# Holographic Phase Retrieval and Reference Design

## TL;DR

This paper introduces a comprehensive mathematical framework and algorithm for holographic phase retrieval, focusing on optimizing reference design and analyzing performance under Poisson shot noise in holographic imaging.

## Contribution

It develops a general recovery algorithm and a formula for expected error, enabling optimized reference design in holographic phase retrieval.

## Key findings

- Derived a generic formula for recovery error under Poisson noise
- Quantified performance of different reference choices
- Provided a new optimization perspective for reference design

## 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.