba import get_psf_kernel_comp, methods_compiled, set_methods_compiled - num_methods_compiled = methods_compiled - else: - methods_compiled = False -else: - from .calculations.calc_psfs import (get_psf_kernel, lambda_char, radial_integral_s, radial_integral, get_kernel_size, - convolute_img_psf, get_bumped_circle, save_psf, read_psf, get_psf_kernel_zerns) - from .zernikepol import ZernPol - from .utils.intmproc import DispenserManager - if numba_installed: - from .calculations.calc_psfs_numba import get_psf_kernel_comp, methods_compiled, set_methods_compiled - num_methods_compiled = methods_compiled - else: - methods_compiled = False +from .calculations.calc_psfs import ( + convolute_img_psf, + get_bumped_circle, + get_kernel_size, + get_psf_kernel, + get_psf_kernel_zerns, + lambda_char, + radial_integral, + radial_integral_s, + read_psf, + save_psf, +) +from .utils.intmproc import DispenserManager +from .zernikepol import ZernPol + +if numba_installed: + from .calculations.calc_psfs_numba import get_psf_kernel_comp # %% Module parameters __docformat__ = "numpydoc" @@ -72,19 +70,18 @@ class ZernPSF: # Class predefined values along with their types for providing reference how the default values computed kernel: np.ndarray = np.ones(shape=(1, 1)); kernel_size: int = 1 # by default, single point as the 2D matrix [[1.0]] NA: float = 1.0; wavelength: float = 0.532; expansion_coeff: float = 0.5 # in um (or other physical unit) - zernpol: ZernPol = ZernPol(m=0, n=0) # by default, Piston as the zero case (Airy pattern) - polynomials = () # empty tuple - holder for provided Sequence with instances of ZernPol + zernpol: Optional[ZernPol] = None; polynomials: tuple = () # several provided polynomials will be stored in the last var. __physical_props_set: bool = False # flag for saving that physical properties have been provided __warn_message: str = ""; pixel_size_nyquist: float = 0.5*0.5*wavelength # based on the Abbe limit pixel_size_nyquist_eStr = "{:.3e}".format(pixel_size_nyquist) pixel_size = 0.98*pixel_size_nyquist # default value based on the limit above alpha: float = expansion_coeff / wavelength # the role of amplitude for PSF calculation airy: bool = False # flag if the Piston is provided as the Zernike polynomial - __ParallelCalc: DispenserManager = None; __integration_params: list = [] # for speeding up the calculations using several Processes + __ParallelCalc: Optional[DispenserManager] = None; __integration_params: list = [] # for speeding up the calculations using Processes n_int_r_points: int = 320; n_int_phi_points: int = 300 # integration parameters on the unit radius and angle - polar coordinates k: float = 2.0*pi/wavelength # angular frequency json_file_path: str = "" # shifted to the __init__ method to prevent putting path to API doc (by pydoc) - coefficients: np.ndarray = None; amplitudes: np.ndarray = None # for storing amplitudes of polynomials + coefficients: Optional[np.ndarray] = None; amplitudes: Optional[np.ndarray] = None # for storing amplitudes of polynomials # Dev. Note: always carefully check the definition of variables above, since the error in their definition may cause hard traceable bug def __init__(self, zernpol: Union[ZernPol, Sequence[ZernPol]]): @@ -110,13 +107,13 @@ def __init__(self, zernpol: Union[ZernPol, Sequence[ZernPol]]): """ self.json_file_path = str(Path(__file__).parent.absolute()) # initialize default path as the root folder containing the script - if not hasattr(zernpol, '__len__') and isinstance(zernpol, ZernPol): + if isinstance(zernpol, ZernPol): self.zernpol = zernpol; m, n = self.zernpol.get_mn_orders() if m == 0 and n == 0: self.airy = True else: self.airy = False - elif hasattr(zernpol, '__len__'): + else: seq_length = len(zernpol) # Empty sequence as the input not acceptable if seq_length == 0: @@ -140,15 +137,13 @@ def __init__(self, zernpol: Union[ZernPol, Sequence[ZernPol]]): if m == 0 and n == 0: self.airy = True # check if Airy pattern is among provided polynomials if all_are_polls: - self.polynomials = zernpol; self.zernpol = None + self.polynomials = tuple(zernpol); self.zernpol = None unique_osa_orders = set(osa_orders) # check that all OSA orders are unique if len(osa_orders) > len(unique_osa_orders): raise ValueError("There might be some repeated polynomials provided, " + f"# of provided: {len(osa_orders)} and # of unique: {len(unique_osa_orders)}") else: raise ValueError("Not all objects in Sequence are instances of the 'ZernPol' class") - else: - ValueError("ZernPSF class requires single 'ZernPol' instance or Sequence (class with __len__ attr.) with 'ZernPol' instances") # %% Set properties def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Union[float, Sequence[float]], pixel_physical_size: float): @@ -195,6 +190,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio raise ValueError("Wavelength should be positive real number") self.k = 2.0*pi/self.wavelength # Calculate angular frequency (k) self.NA = NA; self.wavelength = wavelength # save as the class properties + self.amplitudes: np.ndarray # set explicitly expected data type # Sanity check of provided wavelength, pixel physical size (Nyquist criteria) self.pixel_size_nyquist = 0.5*0.5*wavelength/NA # based on half of the Abbe resolution limit, see references in the docstring self.pixel_size_nyquist_eStr = "{:.3e}".format(self.pixel_size_nyquist) # formatting calculated pixel size in scientific notation @@ -205,7 +201,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio + f" computed from the Abbe's resolution limit (0.5*{lambda_char}/NA)") self.pixel_size = pixel_physical_size # Check which type is provided as the expansion_coeff parameter - if hasattr(expansion_coeff, '__len__'): + if not isinstance(expansion_coeff, float): coeffs_len = len(expansion_coeff) # for checking how many amplitudes provided if coeffs_len != len(self.polynomials): if coeffs_len == 1 and len(self.polynomials) == 0: # polynomials maybe provided also as a sequence with 1 element @@ -213,7 +209,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio # Sanity check for the expansion coefficient of the polynomial self.__warn_message = _sanity_check_expansion_coefficient(abs(expansion_coeff) / wavelength) if len(self.__warn_message) > 0: - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" self.expansion_coeff = expansion_coeff; self.alpha = self.expansion_coeff / self.wavelength else: raise ValueError(f"Length of provided coefficients ({coeffs_len}) is not equal to stored number " @@ -224,7 +220,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio max_module_coeff = max(np.max(self.coefficients), abs(np.min(self.coefficients))) self.__warn_message = _sanity_check_expansion_coefficient(abs(max_module_coeff) / wavelength, max_coeff_check=True) if len(self.__warn_message) > 0: - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" self.amplitudes = self.coefficients / self.wavelength else: # Check consistency of provided type of polynomials and coefficients @@ -237,7 +233,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio # Sanity check for the expansion coefficient of the polynomial self.__warn_message = _sanity_check_expansion_coefficient(abs(expansion_coeff) / wavelength) if len(self.__warn_message) > 0: - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" self.expansion_coeff = expansion_coeff; self.alpha = self.expansion_coeff / self.wavelength # Kernel size estimation (could be changed explicitly in the method 'set_calculation_props'). Redefine it for each call if self.zernpol is not None: # for single polynomial @@ -265,7 +261,7 @@ def set_physical_props(self, NA: float, wavelength: float, expansion_coeff: Unio self.kernel_size += 1 # kernel size should odd self.