We obtain a closed-form analytical expression for the aberration-free point-spread function (PSF) of a system with a hexagonal pupil. The six-fold symmetric PSF consists of a nearly circular bright spot at the center surrounded by a thin dark ring and two each nearly hexagonal bright and dark rings, while maintaining the six-fold symmetry. Beyond that the PSF breaks into six diffraction arms, each of alternating bright and dark strips and normal to a side of the pupil, with some dim structure between two consecutive arms. The ensquared power of the PSF and the optical transfer function are calculated and compared with the corresponding quantities for a system with a circular pupil. The balancing of Seidel aberrations is illustrated and their standard deviations with and without balancing are discussed. The Strehl ratio of these aberrations is plotted as a function of the standard deviation and compared with the approximate expression based on the aberration variance.
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