optiland.zernike.fringe

Fringe Zernike Module

This module contains the FringeZernike class, which defines Zernike polynomials based on the “fringe”, or “University of Arizona”, indexing scheme.

References

  1. https://en.wikipedia.org/wiki/Zernike_polynomials#Fringe/ University_of_Arizona_indices

Kramer Harrison, 2025

Classes

ZernikeFringe([coeffs, num_terms])

Zernike Fringe Coefficients
class ZernikeFringe(coeffs=None, num_terms=36)[source]

Zernike Fringe Coefficients

This class represents Zernike Fringe Coefficients. It is a subclass of the BaseZernike class.

Parameters:

coeffs (list) – the coefficient list for the Zernike polynomials. Defaults to all zeros (36 elements total)

References

  1. https://en.wikipedia.org/wiki/Zernike_polynomials#Fringe/ University_of_Arizona_indices

get_derivative(n=0, m=0, r=0, phi=0)

Calculate the derivative of the Zernike polynomial for the given coefficients and parameters.

Returns a tuple of the radial (dZ / dr) and azimuthal (dZ / dphi) partial derivatives of the Zernike polynomial.

Parameters:

  • n (int) – Radial order of the Zernike term.

  • m (int) – Azimuthal order of the Zernike term.

  • r (float) – Radial distance from the origin.

  • phi (float) – Azimuthal angle in radians.

Returns:

The radial and azimuthal derivatives of the

Zernike polynomial.

Return type:

tuple[float, float]

get_term(coeff: ScalarOrArray = 0, n: int = 0, m: int = 0, r: ScalarOrArray = 0, phi: ScalarOrArray = 0) → ScalarOrArray

Calculate the Zernike term for given coefficients and parameters.

Parameters:

  • coeff (float) – Coefficient value for the Zernike term.

  • n (int) – Radial order of the Zernike term.

  • m (int) – Azimuthal order of the Zernike term.

  • r (float) – Radial distance from the origin.

  • phi (float) – Azimuthal angle in radians.

Returns:

The calculated value of the Zernike term.

Return type:

float

poly(r: ScalarOrArray = 0, phi: ScalarOrArray = 0) → float

Calculate the Zernike polynomial for given radial distance and azimuthal angle.

Parameters:

  • r (float) – Radial distance from the origin.

  • phi (float) – Azimuthal angle in radians.

Returns:

The calculated value of the Zernike polynomial.

Return type:

float

terms(r: ScalarOrArray = 0, phi: ScalarOrArray = 0) → list

Calculate the Zernike terms for given radial distance and azimuthal angle.

Parameters:

  • r (float) – Radial distance from the origin.

  • phi (float) – Azimuthal angle in radians.

Returns:

List of calculated Zernike term values.

Return type:

list