__physical_props_set = True # set internal flag True if no ValueError raised - def set_calculation_props(self, kernel_size: int, n_integration_points_r: int, n_integration_points_phi: int) -> None: + def set_calculation_props(self, kernel_size: int, n_integration_points_r: int, n_integration_points_phi: int): """ Set calculation properties: kernel size, number of integration points on polar coordinates. @@ -301,12 +297,12 @@ def set_calculation_props(self, kernel_size: int, n_integration_points_r: int, n kernel_size += 1; print("Note that kernel_size should be odd integer for centering PSF kernel") if self.__physical_props_set: if kernel_size < self.kernel_size: - self.__warn_message = (f"Empirically estimated kernel size = {self.kernel_size} based on the physical properties " + self.__warn_message = (f"\nEmpirically estimated kernel size = {self.kernel_size} based on the physical properties " + f"is larger than provided size = {kernel_size}. PSF may be truncated.") - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" else: - self.__warn_message = "Please set the physical properties first for estimation of kernel size and after call this method" - warnings.warn(self.__warn_message); self.__warn_message = "" + self.__warn_message = "\nPlease set the physical properties first for estimation of kernel size and after call this method" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" self.kernel_size = kernel_size # overwrite stored property, show before all warnings if kernel size is inconsistent # Sanity checks for n_integration_points_r and n_integration_points_phi if n_integration_points_r < 20: @@ -317,13 +313,13 @@ def set_calculation_props(self, kernel_size: int, n_integration_points_r: int, n # Associated with slow calculations warnings if n_integration_points_r > 500 and n_integration_points_phi > 400: self.__warn_message = "Selected integration precision may be unnecessary for PSF calculation and slow down it significantly" - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" if abs(n_integration_points_phi - 300) < 40 and abs(n_integration_points_r - 320) < 50 and self.kernel_size > 25: print(f"Note that the approximate calc. time: {int(round(self.kernel_size*self.kernel_size*38.5/1000, 0))} sec.") # %% Calculation def calculate_psf_kernel(self, suppress_warnings: bool = False, normalized: bool = True, verbose_info: bool = False, - accelerated: bool = None) -> np.ndarray: + accelerated: Optional[bool] = None) -> np.ndarray: """ Calculate PSF kernel using the specified or default calculation parameters and physical values. @@ -370,10 +366,10 @@ def calculate_psf_kernel(self, suppress_warnings: bool = False, normalized: bool """ if len(self.__warn_message) > 0 and not suppress_warnings: - warnings.warn(self.__warn_message) + warnings.warn(self.__warn_message, stacklevel=2) if not self.__physical_props_set and not suppress_warnings: self.kernel_size = 19; self.__warn_message = "\nPhysical properties haven't been set before, the default ones will be used" - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" global numba_installed # access the flag # Check provided flag if numba_installed and accelerated is None: @@ -383,13 +379,13 @@ def calculate_psf_kernel(self, suppress_warnings: bool = False, normalized: bool # Check if accelerated flag set to True but no numba installed if accelerated and not numba_installed and not suppress_warnings: self.__warn_message = "\nAcceleration isn't possible because 'numba' library not installed in the current environment" - warnings.warn(self.__warn_message); self.__warn_message = "" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" # For providing performance verbose report if verbose_info: t1 = time.perf_counter() # for explicit showing of performance if self.kernel_size*self.kernel_size >= 301: print("Kernel calculation started...") - # Calculation using the vectorised form + # Calculation using the vectorized form if self.zernpol is not None: if not accelerated or (accelerated and not numba_installed): self.kernel = get_psf_kernel(zernike_pol=self.zernpol, len2pixels=self.pixel_size, alpha=self.expansion_coeff, @@ -403,6 +399,7 @@ def calculate_psf_kernel(self, suppress_warnings: bool = False, normalized: bool kernel_size=self.kernel_size, n_int_r_points=self.n_int_r_points, suppress_warns=suppress_warnings, n_int_phi_points=self.n_int_phi_points) elif len(self.polynomials) > 0: + self.amplitudes: np.ndarray # set explicitly expected data type if not accelerated or (accelerated and not numba_installed): self.kernel = get_psf_kernel_zerns(polynomials=self.polynomials, amplitudes=self.amplitudes, len2pixels=self.pixel_size, wavelength=self.wavelength, NA=self.NA, normalize_values=normalized, verbose=verbose_info, @@ -451,7 +448,8 @@ def plot_kernel(self, id_str: str = ""): fig_title = f"Composed kernel for #{len(self.polynomials)} polynomials: {orders} {id_str}" if not plt.isinteractive(): plt.ion() - plt.figure(fig_title, figsize=(6, 6)); plt.imshow(self.kernel, cmap=plt.cm.viridis, origin='upper'); plt.colorbar(); plt.tight_layout() + plt.figure(fig_title, figsize=(6, 6)); plt.imshow(self.kernel, cmap=plt.colormaps["viridis"], origin='upper') + plt.colorbar(); plt.tight_layout() # %% Utilities def convolute_img(self, image: np.ndarray, scale2original: bool = True) -> np.ndarray: @@ -461,7 +459,7 @@ def convolute_img(self, image: np.ndarray, scale2original: bool = True) -> np.nd Parameters ---------- image : numpy.ndarray - Sample image, not colour. + Sample gray-scaled (2D array) image. scale2original : bool Convolution resulting image will be rescaled to the max intensity of the provided image if True. The default is True. @@ -492,10 +490,10 @@ def visualize_convolution(self, radius: float = 4.0, max_intensity: int = 255): target_disk = get_bumped_circle(radius, max_intensity) # get the sample image of the even centered circle with blurred edges if not plt.isinteractive(): plt.ion() - plt.figure("Sample Image: Disk", figsize=(6, 6)); plt.imshow(target_disk, cmap=plt.cm.viridis, origin='upper') + plt.figure("Sample Image: Disk", figsize=(6, 6)); plt.imshow(target_disk, cmap=plt.colormaps["viridis"], origin='upper') plt.axis('off'); plt.tight_layout() convolved_img = self.convolute_img(image=target_disk); plt.figure("Convolved PSF and Disk", figsize=(6, 6)) - plt.imshow(convolved_img, cmap=plt.cm.viridis, origin='upper'); plt.axis('off'); plt.tight_layout() + plt.imshow(convolved_img, cmap=plt.colormaps["viridis"], origin='upper'); plt.axis('off'); plt.tight_layout() def crop_kernel(self, min_part_of_max: float = 0.01): """ @@ -544,7 +542,7 @@ def crop_kernel(self, min_part_of_max: float = 0.01): self.kernel_size = self.kernel.shape[0] # %% I/O methods - def save_json(self, abs_path: Union[str, Path] = None, overwrite: bool = False): + def save_json(self, abs_path: Union[str, Path, None] = None, overwrite: bool = False): """ Save class attributes (PSF kernel, physical properties, etc.) in the JSON file for further reloading and avoiding long computation. @@ -563,13 +561,14 @@ def save_json(self, abs_path: Union[str, Path] = None, overwrite: bool = False): """ if abs_path is None: abs_path = Path(self.json_file_path).joinpath("saved_psfs") # default folder for storing saved JSON files (root for the package) - if not Path.exists(abs_path): - abs_path = "" # the folder "saved_psfs" will be created in the root of the package if isinstance(abs_path, Path): - abs_path = str(abs_path) # convert to the expected string format + if not Path.exists(abs_path): + abs_path = "" # the folder "saved_psfs" will be created in the root of the package + else: + abs_path = str(abs_path) # convert to the expected string format if self.kernel_size == 1: - self.