New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.
@article{Pogosyan2017NewSP,
title={New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.},
author={George S. Pogosyan and Kurt Bernardo Wolf and Alexander Yakhno},
journal={Journal of the Optical Society of America. A, Optics, image science, and vision},
year={2017},
volume={34 10},
pages={
1844-1848
}
}The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on 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 nonorthogonal 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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