Spatial-temporal multiplexed phase coding with self-synthesized fringe-order correction for high-speed 3D shape...

We propose what we believe to be a novel fringe projection profilometry (FPP) framework tailored for high-efficiency and high-accuracy 3D shape measurement in dynamic environments. Conventional temporal phase unwrapping (TPU) techniques often rely on multiple encoded fringe patterns, which restrict their applicability in real-time scenarios. To address this limitation, we introduce a spatial-temporal multiplexed phase-coding strategy that decouples background intensity and modulation amplitude from phase-shifted components, enabling dense fringe-order encoding using only two complementary phase-coded patterns projected in successive frames. Furthermore, we develop a self-synthesized complementary fringe-order correction algorithm that leverages half-period spatial shifting and wrapped phase analysis to resolve boundary misalignments and suppress phase-jump artifacts. This correction is achieved via gradient-constrained local optimization, requiring no additional projections. Experimental results confirm the method's capability to suppress phase-jump errors at geometric discontinuities and under motion artifacts. The framework enables accurate absolute phase reconstruction using only four projected images per frame (three phase-shifted and one phase-coded) for dynamic measurement, and five images for static scenarios, significantly enhancing the real-time performance of 3D reconstruction in industrial and biomedical applications.