Simple and geometrically unconstrained method for phase-3D model calibration

The calibration process of converting from phase information into three-dimensional information is an essential and critical step, in fringe projection profilometry based on projectors and monocular cameras. The existing phase-height model only obtains the height information, while the triangular stereo model treats the projector as an inverse camera, and both the camera and the projector need to be calibrated. To this end, a simple and geometrically constraint-free new calibration method that combined the phase-height model and the triangular stereo model was proposed. Firstly, based on the Zhang Zhengyou's plane calibration method, the internal and external parameters of the camera were calibrated on a zero-height experimental optical displacement stage. Then, based on the height of the calibration plate, the experimental optical displacement information, and the absolute phase information of the corresponding height, the Levenberg-Marquardt algorithm was used to realize the solution of the phase-height nonlinear model. Finally, based on the camera imaging model and the height information, the x and y coordinates were calculated to obtain the three-dimensional geometric information. The proposed calibration method has no geometric constraints and avoids projector calibration, and the root mean square error (RMSE) is 0.082 2 mm after experimental evaluation.