On the inverse problem of source reconstruction from coherence measurements

TL;DR

This paper introduces a stable inversion method for reconstructing complex sources from coherence measurements of partially coherent light, leveraging a novel approximation formula and requiring minimal data.

Contribution

The authors develop a new stable inversion algorithm based on a closed-form approximation of coherence, enabling source reconstruction from limited coherence data in the Fresnel regime.

Findings

Successfully reconstructs complex sources in simulations

Demonstrates stability and efficiency with small data samples

Validates approach with experimental data

Abstract

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which uses the authors' recent closed-form approximation formula for the coherence of the propagated field. The developed algorithms require a small data sample for convergence and yield stable inversion by exploiting information in the coherence as opposed to intensity-only measurements. Examples with both simulated and experimental data demonstrate the ability of the proposed approach to simultaneously recover complex sources in different planes transverse to the direction of propagation.