International Journal of Electrical Engineering and Computer Science
E-ISSN: 2769-2507
Volume 3, 2021
Zernike Polynomials and their Spectral Representation
Authors: ,
Abstract: The Zernike polynomials $$Z_{n}^{m} (ρ, ϕ)$$ are known in optical physics, and they are used for the various diffractions and aberrations problems of lenses. They are defined on a circle, so that their representation decouples radial and axial coordinates. It is know that the Zernike radial polynomials $$R_{n}^{m} (ρ)$$ are represented through Jacobi polynomials. This paper deals with Chebyshev expansions for Jacobi polynomials.We have developed the recursive evaluation for spectral coefficients used in these expansions. These consequently provide a straightforward interpretation of Fourier transform of Zernike polynomials.