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Proceedings Article

Efficient computation with special functions like the circle polynomials of Zernike

[+] Author Affiliations
Philip R. Riera, Geoffrey S. Pankretz, Daniel M. Topa

WaveFront Sciences, Inc. (USA)

Proc. SPIE 4769, Optical Design and Analysis Software II, 130 (September 5, 2002); doi:10.1117/12.481181
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From Conference Volume 4769

  • Optical Design and Analysis Software II
  • Richard C. Juergens
  • Seattle, WA | July 07, 2002

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.

© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

Philip R. Riera ; Geoffrey S. Pankretz and Daniel M. Topa
"Efficient computation with special functions like the circle polynomials of Zernike", Proc. SPIE 4769, Optical Design and Analysis Software II, 130 (September 5, 2002); doi:10.1117/12.481181; http://dx.doi.org/10.1117/12.481181


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