Phase-retrieval algorithms have been used for wave-front sensing to determine the aberrations of an optical system from system point-spread functions (blurred images of point sources). Previously, computationally efficient algorithms were developed and applied to data from the Hubble Space Telescope [Appl. Opt. 32, 1737 (1993); Appl. Opt. 32, 1747 (1993)], but those algorithms, which employ analytic expressions for the gradient of an error metric, required narrow-band light and adequately sampled images. Generalizations of those phase-retrieval algorithms, which accommodate broadband light, allow for undersampled images, permit fitting of multiple images simultaneously, and have a flexible description of the aberrations, are described in this study.
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