New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.
J Opt Soc Am A Opt Image Sci Vis
; 34(10): 1844-1848, 2017 Oct 01.
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| MEDLINE
| ID: mdl-29036055
ABSTRACT
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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