Phase retrieval employs very simple data collection hardware and iterative algorithms to determine the phase of an optical field. We have derived limitations on phase retrieval, as applied to optical surface and wavefront metrology, in terms of the speed of beam (i.e., f-number or numerical aperture) and amount of aberration using arguments based on sampling theory and geometrical optics. These limitations suggest methodologies for expanding these ranges by increasing the complexity of the measurement arrangement, the phase-retrieval algorithm, or both. We have simulated one of these methods where a surface is measured at unusual conjugates.
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