Photon-limited bounds for phase retrieval

We show that the optimal Cramer-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. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Automated summary

In this study, we investigated the optimal Cramer-Rao lower bound on the mean-square error for estimating a coherent signal from photon-limited intensity measurements. We found that this bound can be achieved through specific systems, such as phase-quadrature holography. Additionally, we demonstrated the bounds for classic phase-retrieval and ptychography, highlighting that practical coding strategies can approach optimal performance.