Diversity selection for phase-diverse phase retrieval

Wavefront-sensing performance is assessed for focus-diverse phase retrieval as the aberration spatial frequency and the diversity defocus are varied. The analysis includes analytical predictions for optimal diversity values corresponding to the recovery of a dominant spatial-frequency component in the pupil. The calculation is shown to be consistent with the Cramér-Rao lower bound by considering a sensitivity analysis of the point-spread function to the spatial frequency being estimated. A maximum value of diversity defocus is also calculated, beyond which wavefront-sensing performance decreases as diversity defocus is increased. The results are shown to be consistent with the Talbot imaging phenomena, explaining multiple periodic regions of maximum and minimum contrast as a function of aberration spatial frequency and defocus. Wavefront-sensing performance for an iterative-transform phase-retrieval algorithm is also considered as diversity defocus and aberration spatial frequency are varied.