Holographic Phase Retrieval and Reference Design
David A. Barmherzig, Ju Sun, T. J. Lane, Po-Nan Li, Emmanuel J. Candès
TL;DR
The paper addresses holographic phase retrieval by introducing a framework that integrates a known reference into coherent diffraction imaging, converting the reconstruction into a linear deconvolution problem. It formulates the Referenced Deconvolution algorithm, derives an explicit error expression under Poisson shot noise, and introduces a reference-scaling factor to compare reference choices. Through analysis of three canonical references (pinhole, slit, block), it shows how spectral weighting differs across references and demonstrates optimality swings depending on the signal spectrum, with numerical simulations validating the theory. The findings offer a practical design perspective for reference selection in CDI, enabling faster, provably reliable reconstructions under realistic noise, and motivate extensions such as dual-reference designs and beamstop accommodations.
Abstract
A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered via phase retrieval is a priori known from experimental design. A generic 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. We employ this optimization perspective towards quantifying the performance of various reference choices.