__warn_message = "Kernel most likely hasn't been calculated, the kernel size == 1 - default value" - warnings.warn(self.__warn_message); self.__warn_message = "" + self.__warn_message = "\nKernel most likely hasn't been calculated, the kernel size == 1 - default value" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" if self.zernpol is not None: # single polynomial saving self.json_file_path = save_psf(psf_kernel=self.kernel, NA=self.NA, wavelength=self.wavelength, expansion_coefficient=self.expansion_coeff, pixel_size=self.pixel_size, @@ -577,13 +576,14 @@ def save_json(self, abs_path: Union[str, Path] = None, overwrite: bool = False): n_int_points_phi=self.n_int_phi_points, zernike_pol=self.zernpol, overwrite=overwrite, folder_path=abs_path) elif len(self.polynomials) > 0: # saving several polynomials + self.coefficients: np.ndarray # set explicitly data type for mypy self.json_file_path = save_psf(psf_kernel=self.kernel, NA=self.NA, wavelength=self.wavelength, expansion_coefficient=self.coefficients, pixel_size=self.pixel_size, kernel_size=self.kernel_size, n_int_points_r=self.n_int_r_points, n_int_points_phi=self.n_int_phi_points, zernike_pol=self.polynomials, overwrite=overwrite, folder_path=abs_path) - def read_json(self, abs_path: Union[str, Path] = None): + def read_json(self, abs_path: Union[str, Path, None] = None): """ Read the JSON file with the saved attributes and setting it for the class. @@ -603,7 +603,7 @@ def read_json(self, abs_path: Union[str, Path] = None): abs_path = str(abs_path) json_data = read_psf(abs_path) # raw parsed data from a file if json_data is not None: - wavelen: float; na: float; a: float; pols: list; ps: float; read_props = 0 + wavelen: float; na: float; a: Union[float, Sequence[float]]; pols: list; ps: float; read_props = 0 for key, item in json_data.items(): # Calculation properties + calculated kernel if key == "PSF Kernel": @@ -619,10 +619,8 @@ def read_json(self, abs_path: Union[str, Path] = None): na = item; read_props += 1 elif key == "Wavelength": wavelen = item; read_props += 1 - elif key == "Expansion Coefficient": + elif key == "Expansion Coefficient" or key == "Amplitudes": a = item; read_props += 1 - elif key == "Amplitudes": - a = np.asarray(item); read_props += 1 elif key == "Pixel Size": ps = item; read_props += 1 # Getting and reassigning used polynomial(-s) @@ -639,23 +637,23 @@ def read_json(self, abs_path: Union[str, Path] = None): else: for index in osa_indices: pols.append(ZernPol(osa=index)) - self.polynomials = pols; self.zernpol = None; self.airy = False + self.polynomials = tuple(pols); self.zernpol = None; self.airy = False # Assign read physical properties if read_props == 8: self.set_physical_props(NA=na, wavelength=wavelen, expansion_coeff=a, pixel_physical_size=ps) else: - self.__warn_message = "Provided json file doesn't contain all necessary keys for physical / calculation properties" - warnings.warn(self.__warn_message); self.__warn_message = "" + self.__warn_message = "\nProvided json file doesn't contain all necessary keys for physical / calculation properties" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" else: - self.__warn_message = "Provided path doesn't contain valid JSON data" - warnings.warn(self.__warn_message); self.__warn_message = "" + self.__warn_message = "\nProvided path doesn't contain valid JSON data" + warnings.warn(self.__warn_message, stacklevel=2); self.__warn_message = "" # %% Parallelized computing methods - def initialize_parallel_workers(self): + def __initialize_parallel_workers(self): """ Initialize 4 Processes() for performing integration. - See intmproc.py script (utils module) for implementation details. + See intmproc.py script (utils module) for implementation details.\n Tests showed that this way doesn't provide performance gain. Returns @@ -668,7 +666,7 @@ def initialize_parallel_workers(self): self.__ParallelCalc = DispenserManager(compute_func=radial_integral_s, params_list=self.__integration_params, n_workers=4, verbose_info=False) - def get_psf_point_r_parallel(self, r: float, theta: float) -> float: + def __get_psf_point_r_parallel(self, r: float, theta: float) -> float: """ Parallel implementation of numerical integration. @@ -704,7 +702,7 @@ def get_psf_point_r_parallel(self, r: float, theta: float) -> float: integral_sum = (h_phi/3.0)*(yA + yB + 2.0*even_sum + 4.0*odd_sum); integral_normalization = 1.0/(pi*pi) return np.power(np.abs(integral_sum), 2)*integral_normalization - def get_kernel_parallel(self, normalize_values: bool = True) -> np.ndarray: + def __get_kernel_parallel(self, normalize_values: bool = True) -> np.ndarray: """ Parallelized implementation of PSF kernel calculation. @@ -723,7 +721,7 @@ def get_kernel_parallel(self, normalize_values: bool = True) -> np.ndarray: """ if self.kernel_size < 3 and self.zernpol is not None: self.kernel_size = get_kernel_size(zernike_pol=self.zernpol, len2pixels=self.pixel_size, alpha=self.alpha, - wavelength=self.wavelength) + wavelength=self.wavelength, NA=self.NA) if self.zernpol is None: self.kernel_size = 3 self.kernel = np.zeros(shape=(self.kernel_size, self.kernel_size)); i_center = self.kernel_size//2; j_center = self.kernel_size//2 @@ -736,7 +734,7 @@ def get_kernel_parallel(self, normalize_values: bool = True) -> np.ndarray: theta = np.arctan2((i - i_center), (j - j_center)) # The PSF also has the angular dependency, not only the radial one theta += np.pi # shift angles to the range [0, 2pi] if self.zernpol is not None: - self.kernel[i, j] = self.get_psf_point_r_parallel(r=distance, theta=theta); calculated_points += 1 + self.kernel[i, j] = self.__get_psf_point_r_parallel(r=distance, theta=theta); calculated_points += 1 # print(f"Calculated point {[i, j]} from {[self.kernel_size-1, self.kernel_size-1]}") print(f"Calculated point #{calculated_points} from {self.kernel_size*self.kernel_size}, takes ms: ", int(round(1000*(time.perf_counter() - t1), 0))) @@ -744,7 +742,7 @@ def get_kernel_parallel(self, normalize_values: bool = True) -> np.ndarray: self.kernel /= np.max(self.kernel) return self.kernel - def deinitialize_workers(self): + def __deinitialize_workers(self): """ Release initialized before Processes for performing parallel computation. @@ -786,7 +784,7 @@ def _sanity_check_expansion_coefficient(normalized_coefficient: float, max_coeff return "" -def force_get_psf_compilation(verbose_report: bool = False) -> Union[tuple, None]: +def force_get_psf_compilation(verbose_report: bool = False) -> Optional[Tuple[ZernPSF, ZernPSF]]: """ Force compilation of computing functions for round and ellipse 'precise' shaped objects. @@ -800,15 +798,14 @@ def force_get_psf_compilation(verbose_report: bool = False) -> Union[tuple, None """ if numba_installed: if verbose_report: - print("Precompilation started..."); t1 = time.perf_counter() # for explicit showing of performance + print("Precompilation of 'zernpy' started...", flush=True); t1 = time.perf_counter() # for explicit showing of performance # Check the version of numba for guarantee working of compilation calls try: - if int(numba_ver_n[0]) == 0: - if int(numba_ver_n[1]) <= 57: - if int(numba_ver_n[2]) < 1: - __warn_message = "\nRecommended