Miroslav Vlcek, Pavel Sovka, "Zernike Polynomials and their Spectral Representation," International Journal of Electrical Engineering and Computer Science, vol. 3, pp. 1-5, 2021, DOI:
Miroslav Vlcek, Pavel Sovka. Zernike Polynomials and their Spectral Representation.
International Journal of Electrical Engineering and Computer Science. 2021;3:1-5.
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.
Keywords:
Pages: 1-5 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
WSEAS Transactions on International Journal of Electrical Engineering and Computer Science, E-ISSN: 2769-2507, Volume 3, 2021, Art. #1
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