Title: Holographic Phase Retrieval and Optimal Reference Design

This talk introduces a general mathematical framework for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a “reference” portion of a signal to be recovered via phase retrieval is a priori known from experimental design. A general formula is also derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis, which is then employed towards quantifying the performance of various known reference choices.

Based on insights gained from these results, a new “dual-reference” design is proposed which consists of two reference portions - being ``block'' and ``pinhole'' shaped regions - adjacent to the imaging specimen. Expected error analysis on data following a Poisson shot noise model shows that the dual-reference scheme produces uniformly superior performance over the leading single-reference schemes. Numerical experiments on simulated data corroborate these theoretical results, and demonstrate the advantage of the dual-reference design.