Photon-limited bounds for phase retrieval.

TitlePhoton-limited bounds for phase retrieval.
Publication TypeJournal Article
Year of Publication2021
AuthorsTJ Schulz, DJ Brady, and C Wang
JournalOptics Express
Start Page16736
Pagination16736 - 16748
Date Published05/2021

We show that the optimal Cramér-Rao lower bound on the mean-square error for the estimation of a coherent signal from photon-limited intensity measurements is equal to the number of signal elements, or the number of signal elements minus one when we account for the unobservable reference phase. Whereas this bound is attained by phase-quadrature holography, we also show that it can be attained through a phase-retrieval system that does not require a coherent reference. We also present the bounds for classic phase-retrieval and ptychography, and show that practical coding strategies can approach optimal performance.

Short TitleOptics Express