Spatiotemporal fringe pattern analysis using physics-informed deep learning

In optical metrology, particularly in phase-measuring profilometry techniques, achieving both high measurement accuracy and high temporal resolution remains a long-standing challenge. For high-speed dynamic measurements, many existing methods still adopt a frame-by-frame processing strategy, tending to overlook the rich temporal information embedded across adjacent frames. This constraint makes it difficult to maintain robust performance under ultra-short exposure conditions. Taking fringe projection profilometry (FPP) as a representative example, we propose a physics-informed spatiotemporal fringe pattern analysis (PIST-FPA) framework that unifies physical modeling with deep learning for high-speed, high-fidelity three-dimensional (3D) reconstruction. Rather than processing each frame independently, PIST-FPA jointly analyzes a short sequence of fringe images within a temporal window, exploiting both spatiotemporal correlations and physics-based priors. PIST-FPA incorporates a background-estimation network for illumination correction, a physics-guided optical-flow alignment for motion compensation, and an attention-enhanced U-Net for spatiotemporal phase demodulation, forming a unified and interpretable learning-based processing pipeline. This hybrid paradigm effectively decouples object motion from surface morphology, enabling accurate and temporally consistent phase retrieval even under ultra-short exposure and low-signal-to-noise conditions. Both synthetic and real experiments at 10,000 frames per second demonstrate that PIST-FPA substantially outperforms both the conventional Fourier transform method and single-frame deep-learning method in terms of accuracy, robustness, and spatiotemporal consistency. By bridging physical modeling and data-driven learning in a unified spatiotemporal framework, PIST-FPA establishes a generalizable paradigm for physics-informed dynamic optical metrology, paving the way for next-generation high-speed phase-measuring profilometry and intelligent optical instrumentation.