ZernikeLegendreFit: Fast, precise, high-capacity fitting

Rapid and accurate surface fitting via orthogonality and Legendre quadrature, supporting thousands of Zernike terms.

Function for fitting a surface with Zernike polynomials

Author: Yiwen Fan ([e-mail])

Institute of Optics, University of Rochester

Usage:

[amn, bmn, z_recon_map] = ZernikeLegendreFit(z_map, M, N, J, K, center_x, center_y)

Description:

This function fits a given surface to Zernike polynomials, supporting up to hundreds of terms. It returns the coefficients of the fit and the reconstructed map.

Inputs:

z_map - The sag table of the surface to be fitted.

M - The highest azimuthal fitting order.

N - The highest radial fitting order.

J - The sampling number in the azimuthal direction, default: 2*M+1

K - The sampling number in the radial direction, default: 2*(N+1)

center_x, center_y - The center of the surface. If not provided, it will be calculated by the FindCenter function.

Outputs:

amn, bmn - The coefficients of the fitted Zernike polynomials.

z_recon_map - The surface map reconstructed from the fitted coefficients.

Acknowledgments:

This work was inspired by the research of Greg Forbes and funded by the National Science Foundation I/UCRC Center for Freeform Optics (IIP-1822026, IIP-1822049).

Part of this work was contributed by Ilhan Kaya in 2010, who wrote the initial jacobiZernike function. This function was later revised by Yiwen Fan and renamed jacobiZernike_table.