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.
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