Study of the properties of Zernike’s orthogonal polynomials

Sergey N. Bezdidko

doi:10.1117/12.507927

6 November 2003 Study of the properties of Zernike’s orthogonal polynomials

Sergey N. Bezdidko

Proceedings Volume 5174, Novel Optical Systems Design and Optimization VI; (2003) https://doi.org/10.1117/12.507927
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

Wide application of Zernike’s orthogonal polynomials at lens design and optical engineering generates a need of more detailed study of their properties, assemblage new results and results received previously. In this connection we bring results of our researches on study of properties of Zernike's polynomials, revealing their interrelation with other special functions, obtaining recurrence relations, formulas of differentiation of Zernike's radial polynomials, decomposition of the ratio of two radial polynomials in continuous fractions and so on.

Citation Download Citation

Sergey N. Bezdidko "Study of the properties of Zernike’s orthogonal polynomials", Proc. SPIE 5174, Novel Optical Systems Design and Optimization VI, (6 November 2003); https://doi.org/10.1117/12.507927

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