Phase retrieval via gain-based photonic XY-Hamiltonian optimization

Area of Science:

• Computational physics
• Optics
• Image processing

Background:

• Phase retrieval from coded diffraction patterns (CDP) is crucial for X-ray crystallography, diffraction tomography, and astronomical imaging.
• CDP recovery is a challenging, non-convex inverse problem that limits current applications.

Purpose of the Study:

• To reformulate the CDP recovery problem as a minimization of a continuous-variable XY Hamiltonian.
• To demonstrate the efficacy of gain-based photonic networks for solving this reformulated problem.

Main Methods:

• The study leverages coupled-mode equations from exciton-polariton condensate lattices and driven photon Bose-Einstein condensates.
• A spatial photonic Ising machine with high-speed digital feedback is utilized to implement the update rule, maintaining optical parallelism.

Main Results:

• The gain-based photonic solver consistently outperforms the state-of-the-art Relaxed-Reflect-Reflect (RRR) algorithm in medium-noise conditions (10-40 dB SNR).
• Performance advantages are maintained as problem size scales, demonstrated on diverse datasets including images, vortices, and complex data.

Conclusions:

• The proposed photonic approach offers a promising solution for fast and energy-efficient phase retrieval.
• Readily available photonic hardware can be employed for continuous optimization, advancing the field of phase retrieval.