numba version for compilation >= 0.57.1"; warnings.warn(__warn_message) + if int(numba_ver_n[0]) == 0 and int(numba_ver_n[1]) <= 57 and int(numba_ver_n[2]) < 1: + __warn_message = "\nRecommended numba version for compilation >= 0.57.1"; warnings.warn(__warn_message, stacklevel=2) except ValueError: - __warn_message = "\nCannot parse 'numba' version, expected in format 'x.yy.zz' - all integers"; warnings.warn(__warn_message) + __warn_message = "\nCannot parse 'numba' version, expected in format 'x.yy.zz' - all integers" + warnings.warn(__warn_message, stacklevel=2) # Compilation of methods for single polynomial PSF calculation NA = 0.2; wavelength = 0.55; pixel_size = wavelength / 0.82; ampl = 0.042 zp_prc = ZernPol(m=-1, n=1); zpsf_prc = ZernPSF(zp_prc) # Airy pattern - for compilation methods for single polynomial @@ -822,189 +819,45 @@ def force_get_psf_compilation(verbose_report: bool = False) -> Union[tuple, None zpsf_mpc.kernel_size = 3 # force to calculate only small kernel size for saving sometime # print("Precompilation kernel size for several pol.:", zpsf_mpc.kernel_size) zpsf_mpc.calculate_psf_kernel(normalized=True, accelerated=True, suppress_warnings=True, verbose_info=False) - set_methods_compiled() # setting the flag implicitly in the module - global num_methods_compiled; num_methods_compiled = True # setting copied variable in this script if verbose_report: passed_time_ms = int(round(1000.0*(time.perf_counter() - t1), 0)) if passed_time_ms > 1000: - print(f"Precompilation took: {round(passed_time_ms/1000.0, 2)} sec.") + print(f"Precompilation took: {round(passed_time_ms/1000.0, 2)} sec.", flush=True) else: - print(f"Precompilation took: {passed_time_ms} ms.") - print("--------------------------------------------") + print(f"Precompilation took: {passed_time_ms} ms.", flush=True) + print("--------------------------------------------", flush=True) return zpsf_prc, zpsf_mpc else: __warn_message = "\nAcceleration isn't possible because 'numba' library not installed in the current environment" - warnings.warn(__warn_message) + warnings.warn(__warn_message, stacklevel=2) return None +def clean_zernpy_cache() -> bool: + """ + Clean locally cached files created by numba after compilation of computation methods from the 'calc_psfs_numba' module. + + Returns + ------- + bool \n + Flag if local cache is assumed (at least 6 cached files successfully removed) to be cleaned. + + """ + _local_cache_cleaned = False # flag to show that local numba cache found and has been cleaned + if numba_installed: + root = Path(__file__).resolve().parent; cache_folder = root.joinpath("calculations").joinpath("__pycache__") + if cache_folder.exists() and cache_folder.is_dir(): + _n_cleaned = 0 + for obj in cache_folder.iterdir(): + if obj.is_file() and (obj.suffix == ".nbc" or obj.suffix == ".nbi"): + try: + obj.unlink(missing_ok=True); _n_cleaned += 1 + except (PermissionError, OSError): + _n_cleaned = 0; break # automatically breaks loop assuming that invalid permission is universal + if _n_cleaned >= 6: # 8 - minimal count of caches created by numba, assume that cache is cleaned if no error encountered + _local_cache_cleaned = True + return _local_cache_cleaned + + # %% Define default export classes and methods used with import * statement (import * from zernpsf) -__all__ = ['ZernPSF', 'force_get_psf_compilation'] - - -# %% Test as the main script -if __name__ == "__main__": - plt.close("all") # close all opened before figures - wavelength_um = 0.55 # used below in a several calls - check_other_pols = False; check_small_na_wl = False # flag for checking some other polynomials PSFs - check_airy = False; check_common_psf = False; check_io_kernel = False; check_parallel_calculation = False; check_test = False - check_faster_airy = False; check_test_conditions = False; check_test_conditions2 = False; check_several_pols = False - check_edge_conditions = False; test_acceleration_single_pol = False; test_acceleration_few_pol = False - prepare_pic_readme = False # for plotting the sum of polynomials produced profile - test_io_few_pols = False; standard_path = Path.home().joinpath("Desktop") # for saving json on the Desktop - check_acceleration_flag = False # for testing fallback calculation with the wrong flag for calculate PSF kernel - check_init_several_pols = False # check calculation several pol-s: Airy (Piston) + some of polynomial - check_airy_patterns = False # check the difference between calculated by equation for Airy pattern and diffraction integral - check_precompilation = False # checks precompilation - check_cropping = False # checks how kernel is cropped - - # Common PSF for testing - if check_common_psf: - force_get_psf_compilation(True) - zpsf1 = ZernPSF(ZernPol(m=1, n=1)); zpsf2 = ZernPSF(ZernPol(m=-3, n=3)); ampl = -0.43 - zpsf2.set_physical_props(NA=0.95, wavelength=wavelength_um, expansion_coeff=ampl, pixel_physical_size=wavelength_um/5.05) - zpsf1.set_physical_props(NA=0.5, wavelength=0.6, expansion_coeff=0.25, pixel_physical_size=wavelength_um/5.5) - zpsf2.set_calculation_props(kernel_size=zpsf2.kernel_size, n_integration_points_r=250, n_integration_points_phi=320) - zpsf1.set_calculation_props(kernel_size=zpsf2.kernel_size, n_integration_points_r=220, n_integration_points_phi=360) - kernel3 = zpsf2.calculate_psf_kernel(suppress_warnings=False, verbose_info=True); zpsf2.plot_kernel("for loop") - zpsf2.visualize_convolution() # Visualize convolution on the disk image - if check_io_kernel: - # default_path = Path(__file__).parent.joinpath("saved_psfs").absolute() # default path for storing JSON files - zpsf2.save_json(overwrite=True, abs_path=standard_path) - zpsf1.read_json(zpsf2.json_file_path) # for testing reading and assigning values to ZernPSF class (substitution) - if check_parallel_calculation: - zpsf2.initialize_parallel_workers(); kernel2 = zpsf2.get_kernel_parallel() - zpsf2.plot_kernel("parallel"); zpsf2.deinitialize_workers() - - # Another Zernike polynomial, big NA - if check_other_pols: - zpsf3 = ZernPSF(ZernPol(m=0, n=4)) - zpsf3.set_physical_props(NA=1.25, wavelength=wavelength_um, expansion_coeff=0.4, pixel_physical_size=wavelength_um/5.25) - zpsf3.calculate_psf_kernel(suppress_warnings=False, verbose_info=True); zpsf3.plot_kernel() - - # Another Zernike polynomial, average to small NA and wavelength - if check_small_na_wl: - NA = 0.45; wavelength = 0.4; pixel_size = wavelength / 5.25; ampl = 0.18 - zp2 = ZernPol(m=1, n=3); zpsf2 = ZernPSF(zp2) # horizontal coma - zpsf2.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) - zpsf2.calculate_psf_kernel(normalized=True); zpsf2.plot_kernel() - - if check_airy: - NA = 0.12; wavelength = 0.8; pixel_size = wavelength / 4.0; ampl = 1.25 - zp4 = ZernPol(m=0, n=0); zpsf4 = ZernPSF(zp4) # piston for the Airy pattern - zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) - zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel("Plus") - zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=-ampl, pixel_physical_size=pixel_size) - zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel("Minus") - - if check_faster_airy: # For set the test for pytest library - NA = 0.35; wavelength = 0.55; pixel_size = wavelength / 3.05; ampl = -0.4 - zp4 = ZernPol(m=0, n=0); zpsf4 = ZernPSF(zp4) # piston for the Airy pattern - zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) - zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel() - - if check_test_conditions: - NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 5.0; ampl = 0.55 - zp6 = ZernPol(m=0, n=2); zpsf6 = ZernPSF(zp6) # defocus - zpsf6.