Adaptive optics in the formation of optical beams and images

Лукин, В. П.

doi:10.3367/ufnr.0184.201406b.0599

Cited by 19 publications

(1 citation statement)

References 119 publications

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“…The use of Zernike polynomials [1] for describing the classical aberrations of an optical system is well known [2][3][4]. There have been many other applications, such as to describe the statistical strength of aberrations produced by atmospheric turbulence, atmospheric thermal blooming effects, optical testing, opthalmic optics, corneal topography, interferometer measurements, ocular aberrometry, just to mention a few of them.…”

Section: Introductionmentioning

confidence: 99%

Recursive computation of generalised Zernike polynomials

Area

Dimitrov

Godoy

2017

Journal of Computational and Applied Mathematics

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An algorithmic approach for generating generalised Zernike polynomials by differential operators and connection matrices is proposed. This is done by introducing a new order of generalised Zernike polynomials such that it collects all the polynomials of the same total degree in a column vector. The connection matrices between these column vectors composed by the generalised Zernike polynomials and a family of polynomials generated by a Rodrigues formula are given explicitly. This yields a Rodrigues type formula for the generalised Zernike polynomials themselves with properly defined differential operators. Another consequence of our approach is the fact that the generalised Zernike polynomials obey a rather simple partial differential equation. We recall also how to define Hermite-Zernike polynomials.

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