Recursive formula to compute Zernike radial polynomials

被引：40

作者：

Shakibaei, Barmak Honarvar ^{[1
]}

Paramesran, Raveendran ^{[1
]}

机构：

[1] Univ Malaya, Dept Elect Engn, Kuala Lumpur 50603, Malaysia

来源：

OPTICS LETTERS | 2013年 / 38卷 / 14期

关键词：

EXPANSION COEFFICIENTS; PUPIL SIZES; MOMENTS;

D O I：

10.1364/OL.38.002487

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity. (C) 2013 Optical Society of America

引用

页码：2487 / 2489

页数：3

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