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Proceedings Paper

Fitting high-order Zernike polynomials to finite data
Author(s): Benjamin Lewis; James H. Burge
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Paper 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.

Paper Details

Date Published: 13 September 2012
PDF: 10 pages
Proc. SPIE 8493, Interferometry XVI: Techniques and Analysis, 84930E (13 September 2012); doi: 10.1117/12.930774
Show Author Affiliations
Benjamin Lewis, College of Optical Sciences, The Univ. of Arizona (United States)
James H. Burge, College of Optical Sciences, The Univ. of Arizona (United States)

Published in SPIE Proceedings Vol. 8493:
Interferometry XVI: Techniques and Analysis
Joanna Schmit; Katherine Creath; Catherine E. Towers; Jan Burke, Editor(s)

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