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) # normal assignment - zpsf6.set_calculation_props(kernel_size=zpsf6.kernel_size, n_integration_points_r=250, n_integration_points_phi=300) - zpsf6.calculate_psf_kernel(normalized=True); zpsf6.plot_kernel() - if check_test_conditions2: - zp7 = ZernPol(m=1, n=3); zpsf7 = ZernPSF(zp7) # horizontal coma - NA = 0.4; wavelength = 0.4; pixel_size = wavelength / 3.2; ampl = 0.185 # Common physical properties - zpsf7.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) - zpsf7.calculate_psf_kernel(normalized=True); zpsf7.plot_kernel() - - # Test calculation of a PSF for several polynomials and I/O operations (see flags) - if check_several_pols: - zp1 = ZernPol(m=-2, n=2); zp2 = ZernPol(m=0, n=2); zp3 = ZernPol(m=2, n=2); pols = (zp1, zp2, zp3); coeffs = (-0.36, 0.25, 0.4) - zpsf8 = ZernPSF(pols); zpsf8.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=coeffs, pixel_physical_size=0.5/4.5) - composed_kernel = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf8.plot_kernel() - if test_io_few_pols: - zpsf14 = ZernPSF(ZernPol(osa=19)); zpsf14.set_physical_props(NA=0.1, wavelength=0.4, expansion_coeff=0.82, - pixel_physical_size=0.05) - zpsf8.save_json(overwrite=True, abs_path=standard_path); zpsf14.read_json(zpsf8.json_file_path) # save / read calculated kernel - - # Test some edge conditions - e.g., specifying 1 polynomial in a list with huge coefficient - if check_edge_conditions: - zp4 = ZernPol(m=3, n=3); pols2 = [zp4]; coeff = 5.1 - zpsf9 = ZernPSF(pols2); zpsf9.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=coeff, pixel_physical_size=0.5/4.75) - zpsf9.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=(-0.67), pixel_physical_size=0.5/4.75) - zpsf9.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf9.plot_kernel() - # Test acceleration by using numba library utilities - if test_acceleration_single_pol: - force_get_psf_compilation(); NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 4.6; ampl = -0.16 - zp6 = ZernPol(m=0, n=2); zpsf6 = ZernPSF(zp6) # defocus - zpsf6.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) - kernel_acc = zpsf6.calculate_psf_kernel(normalized=True, accelerated=True, verbose_info=True); zpsf6.plot_kernel("Accelerated") - kernel_norm = zpsf6.calculate_psf_kernel(normalized=True); zpsf6.plot_kernel("Normal") - if test_acceleration_few_pol: - force_get_psf_compilation() - zp1 = ZernPol(m=-2, n=2); zp2 = ZernPol(m=0, n=2); zp3 = ZernPol(m=2, n=2); pols = (zp1, zp2, zp3); coeffs = (-0.12, 0.15, 0.1) - zpsf8 = ZernPSF(pols); zpsf8.set_physical_props(NA=0.35, wavelength=0.5, expansion_coeff=coeffs, pixel_physical_size=0.5/1.5) - composed_kernel = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf8.plot_kernel("Normal") - composed_kernel_acc = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True, accelerated=True) - zpsf8.plot_kernel("Accelerated") - if prepare_pic_readme: - force_get_psf_compilation(verbose_report=True) - zp1 = ZernPol(m=-1, n=3); zp2 = ZernPol(m=2, n=4); zp3 = ZernPol(m=0, n=4); pols = (zp1, zp2, zp3); coeffs = (0.5, 0.21, 0.15) - zpsf_pic = ZernPSF(pols); zpsf_pic.set_physical_props(NA=0.65, wavelength=0.6, expansion_coeff=coeffs, pixel_physical_size=0.6/5.0) - zpsf_pic.calculate_psf_kernel(normalized=True, verbose_info=True, accelerated=True) - zpsf_pic.plot_kernel("Vert. Coma Vert. 2nd Astigmatism Spherical") - if check_acceleration_flag: - zp16 = ZernPol(m=-1, n=3); zp18 = ZernPol(m=2, n=4); pols10 = (zp16, zp18); coeffs10 = (-0.1, 0.13); zpsf_acc = ZernPSF(pols10) - zpsf_norm = ZernPSF(pols10); zpsf_acc.set_physical_props(NA=0.43, wavelength=0.6, expansion_coeff=coeffs10, - pixel_physical_size=0.6/3.0) - zpsf_norm.set_physical_props(NA=0.43, wavelength=0.6, expansion_coeff=coeffs10, pixel_physical_size=0.6/3.0) - kern_acc = zpsf_acc.calculate_psf_kernel(normalized=True, accelerated=True) - kern_norm = zpsf_norm.calculate_psf_kernel(normalized=True) - kern_diff = np.round(kern_acc - kern_norm, 9) # for checking the difference in calculations - - if check_test: - pols = (ZernPol(osa=10), ZernPol(osa=15)); coeffs = (0.28, -0.33); NA = 0.35; wavelength = 0.55 - zpsf = ZernPSF(pols); zpsf.set_physical_props(NA, wavelength, expansion_coeff=coeffs, pixel_physical_size=wavelength / 3.5) - zpsf.set_calculation_props(kernel_size=25, n_integration_points_r=200, n_integration_points_phi=180) - psf_kernel = zpsf.calculate_psf_kernel(normalized=False); zpsf.plot_kernel() - - if check_init_several_pols: - force_get_psf_compilation(True) - zpsf30 = ZernPSF(zernpol=(ZernPol(osa=1), ZernPol(osa=5))) - try: - zpsf30.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=0.5, pixel_physical_size=0.5/5.0) - except ValueError: - print("Check for 1 ampl. and 2 pol-s passed") # as expected, transfer to test function - zpsf31 = ZernPSF(zernpol=(ZernPol(osa=0), ZernPol(m=-1, n=3))) - zpsf31.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=[1.5, 0.24], pixel_physical_size=0.5/3.8) - # zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=False); zpsf31.plot_kernel("Not accelerated 2 pol-s") - # kernel_not_acc = np.copy(zpsf31.kernel) - zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=True); zpsf31.plot_kernel("Airy 1.5") - kernel_acc = np.copy(zpsf31.kernel) - # zpsf31.kernel = np.abs(kernel_acc - kernel_not_acc); zpsf31.plot_kernel("Diff. 2 pol-s") - zpsf31.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=[-1.5, 0.24], pixel_physical_size=0.5/3.8) - zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=True); zpsf31.plot_kernel("Airy -1.5") - kernel_neg_acc = np.copy(zpsf31.kernel) - zpsf31.kernel = np.abs(kernel_acc - kernel_neg_acc); zpsf31.plot_kernel("Diff. neg. pos. Airy + Coma") - - if check_airy_patterns: - force_get_psf_compilation(verbose_report=True) - zpsf40 = ZernPSF(zernpol=ZernPol(osa=0)) - zpsf40.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=3.0, pixel_physical_size=0.5/4.0) - zpsf40.calculate_psf_kernel(verbose_info=True, accelerated=False, normalized=False); zpsf40.plot_kernel("Not accelerated Airy") - kernel_not_acc = np.copy(zpsf40.kernel) - zpsf40.calculate_psf_kernel(verbose_info=True, accelerated=True, normalized=False); zpsf40.plot_kernel("Accelerated Airy") - kernel_acc = np.copy(zpsf40.kernel) - zpsf40.kernel = np.abs(kernel_acc - kernel_not_acc); zpsf40.plot_kernel("Diff. Airy") - - if check_precompilation: - force_get_psf_compilation(True) - zpsf50 = ZernPSF(zernpol=(ZernPol(m=1, n=3))) - zpsf50.set_physical_props(NA=1.25, wavelength=0.52, expansion_coeff=0.5, pixel_physical_size=0.5/4.85) - zpsf50.calculate_psf_kernel(verbose_info=True, accelerated=True, normalized=True); zpsf50.plot_kernel() - - if check_cropping: - zpsf60 = ZernPSF(zernpol=(ZernPol(m=0, n=4))) - zpsf60.set_physical_props(NA=1.25, wavelength=0.5, expansion_coeff=0.47, pixel_physical_size=0.5/5.0) - zpsf60.calculate_psf_kernel(accelerated=True, verbose_info=True); zpsf60.plot_kernel("Not Cropped") - original_kernel = np.copy(zpsf60.kernel) - zpsf60.crop_kernel(min_part_of_max=0.025); zpsf60.plot_kernel("Cropped"); cropped_kernel = np.copy(zpsf60.kernel) - print("Original kernel shape:", original_kernel.shape, "\nCropped kernel shape:", cropped_kernel.shape) +__all__ = ['ZernPSF', 'force_get_psf_compilation', 'clean_zernpy_cache'] diff --git a/tests/run_zernikepol_as_main.py b/tests/run_zernikepol_as_main.py new file mode 100644 index 0000000..95a52d5 --- /dev/null +++ b/tests/run_zernikepol_as_main.py @@ -0,0 +1,194 @@ +# -*- coding: utf-8 -*- +""" +Run