Phase Retrieval via Gain-Based Photonic XY-Hamiltonian Optimization

TL;DR

This paper introduces a novel photonic hardware-based method for phase retrieval from coded diffraction patterns, reformulating it as XY Hamiltonian minimization and demonstrating superior performance over existing algorithms.

Contribution

It presents a new approach using gain-based photonic networks to solve phase retrieval problems efficiently and scalably, leveraging physical mean-field dynamics.

Findings

Outperforms state-of-the-art RRR algorithm in medium-noise regimes

Maintains high accuracy as problem size increases

Offers fast, energy-efficient phase retrieval on photonic hardware

Abstract

Phase-retrieval from coded diffraction patterns (CDP) is important to X-ray crystallography, diffraction tomography and astronomical imaging, yet remains a hard, non-convex inverse problem. We show that CDP recovery can be reformulated exactly as the minimisation of a continuous-variable XY Hamiltonian and solved by gain-based photonic networks. The coupled-mode equations we exploit are the natural mean-field dynamics of exciton-polariton condensate lattices, coupled-laser arrays and driven photon Bose-Einstein condensates, while other hardware such as the spatial photonic Ising machine can implement the same update rule through high-speed digital feedback, preserving full optical parallelism. Numerical experiments on images, two- and three-dimensional vortices and unstructured complex data demonstrate that the gain-based solver consistently outperforms the state-of-the-art Relaxed-Reflect-Reflect (RRR) algorithm in the medium-noise regime (signal-to-noise ratios 10--40 dB) and retains this advantage as problem size scales. Because the physical platform performs the continuous optimisation, our approach promises fast, energy-efficient phase retrieval on readily available photonic hardware. uch as two- and three-dimensional vortices, and unstructured random data. Moreover, the solver's accuracy remains high as problem sizes increase, underscoring its scalability.