New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion
arXiv:1705.08482 · doi:10.1364/JOSAA.34.001844
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.
Submitted to JOSA A, 2 figures