AI Article Synopsis
- A new set of orthonormal polynomial solutions for classifying wavefront aberrations in circular pupils has been developed, incorporating Legendre and Gegenbauer polynomials in nearly Cartesian coordinates.
- The relationships between the original Zernike basis and the new solutions are explored, revealing that the overlaps correspond to Clebsch-Gordan coefficients.
- This advancement enhances the understanding of wavefront analysis in optics, providing alternative methods for polynomial basis representation.
Article 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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| http://dx.doi.org/10.1364/JOSAA.34.001844 | DOI Listing |
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