optiland.zernike.fit

Zernike Fit Module

This module contains the ZernikeFit class, which can be used to fit Zernike polynomial to a set of points. This is commonly used for wavefront calculations, but the class can be used for any fitting operation requiring Zernike polynomials.

Kramer Harrison, 2025

Classes

ZernikeFit(x, y, z[, zernike_type, num_terms])

Fit Zernike polynomials to wavefront or arbitrary data points.
class ZernikeFit(x: ScalarOrArray, y: ScalarOrArray, z: ScalarOrArray, zernike_type: Literal['fringe', 'standard', 'noll'] = 'fringe', num_terms: int = 36)[source]

Fit Zernike polynomials to wavefront or arbitrary data points.

This class constructs a linear design matrix of Zernike basis functions and solves for the coefficients via least squares.

Parameters:

  • x (array-like) – X-coordinates of data points.

  • y (array-like) – Y-coordinates of data points.

  • z (array-like) – Values at (x, y) to fit.

  • zernike_type (str) – Type of Zernike basis: ‘fringe’, ‘standard’, or ‘noll’.

  • num_terms (int) – Number of Zernike terms to include in the fit.

x

Flattened x-coordinates.

Type:

array-like

y

Flattened y-coordinates.

Type:

array-like

z

Flattened target values.

Type:

array-like

radius

Radial coordinate of each point.

Type:

array-like

phi

Azimuthal coordinate of each point.

Type:

array-like

num_pts

Number of data points.

Type:

int

zernike

Zernike basis instance with fitted coefficients.

Type:

BaseZernike

property coeffs: BEArray

The fitted Zernike coefficients.

Type:

Tensor

view(fig_to_plot_on: Figure | None = None, projection: str = '2d', num_points: int = 128, figsize: tuple[float, float] = (7, 5.5), z_label: str = 'OPD (waves)') → tuple[Figure, Axes][source]

Visualize the fitted Zernike surface.

Parameters:

  • fig_to_plot_on (plt.Figure, optional) – Figure to plot on. If None, a new figure is created.

  • projection (str) – ‘2d’ for image plot, ‘3d’ for surface plot.

  • num_points (int) – Grid resolution for display.

  • figsize (tuple) – Figure size in inches.

  • to (defaults)

  • z_label (str) – Label for the z-axis or colorbar.

  • 'OPD (defaults to)

Returns:

A tuple containing the figure and axes objects.

Return type:

tuple

Raises:

ValueError – If projection is not ‘2d’ or ‘3d’.

view_residual(fig_to_plot_on: Figure | None = None, figsize: tuple[float, float] = (7, 5.5), z_label: str = 'Residual (waves)')[source]

Scatter plot of residuals between fitted surface and original data.

Parameters:

  • fig_to_plot_on (plt.Figure, optional) – Figure to plot on. If None, a new figure is created.

  • figsize (tuple) – Figure size in inches. Defaults to (7, 5.5).

  • z_label (str) – Label for the colorbar. Defaults to ‘Residual (waves)’.

Returns:

A tuple containing the figure and axes objects.

Return type:

tuple