Theoretical model and experimental investigation on integrated calibration in MFPP with a bi-telecentric camera and a Scheimpflug projector

This work establishes a microscopic fringe projection profilometry (MFPP) system consisting of a bi-telecentric camera and a pinhole Scheimpflug projector to maximize the common focus area between them. Currently phase-height mapping (PHM) and stereoscopy (SV) based calibration approaches are still two representative families. The former generally relies on a precise translation stage accompanied by two separated procedures including the camera parameters calibration and the PHM process, making the calibration task relatively complicated and expensive in terms of required operation and devices. The latter only via a calibration target is relatively simple and low-cost to implement, but its accuracy fails to be guaranteed because it is difficult to undistort the projector by indirectly resorting to the camera. To cope with these issues, we propose a flexible integrated calibration (IC) solution for the especially designed 3D system while maintaining a high measurement accuracy and a low requirement of operation and devices. It implements a pixel-wise Look-Up-Table (LUT) 3D coordinate computation only via a low-cost calibration target. The phase artifacts of the dot target is addressed by phase optimization strategy. Furthermore, an optimization strategy is presented to exclude the measurement errors caused by projector’s distortion and Scheimflug projection structure. The proposed framework effectively simplifies the calibration procedure and reserves the reconstruction accuracy. Theoretical model of the calibration solution is mathematically derived, and rich comparative experiments imply that it is able to obtain an average height error of 7 μm around within the volume of 28 mm×23 mm×5 mm, as well as a standard deviation of plane fitting error better than 5 μm.