The pupil of a human eye is slightly elliptical . The pupil for off-axis imaging by a system with an axial circular pupil may be vignetted, but can be approximated by an ellipse. When a flat mirror is tested by shining a circular beam on it at some angle (other than normal incidence), the illuminated spot is elliptical. Similarly, the overlap region of two circular wavefronts that are displaced from each other, as in lateral shearing interferometry or in the calculation of the optical transfer function of a system, can also be approximated by an ellipse.
Starting with the pupil function of a system with an elliptical pupil, we scale the coordinates of a point on the pupil and transform it to a circular pupil. The aberration-free PSF and OTF are then obtained as for a system with a circular pupil. The corresponding PSF and OTF obtained by unscaling the coordinates represent the results for the elliptical pupil. Then we discuss the polynomials that are orthonormal over and represent balanced classical aberrations for a unit elliptical pupil. These polynomials cannot be obtained by scaling the coordinates of the Zernike circle polynomials. The balancing of a Seidel aberration over an elliptical pupil is discussed, and its standard deviation with and without balancing is determined.
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