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Phase diversity wavefront sensing (PDWFS) is concerned with estimating aberration coefficients from multiple images collected with known differences in pupil phase. Using previous work by other authors, the Cramer-Rao lower-bound (CRLB) expression for the phase diversity aberration estimation problem is developed, generalized slightly to allow for multiple diversity images, various beamsplitting configurations, and the imaging of extended objects. The CRLB for a given problem depends on the actual value of the aberration being stated. Therefore, we turn to numerical simulation and a Monte Carlo analysis of the CRLBs of an ensemble of simulated aberration phase screens and draw tentative conclusions about various phase diversity imaging situations. The 'average' CRLB value for a given phase screen ensemble and imaging scenario is used as a figures of merit in comparing various PDWFS configurations. For simulated point-source imaging, we quantify the impact of varying the amounts of focus diversity, both symmetrically to both images, and asymmetrically, to a single image. We find reason to believe that a symmetrically defocused image collection scheme may be more advantageous for PDWFS. We also explore the impact of splitting the light among two images asymmetrically, as well as splitting the light among three images. Deviations from a traditional 50-50 beamsplit among 2 images are shown to be disadvantageous in a CRLB sense.Finally we verify that CRLB values are orders of magnitude higher for imaging of an extended object, when compared to point-source PDWFS imaging.
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