Recursive formula to compute Zernike radial polynomials

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 relationshi...

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Bibliographic Details
Published in:Optics letters 2013-07, Vol.38 (14), p.2487-2489
Main Authors: Honarvar Shakibaei, Barmak, Paramesran, Raveendran
Format: Article
Language:English
Subjects:
Aberration
Algorithms
Boundaries
Mathematical analysis
Polynomials
Recursive
Wave fronts
Zernike polynomials
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Summary: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.
ISSN:0146-9592
1539-4794
DOI:10.1364/OL.38.002487