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Proceedings Paper

Efficient computation with special functions like the circle polynomials of Zernike
Author(s): Philip R. Riera; Geoffrey S. Pankretz; Daniel M. Topa
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Paper Abstract

The circle polynomials of Zernike play a prominent role in optical analysis. While decompositions of wavefronts into Zernike polynomial series can yield valuable insight, computing with the polynomials themselves is quite inefficient. Here we outline how rational polynomials like those of Zernike, Legendre, Chebyshev and Laguerre can be handled as affine combinations of a Taylor monomial set. We demonstrate how calculations can be performed much more rapidly in the Taylor basis and how to use integer transformations to recover the exact amplitudes in the desired basis. We also explore C++ optimizations for storing the Zernike amplitudes and transforming between Zernike polynomials and Taylor monomials.

Paper Details

Date Published: 4 September 2002
PDF: 15 pages
Proc. SPIE 4769, Optical Design and Analysis Software II, (4 September 2002); doi: 10.1117/12.481181
Show Author Affiliations
Philip R. Riera, WaveFront Sciences, Inc. (United States)
Geoffrey S. Pankretz, WaveFront Sciences, Inc. (United States)
Daniel M. Topa, WaveFront Sciences, Inc. (United States)

Published in SPIE Proceedings Vol. 4769:
Optical Design and Analysis Software II
Richard C. Juergens, Editor(s)

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