Unsupervised fringe pattern analysis based on regularized phase tracking

Deep learning has recently achieved remarkable success in fringe pattern analysis for optical metrology. However, most existing approaches rely on supervised learning with extensive labeled datasets that are costly to acquire, system-dependent, and often lack physical interpretability, thereby limiting their generalization and reliability in practical measurements. Here, we propose a physics-embedded unsupervised learning fringe pattern analysis framework based on regularized phase tracking (RPT-ulFPA). To provide physically meaningful inputs for the unsupervised fringe demodulation network, variational image decomposition and Hilbert spiral transform are employed to suppress background and modulation components, yielding phase-related orthogonal fringe representations. As a classic single-frame fringe demodulation method, regularized phase tracking (RPT) achieves continuous phase estimation without explicit unwrapping by jointly optimizing the photometric consistency and phase regularity constraints within spatial neighborhoods. In our method, the physical irradiance model and phase smoothness priors derived from RPT are formally embedded into the network loss function to leverage global continuous phase optimization rather than local iterative updates, thereby enabling more stable end-to-end phase recovery without any labeled data or pre-training. Furthermore, a two-step phase optimization strategy is introduced, where a reference-plane phase resolves single-frame phase ambiguity and a subsequent refinement step enables high-precision absolute phase recovery. Experimental results on both static and dynamic scenes demonstrate that RPT-ulFPA achieves accurate absolute phase retrieval from a single high-frequency fringe, enabling single-shot 3D reconstruction with accuracy comparable to multi-frame phase-shifting methods, while significantly outperforming conventional Fourier-transform-based approaches in noise robustness and data completeness. This work establishes a physics-consistent unsupervised learning paradigm for fringe pattern analysis by embedding well-defined physical priors into deep neural networks, offering a generalizable and interpretable solution for next-generation intelligent optical metrology.