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We generalize the analytical form of the orthonormal elliptical polynomials for any arbitrary aspect ratio to arbitrary orientation and give expression for them up to the 4th order. The utility of the polynomials is demonstrated by obtaining the expansion up to the 8th order in two examples of an off-axis wavefront exiting from an optical system with a vignetted pupil.
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Díaz et al. (2014) studied this question.
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