Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration: comment

摘要

Recently, Hasan and Shaker published a set of orthonormal polynomials for an annular elliptical pupil obtained by the Gram-Schmidt orthogonalization of the Zernike circle polynomials [Appl. Opt. 51, 8490 (2012)]. However, the expressions for many of the polynomials are incorrect, apparently due to wrong usage of the Gram-Schmidt orthogonalization process. We provide the correct equations for the orthogonalization process and the expressions for the orthonormal polynomials obtained by applying them.