Computation of the circle polynomials of Zernike

Phillip R. Riera

doi:10.1117/12.507565

11 December 2003 Computation of the circle polynomials of Zernike

Phillip R. Riera

Proceedings Volume 5162, Advanced Wavefront Control: Methods, Devices, and Applications; (2003) https://doi.org/10.1117/12.507565
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

The circle polynomials of Zernike are a vital tool in the analysis of optical systems. Decomposition of wavefronts into Zernike polynomials can be insightful. Computation in the Zernike basis, however, is quite cumbersome and inefficient. This paper will address how rational polynomials such as Zernike, Laguerre, Legendre and Chebyshev can be represented as affine combinations of a Taylor monomial set. This paper also demonstrates the efficiency of common routines using a Taylor basis as well as implementation and optimization issues.

Citation Download Citation

Phillip R. Riera "Computation of the circle polynomials of Zernike", Proc. SPIE 5162, Advanced Wavefront Control: Methods, Devices, and Applications, (11 December 2003); https://doi.org/10.1117/12.507565

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