zernike.noll

Noll Zernike Module

This module contains the NollZernike class, which defines Zernike polynomials based on the “Noll” indexing scheme. Note that the Noll notation is used for the “Zernike Standard Coefficients” in Ansys Zemax OpticStudio.

References

  1. https://en.wikipedia.org/wiki/ Zernike_polynomials#Noll’s_sequential_indices

  2. Noll, R. J. (1976). “Zernike polynomials and atmospheric turbulence”. J. Opt. Soc. Am. 66 (3): 207

Kramer Harrison, 2025

Classes

ZernikeNoll([coeffs, num_terms])

Zernike Coefficients - Noll Standard
class ZernikeNoll(coeffs=None, num_terms=36)[source]

Zernike Coefficients - Noll Standard

This class represents Zernike Noll Coefficients. It is a subclass of the BaseZernike class. Note that the Noll notation is used for the “Zernike Standard Coefficients” in Ansys Zemax OpticStudio.

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#Noll’s_sequential_indices

  2. Noll, R. J. (1976). “Zernike polynomials and atmospheric turbulence”. J. Opt. Soc. Am. 66 (3): 207

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