Fig. 1. Typical system diagram of the fringe projection profilometry

Fig. 2. Basic elements of the fringe projection profilometry and their internal relations. Here φ denotes the phase distribution; m is the 2D image coordinate; X is the 3D space coordinate; θ is the parameter vector containing multiple parameters

Fig. 3. Schematic diagram of the phase-to-height conversion. (a) Reference plane only; (b) 3D imaging for the object

Fig. 4. Schematic illustration of an arbitrarily arranged FPP setup^[35]

Fig. 5. Ray tracing of one pixel in FPP^[42]

Fig. 6. Camera model

Fig. 7. Determination of the homologous image coordinate in the projection pattern according to the orthogonal phase maps

Fig. 8. Schematic of the binocular stereo vision model

Fig. 9. Translating the calibration object attached dot matrix to acquire the calibration data^[47]

Fig. 10. Blocks gauges for system calibration^[52]. (a) Top view of the calibration gauges; (b) Representative fringe image; (c) Calibration regions; (d) 2D shape map; (e) 3D shape map

Fig. 11. System calibration of the hybrid phase-3D model

Fig. 12. System calibration of the stereo vision model

Fig. 13. Calibrating the FPP system with the BA strategy^[62]. (a) BA network consisting of different poses and benchmarks; (b) Details for the camera including the i^th pose and the j^th benchmark

Fig. 14. Automatic coding of the dot matrix. (a)-(c) Three dot matrix patterns that can realize automatic coding^{[85, 91, 97]}; (d) Result of automatic coding

Fig. 15. Results of 3D reconstruction. (a) Residual error of plane fitting^[61]; (b) Measured 3D shape of a step^[60]

Fig. 16. Gauge spheres and its measured shape. (a) Ceramic gauge sphere pair; (b) Measured 3D data corresponding to different poses

Fig. 17. Recommended arrangement of artefacts for determination of the sphere-spacing error^[101]

Fig. 18. Recommended arrangement of artefacts for determination of the flatness measurement error^[101]