zernike.standard

Standard Zernike Module

This module contains the ZernikeStandard class, which defines Zernike polynomials based on the “standard” indexing scheme.

References

  1. https://en.wikipedia.org/wiki/Zernike_polynomials#OSA/ANSI_standard_indices

  2. Thibos LN, Applegate RA, Schwiegerling JT, Webb R; VSIA Standards Taskforce Members. Vision science and its applications. Standards for reporting the optical aberrations of eyes. J Refract Surg. 2002 Sep-Oct;18(5):S652-60. doi: 10.3928/1081-597X-20020901-30. PMID: 12361175.

Kramer Harrison, 2025

Classes

ZernikeStandard([coeffs, num_terms])

OSA/ANSI Standard Zernike
class ZernikeStandard(coeffs=None, num_terms=36)[source]

OSA/ANSI Standard Zernike

This class represents the OSA/ANSI Standard Zernike polynomials. It provides methods to calculate the Zernike terms, Zernike polynomials, and other related functions.

Parameters:

  • coeffs (array-like) – The Zernike coefficients. Defaults to None.

  • num_terms (int) – the maximum number of terms. Only used if coeffs is None. Defaults to 36.

References

  1. https://en.wikipedia.org/wiki/Zernike_polynomials#OSA/ ANSI_standard_indices

  2. Thibos LN, Applegate RA, Schwiegerling JT, Webb R; VSIA Standards Taskforce Members. Vision science and its applications. Standards for reporting the optical aberrations of eyes. J Refract Surg. 2002 Sep-Oct;18(5):S652-60. doi: 10.3928/1081-597X-20020901-30. PMID: 12361175.

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