Phase Retrieval with Random Phase Illumination

TL;DR

This paper investigates the effectiveness of standard phasing algorithms with random phase illumination, demonstrating rapid convergence and high accuracy across various resolutions and noise conditions, with theoretical convergence guarantees.

Contribution

It provides a comprehensive numerical analysis of phase retrieval using RPI, establishing conditions for unique solutions and convergence of algorithms.

Findings

High-resolution RPI ensures unique solutions up to a global phase.

Standard algorithms converge rapidly without stagnation.

RPI with lower oversampling ratios suffices under certain image conditions.

Abstract

This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution RPI in the presence of additive as well multiplicative noises. It is shown that RPI with $\sigma=2$ is sufficient for phasing complex-valued images under a sector condition and $\sigma=1$ for phasing nonnegative images. The Error Reduction algorithm with RPI is proved to converge to the true solution under proper conditions.