a few methods from 'zernikepol' as the main one for performing tests in IDE. + +@author: Sergei Klykov, '@sklykov' on GitHub + +@licence: MIT, @year: 2026 + +""" +# %% Imports and checking its validity +import importlib +import time +from contextlib import suppress +from typing import Tuple + +import matplotlib +import numpy as np + +# Explicit backend assignment for matplotlib - for compatibility between running configurations in Spyder and PyCharm IDEs +with suppress(ImportError): # will be thrown in the environment doesn't contain Qt-like library + matplotlib.use('Qt5Agg') +import matplotlib.pyplot as plt + +# Import of developed version of package, install in the editable mode: pip install -e . +import zernpy.zernikepol + +importlib.reload(zernpy.zernikepol) # trick to guarantee local changes to be always used for run +from zernpy.zernikepol import ZernPol, fit_polynomials, generate_phases_image, generate_random_phases, zernikes_surface + + +# %% Test functions for the external call +def compare_performances(min_order: int, max_order: int) -> Tuple[int, int, str]: + """ + Compare performances of radial polynomials calculation by using recursive and exact equations. + + Comparison achieved by simple measuring of time in msec needed for calculation of all radial + polynomials from minimal radial order up to maximum radial order returned as tuple. + + Parameters + ---------- + min_order : int + Minimum radial order of used polynomials (n). + max_order : int + Maximum radial order of used polynomials (n). + + Returns + ------- + tuple + Composed by time for recursive calculation and time for exact calculation. + + """ + # Generation of orders in OSA/ANSI indexing scheme for initializing Zernike polynomials + zernpols = [] + for order in range(min_order, max_order+1): + m = -order; n = order + zernpols.append(ZernPol(m=m, n=n)) + for _ in range(0, order): + m += 2; zernpols.append(ZernPol(m=m, n=n)) + # Generation numpy array with radii + n_points = 251 + test_r = np.zeros(shape=(n_points, )) + for i in range(n_points): + test_r[i] = i/(n_points-1) + test_r = np.round(test_r, 6) + # Measuring performance of radial polynomials calculations using recursive implementation + t1 = time.perf_counter() + for polynomial in zernpols: + polynomial.radial(test_r) # calculate radial polynomials over vector of radii + t2 = time.perf_counter() + t_recursive_ms = round(1000*(t2-t1), 3) + # Measuring performance of radial polynomials calculations using exact implementation + t1 = time.perf_counter() + for polynomial in zernpols: + polynomial.radial(test_r, use_exact_eq=True) # calculate radial polynomials over vector of radii + t2 = time.perf_counter() + t_exact_ms = round(1000*(t2-t1), 3) + return t_recursive_ms, t_exact_ms, f"Used polynomials: {i}", f"Radii: {n_points}" + + +def _estimate_high_order_calc_times(): + """ + Estimate slowing down of radial polynomial calculation with increasing of radial order. + + Returns + ------- + None. + + """ + r = 0.55 + high_order_pols = [ZernPol(m=-2, n=46), ZernPol(m=1, n=47), ZernPol(m=2, n=48), ZernPol(m=-1, n=49), + ZernPol(m=2, n=50), ZernPol(m=1, n=51), ZernPol(m=-2, n=52)] + times = [] + # Single polynomials values + for pol in high_order_pols: + # calculate radial polynomials over vector of radii + t1 = time.perf_counter(); pol.radial(r); t2 = time.perf_counter() + times.append(f"{pol.get_mn_orders()}: {int(round(1000*(t2-t1), 0))} ms") + # Delete polynomials with too high orders for derivatives calculates + high_order_pols.pop(len(high_order_pols)-1); high_order_pols.pop(len(high_order_pols)-1) + high_order_pols.pop(len(high_order_pols)-1) + print(times); times = [] + # Single derivative polynomials values + for pol in high_order_pols: + # calculate derivatives of radial polynomials over vector of radii + t1 = time.perf_counter(); pol.radial_dr(r); t2 = time.perf_counter() + times.append(f"Deriv. {pol.get_mn_orders()}: {int(round(1000*(t2-t1), 0))} ms") + print(times) + + +# %% Tests +if __name__ == "__main__": + _test_plots = True # regulates testing of plotting various plots + _test_calculations = False # regulates tests below concerning calculations + + # Testing plotting, the plots will be opened in the additional pop-up windows + if _test_plots: + plt.close("all") # close all previously opened plots + t1 = time.perf_counter(); zp = ZernPol(m=0, n=2); ZernPol.plot_profile(zp, color_map="jet", show_title=True) # basic plot + t2 = time.perf_counter(); print("Plotting of 1 non-zero polynomial takes ms: ", int(round(1000*(t2-t1), 0))) + coordinates = ZernPol.gen_polar_coordinates(r_step=0.005) + zp = ZernPol(m=-10, n=30); ZernPol.plot_profile(zp, color_map="jet", show_title=False, polar_coordinates=coordinates) # high order plot + zp = ZernPol(m=0, n=0); ZernPol.plot_profile(zp, color_map="turbo", show_title=True) # plot of piston polynomial + + # Testing 3D surface plotting + ZernPol.plot_profile(ZernPol(m=0, n=2), color_map="viridis", projection="3d") + + # Testing 3D figure plotting on the externally initialized Figure class + fig3d = plt.figure(figsize=(6.8, 6.8)) + zern_surface = ZernPol.gen_zernikes_surface([1.0], [ZernPol(m=0, n=2)], equal_n_coordinates=True, n_points=400) + ZernPol.plot_sum_zernikes_on_fig(figure=fig3d, use_defaults=False, zernikes_sum_surface=zern_surface, + show_range=True, color_map="magma", projection="3D") + fig3d2 = plt.figure(figsize=(5.8, 5.8)) + ZernPol.plot_sum_zernikes_on_fig(figure=fig3d2, coefficients=[1.0], polynomials=[ZernPol(m=0, n=2)], + show_range=True, color_map="bwr", projection="3D") + + # Testing accelerated plotting / sum calculation + fig3 = plt.figure(figsize=(3, 3)) + t1 = time.perf_counter(); n_pols = 31; polynomials = []; coefficients = [0.0]*n_pols + for i in range(n_pols): + polynomials.append(ZernPol(osa=58+i)) + coefficients[0] = 1.0 # only 1st polynomial will be plotted + fig3 = ZernPol.plot_sum_zernikes_on_fig(figure=fig3, coefficients=coefficients, polynomials=polynomials, + show_range=False, color_map="turbo") + fig3.subplots_adjust(0, 0, 1, 1) + t2 = time.perf_counter(); print("Plotting of 1 non-zero and 30 zero pol-s takes ms: ", int(round(1000*(t2-t1), 0))) + + # Tests with generation / restoring Zernike profiles (phases images) + phases_image, polynomials_ampls, polynomials = generate_random_phases(img_height=301, img_width=321) + plt.figure(); plt.axis("off"); plt.imshow(phases_image, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) + polynomials_amplitudes, cropped_img = fit_polynomials(phases_image, polynomials, return_cropped_image=True, + strict_circle_border=False, crop_radius=1.0) + plt.figure(); plt.axis("off"); plt.imshow(cropped_img, cmap="jet") + plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) + + # Updated test of fitting including piston polynomial + height = 500; width = 481; crop_r = 1.0; strict_border = True; pols_coeffs = [-0.75, 0.86, 0.41]; fig4 = plt.figure(figsize=(4, 4)) + polynomials = [ZernPol(osa=0), ZernPol(m=0, n=2), ZernPol(m=-3, n=3)]; rs, angles = ZernPol.gen_polar_coordinates() + phase_profile = ZernPol.sum_zernikes(coefficients=pols_coeffs, polynomials=polynomials, r=rs, theta=angles, get_surface=True) + # Below - plotting specified polynomials on the polar coordinates + ZernPol.plot_sum_zernikes_on_fig(figure=fig4, use_defaults=False, zernikes_sum_surface=zernikes_surface(phase_profile, rs, angles), + color_map="jet") + # Below - generate phases image with the cartesian coordinates + phases_image2 = generate_phases_image(polynomials=tuple(polynomials), polynomials_amplitudes=tuple(pols_coeffs), + img_height=height, img_width=width) + plt.figure(); plt.axis("off"); im = plt.imshow(phases_image2, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) + plt.colorbar(mappable=im) + # Below - fitting procedure on the provided phases image + polynomials_amplitudes2, cropped_img2 = fit_polynomials(phases_image2, polynomials, return_cropped_image=True, + strict_circle_border=strict_border, crop_radius=crop_r) + print("Difference between used amplitudes and fitted ones:", np.asarray(pols_coeffs) - polynomials_amplitudes2) + plt.figure(); plt.axis("off"); im = plt.imshow(cropped_img2, cmap="jet"); plt.tight_layout(); plt.subplots_adjust(0, 0, 1, 1) + plt.colorbar(mappable=im) + + plt.show() # show all images created by plt.figure() calls + + # Testing calculations and their performance comparison + if _test_calculations: + # Simple test of two concepts of calculations - exact and recursive equations + z = ZernPol(n=30, m=-2); print("Diff. between recursive and exact equations:", + round(z.radial(0.85) - z.radial(0.85, use_exact_eq=True), 9)) + z = ZernPol(n=32, l=0); print("Diff. between recursive and exact equations:", + round(z.radial(0.35) - z.radial(0.35, use_exact_eq=True), 9)) + r = 0.955; theta = np.pi/8; z = ZernPol(osa=55) + print("Diff. between recursive and exact equations:", + round(z.polynomial_value(r, theta) - z.polynomial_value(r, theta, use_exact_eq=True), 9)) + z = ZernPol(n=35, l=-1); print("Diff. between recursive & exact eq-s for derivatives:", + round(z.radial_dr(0.78) - z.radial_dr(0.78, use_exact_eq=True), 9)) + z = ZernPol(n=38, m=-2); print("Diff. between recursive & exact eq-s for derivatives:", + round(z.radial_dr(0.9) - z.radial_dr(0.9, use_exact_eq=True), 9)) + # Compare performances + print("Tabular (10th order) / exact calc. times:", compare_performances(1, 10)) + print("Recursive / exact calc. times for high orders:", compare_performances(12, 40)) + # Statement below producing expected warnings, it's used for performance estimation + _estimate_high_order_calc_times() diff --git a/tests/run_zernpsf_as_main.py b/tests/run_zernpsf_as_main.py new file mode 100644 index 0000000..da8af1e --- /dev/null +++ b/tests/run_zernpsf_as_main.py @@ -0,0 +1,197 @@ +# -*- coding: utf-8 -*- +""" +Run a few methods from 'zernpsf' as the main one for performing tests in IDE. + +@author: Sergei Klykov, '@sklykov' on GitHub + +@licence: MIT, @year: 2026 + +""" +import importlib +from contextlib import suppress +from pathlib import Path + +import matplotlib +import numpy as np + +# Explicit backend assignment for matplotlib - for compatibility between running configurations in Spyder and PyCharm IDEs +with suppress(ImportError): + matplotlib.use('Qt5Agg') +import matplotlib.pyplot as plt + +# Import of developed version of package, install in the editable mode: pip install -e . +import zernpy.zernikepol +import zernpy.zernpsf + +importlib.reload(zernpy.zernikepol) # trick to guarantee local changes to be always used for run +importlib.reload(zernpy.zernpsf) + +from zernpy.zernikepol import ZernPol +from zernpy.zernpsf import ZernPSF, force_get_psf_compilation + +# %% Test as the main script +if __name__ == "__main__": + plt.close("all") # close all opened before figures + wavelength_um = 0.55 # used below in a several calls + check_other_pols = False; check_small_na_wl = False # flag for checking some other polynomials PSFs + check_airy = False; check_common_psf = True; check_io_kernel = False; check_parallel_calculation = False; check_test = False + check_faster_airy = True; check_test_conditions = False; check_test_conditions2 = False; check_several_pols = False + check_edge_conditions = False; test_acceleration_single_pol = False; test_acceleration_few_pol = False + prepare_pic_readme = False # for plotting the sum of polynomials produced profile + test_io_few_pols = False; standard_path = Path.home().joinpath("Desktop") # for saving json on the Desktop + check_acceleration_flag = False # for testing fallback calculation with the wrong flag for calculate PSF kernel + check_init_several_pols = False # check calculation several pol-s: Airy (Piston) + some of polynomial + check_airy_patterns = False # check the difference between calculated by equation for Airy pattern and diffraction integral + check_precompilation = False # checks precompilation + check_cropping = False # checks how kernel is cropped + + # Common PSF for testing + if check_common_psf: + force_get_psf_compilation(True) + zpsf1 = ZernPSF(ZernPol(m=1, n=1)); zpsf2 = ZernPSF(ZernPol(m=-3, n=3)); ampl = -0.43 + zpsf2.set_physical_props(NA=0.95, wavelength=wavelength_um, expansion_coeff=ampl, pixel_physical_size=wavelength_um/5.05) + zpsf1.set_physical_props(NA=0.5, wavelength=0.6, expansion_coeff=0.25, pixel_physical_size=wavelength_um/5.5) + zpsf2.set_calculation_props(kernel_size=zpsf2.kernel_size, n_integration_points_r=250, n_integration_points_phi=320) + zpsf1.set_calculation_props(kernel_size=zpsf2.kernel_size, n_integration_points_r=220, n_integration_points_phi=360) + kernel3 = zpsf2.calculate_psf_kernel(suppress_warnings=False, verbose_info=True); zpsf2.plot_kernel("for loop") + zpsf2.visualize_convolution() # Visualize convolution on the disk image + if check_io_kernel: + # default_path = Path(__file__).parent.joinpath("saved_psfs").absolute() # default path for storing JSON files + zpsf2.save_json(overwrite=True, abs_path=standard_path) + zpsf1.read_json(zpsf2.json_file_path) # for testing reading and assigning values to ZernPSF class (substitution) + if check_parallel_calculation: + zpsf2.initialize_parallel_workers(); kernel2 = zpsf2.get_kernel_parallel() + zpsf2.plot_kernel("parallel"); zpsf2.deinitialize_workers() + + # Another Zernike polynomial, big NA + if check_other_pols: + zpsf3 = ZernPSF(ZernPol(m=0, n=4)) + zpsf3.set_physical_props(NA=1.25, wavelength=wavelength_um, expansion_coeff=0.4, pixel_physical_size=wavelength_um/5.25) + zpsf3.calculate_psf_kernel(suppress_warnings=False, verbose_info=True); zpsf3.plot_kernel() + + # Another Zernike polynomial, average to small NA and wavelength + if check_small_na_wl: + NA = 0.45; wavelength = 0.4; pixel_size = wavelength / 5.25; ampl = 0.18 + zp2 = ZernPol(m=1, n=3); zpsf2 = ZernPSF(zp2) # horizontal coma + zpsf2.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) + zpsf2.calculate_psf_kernel(normalized=True); zpsf2.plot_kernel() + + if check_airy: + NA = 0.12; wavelength = 0.8; pixel_size = wavelength / 4.0; ampl = 1.25 + zp4 = ZernPol(m=0, n=0); zpsf4 = ZernPSF(zp4) # piston for the Airy pattern + zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) + zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel("Plus") + zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=-ampl, pixel_physical_size=pixel_size) + zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel("Minus") + + if check_faster_airy: # For set the test for pytest library + NA = 0.35; wavelength = 0.55; pixel_size = wavelength / 3.05; ampl = -0.4 + zp4 = ZernPol(m=0, n=0); zpsf4 = ZernPSF(zp4) # piston for the Airy pattern + zpsf4.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) + zpsf4.calculate_psf_kernel(normalized=True); zpsf4.plot_kernel() + + if check_test_conditions: + NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 5.0; ampl = 0.55 + zp6 = ZernPol(m=0, n=2); zpsf6 = ZernPSF(zp6) # defocus + zpsf6.