Fitting high-order Zernike polynomials to finite data

Benjamin Lewis; James H. Burge

doi:10.1117/12.930774

13 September 2012 Fitting high-order Zernike polynomials to finite data

Benjamin Lewis, James H. Burge

Proceedings Volume 8493, Interferometry XVI: Techniques and Analysis; 84930E (2012) https://doi.org/10.1117/12.930774
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

While the use of Zernike polynomials to represent simulated or measured data on a grid of points is common, the accuracy of the coefficients can be limited by the non-orthogonality of the functions over the pixelated domains. The Zernike polynomials are defined to be analytically orthogonal over a circular domain, but this breaks down for discrete data. A simple correction is presented that uses a weighted scalar product to determine coefficients. This method preserves the meaning of the Zernike polynomials and allows efficient calculations using an inner product. The algorithm for defining the weighting function is provided, and simulations are included that demonstrate nearly an order of magnitude improvement in accuracy when the new weighted scalar product is used.

Citation Download Citation

Benjamin Lewis and James H. Burge "Fitting high-order Zernike polynomials to finite data", Proc. SPIE 8493, Interferometry XVI: Techniques and Analysis, 84930E (13 September 2012); https://doi.org/10.1117/12.930774

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