Fig. 1. Diagrams of the physics-driven method, physics-informed deep learning approach, and data-driven deep learning approach for fringe pattern analysis.

Fig. 2. Overview of the proposed PI-FPA. (a) PI-FPA including a LeFTP module and a lightweight network. (b) Net head and Net tail. (c) The phase retrieval process of the LeFTP module.

Fig. 3. Comparative results for single-shot fringe pattern analysis of the David model. (a–e) The phase retrieval process, wrapped phases, phase errors, and magnified views of the phase errors using FTP, LeFTP, Net head + LeFTP, U-Net, and PI-FPA.

Fig. 4. Comparative fringe analysis results of the industrial part. (a) The industrial part and the phase errors using FTP, U-Net, and PI-FPA. (b) The magnified views of the phase errors. (c) Single-shot 3D imaging results using different methods. (d) The magnified views of (c). (e) The line profiles in (d).

Fig. 5. Precision analysis for a ceramic plane and a standard sphere moving along the Z axis. (a) 3D reconstruction results using PI-FPA at different time points. (b–c) the error distributions of the sphere and plane. (d–e) temporal precision analysis results of the plane and sphere over a 1.62 s period using 3-step PS, FTP, U-Net, and PI-FPA. (f–i) the color-coded 3D reconstruction and the corresponding error distributions of the plane and the standard sphere using different methods at T = 0.81 s.

Fig. 6. Fast 3D measurement results using different fringe pattern analysis methods. (a) The representative fringe images at different time points and the corresponding color-coded 3D reconstructions results for the rotated workpiece model using 3-step PS, FTP, U-Net, and PI-FPA. (b) The representative fringe images at different time points and the corresponding color-coded 3D reconstructions results for non-rigid dynamic face using 3-step PS, FTP, U-Net, and PI-FPA. (c) 360-degree 3D reconstruction of the workpiece model using PI-FPA. (d) 3D measurement results of non-rigid dynamic face using PI-FPA.