Phase retrieval via gain-based photonic XY-Hamiltonian optimization

TL;DR

The paper presents a new method for solving phase retrieval problems using photonic networks, which outperforms existing methods in terms of speed and efficiency.

Contribution

The novel contribution is reformulating phase retrieval as an XY Hamiltonian minimization problem solvable via gain-based photonic networks.

Findings

The gain-based photonic solver outperforms the RRR algorithm in the medium-noise regime.

The method retains performance advantage as problem size increases.

The approach is suitable for optical parallelism and energy-efficient computation.

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 minimization 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.

Recovering missing phase from measured intensity is central to X-ray crystallography and diffraction imaging but is a hard, non-convex inverse problem. The authors reformulate coded diffraction pattern phase retrieval exactly as minimizing a continuous XY energy and solve it with gain-based photonic oscillator networks with efficient scaling and noise tolerance.

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