Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters

Fringe projection profilometry (FPP) technology is an important method for 3D reconstruction. In this paper, we proposed a flexible calibration method of an FPP system based on the imaging principle and geometrical structure of the system. The target coordinates are only related to its pixel coordinates and phase. First, the fringe images are projected onto the calibration plate, and the phase can be calculated through the four-step phase-shifting method. Then, the pixel coordinates of the feature points can be located with the binarized fringe images and the centroid method. Finally, the calibration parameters are calculated by the nonlinear least-squares method (NLSM). The reconstructed experiment of 162 testing points was carried out, and the result shows that the maximum relative errors on coordinates X, Y, and h are 0.27%, 0.42%, and 0.59%, respectively. The other two surface reconstruction experiments also verify the feasibility of the calibration method.