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arXiv · 1705.08482

New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion

George S. Pogosyan·Kurt Bernardo Wolf·Alexander Yakhno
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Abstract

The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases, involving Legendre and Gegenbauer polynomials, in non-orthogonal coordinates close to Cartesian ones. We find the overlaps between the original Zernike basis and a representative of the new set, which turn out to be Clebsch-Gordan coefficients.

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George S. Pogosyan, Kurt Bernardo Wolf, Alexander Yakhno. 2017-05-23. New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion. https://doi.org/10.1364/josaa.34.001844

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