Phase retrieval via media diversity

TL;DR

This paper introduces a novel phase retrieval method using media diversity, enabling unique phase recovery from multi-plane intensity data without boundary conditions, supported by explicit algorithms and numerical validation.

Contribution

It demonstrates that media diversity allows for unique phase retrieval without boundary constraints and provides explicit reconstruction algorithms.

Findings

Unique phase retrieval achieved with multiple media

No boundary conditions needed for phase in incidence plane

Algorithms validated through numerical simulations

Abstract

This work studies phase retrieval for wave fields, aiming to recover the phase of an incoming wave from multi-plane intensity measurements behind different types of linear and nonlinear media. We show that unique phase retrieval can be achieved by utilizing intensity data produced by multiple media. This uniqueness does not require prescribed boundary conditions for the phase in the incidence plane, in contrast to existing phase retrieval methods based on the transport of intensity equation. Moreover, the uniqueness proofs lead to explicit phase reconstruction algorithms. Numerical simulations are presented to validate the theory.