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) # normal assignment + zpsf6.set_calculation_props(kernel_size=zpsf6.kernel_size, n_integration_points_r=250, n_integration_points_phi=300) + zpsf6.calculate_psf_kernel(normalized=True); zpsf6.plot_kernel() + if check_test_conditions2: + zp7 = ZernPol(m=1, n=3); zpsf7 = ZernPSF(zp7) # horizontal coma + NA = 0.4; wavelength = 0.4; pixel_size = wavelength / 3.2; ampl = 0.185 # Common physical properties + zpsf7.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) + zpsf7.calculate_psf_kernel(normalized=True); zpsf7.plot_kernel() + + # Test calculation of a PSF for several polynomials and I/O operations (see flags) + if check_several_pols: + zp1 = ZernPol(m=-2, n=2); zp2 = ZernPol(m=0, n=2); zp3 = ZernPol(m=2, n=2); pols = (zp1, zp2, zp3); coeffs = (-0.36, 0.25, 0.4) + zpsf8 = ZernPSF(pols); zpsf8.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=coeffs, pixel_physical_size=0.5/4.5) + composed_kernel = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf8.plot_kernel() + if test_io_few_pols: + zpsf14 = ZernPSF(ZernPol(osa=19)); zpsf14.set_physical_props(NA=0.1, wavelength=0.4, expansion_coeff=0.82, + pixel_physical_size=0.05) + zpsf8.save_json(overwrite=True, abs_path=standard_path); zpsf14.read_json(zpsf8.json_file_path) # save / read calculated kernel + + # Test some edge conditions - e.g., specifying 1 polynomial in a list with huge coefficient + if check_edge_conditions: + zp4 = ZernPol(m=3, n=3); pols2 = [zp4]; coeff = 5.1 + zpsf9 = ZernPSF(pols2); zpsf9.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=coeff, pixel_physical_size=0.5/4.75) + zpsf9.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=(-0.67), pixel_physical_size=0.5/4.75) + zpsf9.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf9.plot_kernel() + # Test acceleration by using numba library utilities + if test_acceleration_single_pol: + force_get_psf_compilation(); NA = 0.95; wavelength = 0.55; pixel_size = wavelength / 4.6; ampl = -0.16 + zp6 = ZernPol(m=0, n=2); zpsf6 = ZernPSF(zp6) # defocus + zpsf6.set_physical_props(NA=NA, wavelength=wavelength, expansion_coeff=ampl, pixel_physical_size=pixel_size) + kernel_acc = zpsf6.calculate_psf_kernel(normalized=True, accelerated=True, verbose_info=True); zpsf6.plot_kernel("Accelerated") + kernel_norm = zpsf6.calculate_psf_kernel(normalized=True); zpsf6.plot_kernel("Normal") + if test_acceleration_few_pol: + force_get_psf_compilation() + zp1 = ZernPol(m=-2, n=2); zp2 = ZernPol(m=0, n=2); zp3 = ZernPol(m=2, n=2); pols = (zp1, zp2, zp3); coeffs = (-0.12, 0.15, 0.1) + zpsf8 = ZernPSF(pols); zpsf8.set_physical_props(NA=0.35, wavelength=0.5, expansion_coeff=coeffs, pixel_physical_size=0.5/1.5) + composed_kernel = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True); zpsf8.plot_kernel("Normal") + composed_kernel_acc = zpsf8.calculate_psf_kernel(normalized=True, verbose_info=True, accelerated=True) + zpsf8.plot_kernel("Accelerated") + if prepare_pic_readme: + force_get_psf_compilation(verbose_report=True) + zp1 = ZernPol(m=-1, n=3); zp2 = ZernPol(m=2, n=4); zp3 = ZernPol(m=0, n=4); pols = (zp1, zp2, zp3); coeffs = (0.5, 0.21, 0.15) + zpsf_pic = ZernPSF(pols); zpsf_pic.set_physical_props(NA=0.65, wavelength=0.6, expansion_coeff=coeffs, pixel_physical_size=0.6/5.0) + zpsf_pic.calculate_psf_kernel(normalized=True, verbose_info=True, accelerated=True) + zpsf_pic.plot_kernel("Vert. Coma Vert. 2nd Astigmatism Spherical") + if check_acceleration_flag: + zp16 = ZernPol(m=-1, n=3); zp18 = ZernPol(m=2, n=4); pols10 = (zp16, zp18); coeffs10 = (-0.1, 0.13); zpsf_acc = ZernPSF(pols10) + zpsf_norm = ZernPSF(pols10); zpsf_acc.set_physical_props(NA=0.43, wavelength=0.6, expansion_coeff=coeffs10, + pixel_physical_size=0.6/3.0) + zpsf_norm.set_physical_props(NA=0.43, wavelength=0.6, expansion_coeff=coeffs10, pixel_physical_size=0.6/3.0) + kern_acc = zpsf_acc.calculate_psf_kernel(normalized=True, accelerated=True) + kern_norm = zpsf_norm.calculate_psf_kernel(normalized=True) + kern_diff = np.round(kern_acc - kern_norm, 9) # for checking the difference in calculations + + if check_test: + pols = (ZernPol(osa=10), ZernPol(osa=15)); coeffs = (0.28, -0.33); NA = 0.35; wavelength = 0.55 + zpsf = ZernPSF(pols); zpsf.set_physical_props(NA, wavelength, expansion_coeff=coeffs, pixel_physical_size=wavelength / 3.5) + zpsf.set_calculation_props(kernel_size=25, n_integration_points_r=200, n_integration_points_phi=180) + psf_kernel = zpsf.calculate_psf_kernel(normalized=False); zpsf.plot_kernel() + + if check_init_several_pols: + force_get_psf_compilation(True) + zpsf30 = ZernPSF(zernpol=(ZernPol(osa=1), ZernPol(osa=5))) + try: + zpsf30.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=0.5, pixel_physical_size=0.5/5.0) + except ValueError: + print("Check for 1 ampl. and 2 pol-s passed") # as expected, transfer to test function + zpsf31 = ZernPSF(zernpol=(ZernPol(osa=0), ZernPol(m=-1, n=3))) + zpsf31.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=[1.5, 0.24], pixel_physical_size=0.5/3.8) + # zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=False); zpsf31.plot_kernel("Not accelerated 2 pol-s") + # kernel_not_acc = np.copy(zpsf31.kernel) + zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=True); zpsf31.plot_kernel("Airy 1.5") + kernel_acc = np.copy(zpsf31.kernel) + # zpsf31.kernel = np.abs(kernel_acc - kernel_not_acc); zpsf31.plot_kernel("Diff. 2 pol-s") + zpsf31.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=[-1.5, 0.24], pixel_physical_size=0.5/3.8) + zpsf31.calculate_psf_kernel(verbose_info=True, accelerated=True); zpsf31.plot_kernel("Airy -1.5") + kernel_neg_acc = np.copy(zpsf31.kernel) + zpsf31.kernel = np.abs(kernel_acc - kernel_neg_acc); zpsf31.plot_kernel("Diff. neg. pos. Airy + Coma") + + if check_airy_patterns: + force_get_psf_compilation(verbose_report=True) + zpsf40 = ZernPSF(zernpol=ZernPol(osa=0)) + zpsf40.set_physical_props(NA=0.95, wavelength=0.5, expansion_coeff=3.0, pixel_physical_size=0.5/4.0) + zpsf40.calculate_psf_kernel(verbose_info=True, accelerated=False, normalized=False); zpsf40.plot_kernel("Not accelerated Airy") + kernel_not_acc = np.copy(zpsf40.kernel) + zpsf40.calculate_psf_kernel(verbose_info=True, accelerated=True, normalized=False); zpsf40.plot_kernel("Accelerated Airy") + kernel_acc = np.copy(zpsf40.kernel) + zpsf40.kernel = np.abs(kernel_acc - kernel_not_acc); zpsf40.plot_kernel("Diff. Airy") + + if check_precompilation: + force_get_psf_compilation(True) + zpsf50 = ZernPSF(zernpol=(ZernPol(m=1, n=3))) + zpsf50.set_physical_props(NA=1.25, wavelength=0.52, expansion_coeff=0.5, pixel_physical_size=0.5/4.85) + zpsf50.calculate_psf_kernel(verbose_info=True, accelerated=True, normalized=True); zpsf50.plot_kernel() + + if check_cropping: + zpsf60 = ZernPSF(zernpol=(ZernPol(m=0, n=4))) + zpsf60.set_physical_props(NA=1.25, wavelength=0.5, expansion_coeff=0.47, pixel_physical_size=0.5/5.0) + zpsf60.calculate_psf_kernel(accelerated=True, verbose_info=True); zpsf60.plot_kernel("Not Cropped") + original_kernel = np.copy(zpsf60.kernel) + zpsf60.crop_kernel(min_part_of_max=0.025); zpsf60.plot_kernel("Cropped"); cropped_kernel = np.copy(zpsf60.kernel) + print("Original kernel shape:", original_kernel.shape, "\nCropped kernel shape:", cropped_kernel.shape) diff --git a/tests/test_package_import.py b/tests/test_package_import.py index 177974f..a307404 100644 --- a/tests/test_package_import.py +++ b/tests/test_package_import.py @@ -9,7 +9,7 @@ def test_initialization(): try: - from zernpy import ZernPol, generate_polynomials, ZernPSF, force_get_psf_compilation + from zernpy import ZernPol, ZernPSF, force_get_psf_compilation, generate_polynomials try: import numba if numba is not None: