Computing Zernike polynomials of arbitrary degree using the discrete Fourier transform

A. J.E.M. Janssen; P. Dirksen

doi:10.2971/jeos.2007.07012

Journal of the European Optical Society - Rapid publications, Vol 2 (2007)

Computing Zernike polynomials of arbitrary degree using the discrete Fourier transform

A. J.E.M. Janssen, P. Dirksen

Abstract

The conventional representation of Zernike polynomials R_n^m(rho) gives unacceptable results for large values of the degree n. We present an algorithm for the computation of Zernike polynomials of arbitrary degree n. The algorithm has the form of a discrete cosine transform which comes with advantages over other methods in terms of computation time, accuracy and transparancy. As an application we consider the effect of NA-scaling on the lower-order aberrations of an optical system in the presence of a very high order aberration.

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