Physics‐Embedded End‐To‐End Differentiable Framework for High‐Precision and Robust Interferometry

Abstract

Interferometric phase retrieval is fundamental to high‐precision optical metrology, yet reconciling the expressive power of deep learning with the global physical consistency required for phase reconstruction remains a fundamental challenge. Here, we propose a physics‐embedded, end‐to‐end differentiable framework (PE‐E2ED) that reformulates two‐frame phase retrieval as a physics‐constrained learning problem. Instead of treating phase unwrapping as a decoupled post‐processing step, we embed a weighted least‐squares (WLS) phase unwrapping solver as a differentiable physical layer within the network, enabling global phase integrability to be enforced during training. To enhance robustness against noise and fringe occlusion, a Bayesian‐inspired uncertainty estimation module predicts pixel‐wise reliability and translates it into confidence weights that guide the WLS solver. In parallel, large‐kernel sensing and cross‐attention mechanisms are employed to capture long‐range fringe dependencies, while a physics‐informed curriculum learning strategy stabilizes the training process. Extensive simulations and real point‐diffraction interferometry experiments demonstrate that the proposed framework achieves high reconstruction accuracy, strong structural robustness, and effective zero‐shot generalization from synthetic to real data. This work establishes a physics‐embedded end‐to‐end paradigm for high‐precision interferometric phase retrieval. The code is available at https://github.com/srzzz76/PE‐E2ED .