Self-supervised model-driven deep learning for two-step phase-shifting interferometry

Data-driven deep learning methods are widely applied in interferometry. However, their performance depends heavily on the quality of the training datasets, which limits both accuracy and generalization. This Letter introduces a model-driven deep-learning approach for two-step phase-shifting interferometry. The framework first employs a pre-trained normalization network (PNNet) to normalize two interferograms with arbitrary phase shifts. Subsequently, an untrained model-driven network (UMNet) learns to generate phase maps and phase shifts from the normalized interferograms using a physics-based model-driven approach. During training, ground truth phase maps are not required; instead, the interferometric model enables self-supervised learning, resulting in accurate and robust phase retrieval. Compared with data-driven methods, this approach reduces errors by over 30%, demonstrating the potential of self-supervised, model-driven approaches in high-accuracy phase-shifting interferometry.