Wavefront fitting with discrete orthogonal polynomials in a unit radius circle

Daniel Malacara-Hernandez; Martin Carpio-Valadez; Jose Javier Sanchez-Mondragon

doi:10.1117/12.55629

1 June 1990 Wavefront fitting with discrete orthogonal polynomials in a unit radius circle

Daniel Malacara-Hernandez, Martin Carpio-Valadez, Jose Javier Sanchez-Mondragon

Author Affiliations +

Optical Engineering, Vol. 29, Issue 6, (June 1990). https://doi.org/10.1117/12.55629

Abstract

Zernike polynomials have been used for some time to fit wavefront deformation measurements to a two-dimensional polynomial. Their orthogonality properties make them ideal for this kind of application. The typical procedure consists of first obtaining the fitting using x-y polynomials and then transforming them to Zernike polynomials by means of a matrix multiplication. Here, we present a new method for making this fitting faster by using a set of orthogonal polynomials on a discrete base of data points on a unitary circle.

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Daniel Malacara-Hernandez, Martin Carpio-Valadez, and Jose Javier Sanchez-Mondragon "Wavefront fitting with discrete orthogonal polynomials in a unit radius circle," Optical Engineering 29(6), (1 June 1990). https://doi.org/10.1117/12.55629

Published: 1 June 1990

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