Fourier phase retrieval using physics-enhanced deep learning

Fourier phase retrieval (FPR) aims to reconstruct an object image from the magnitude of its Fourier transform. Despite its widespread utility in various fields of engineering and science, the inherent ill-posed nature of the FPR problem poses a significant challenge. Here we propose a learning-based approach that incorporates the physical model of the FPR imaging system with a deep neural network. Our method includes two steps: First, we leverage the image formation model of the FPR to guide the generation of data for network training in a self-supervised manner. Second, we exploit the physical model to fine-tune the pre-trained model to impose the physics-consistency constraint on the network prediction. This allows us to integrate both implicit prior from training data and explicit prior from the physics of the imaging system to address the FPR problem. Simulation and experiments demonstrate that the proposed method is accurate and stable, showcasing its potential for wide application in fields utilizing the FPR. We have made our source code available for non-commercial use.