Phase-to-depth calibration in fringe projection profilometry based on blockwise surface fitting

Abstract

A new classification method is proposed in this paper which categorizes the phase-to-depth calibration methods for fringe projection profilometry into pixel-dependent (P-D) ones and pixel-independent (P-I) ones. In P-D methods, depth is expressed as a function of the unwrapped phase, and parameters of the function are different from pixel to pixel. In P-I calibration methods, depth is expressed as a function of both phase and pixel coordinate, and there is only one set of parameters which applies to all pixels. P-D method is resistant to distortion of the projector or the camera but is time-consuming because a number of phase maps need to be recorded; P-I method requires only two or three phase maps but is sensitive to distortion. To address this problem, we further propose a blockwise calibration method. It requires the same number of phase maps as the P-I method and meanwhile can be as resistant to distortion as the P-D method. Simulation results show that when phase maps are contaminated by random additive noise, error produced by the proposed blockwise method is even less than that of the P-D method which uses 18 phase maps. In the experiment the proposed method and the P-D method were utilized to calibrate a fiber-optic fringe projection profilometer and then heights of a 4 mm and a 7 mm gauge block were measured. Difference between results of the two methods was less than the accuracy of the translation stage (0.01 mm), which verified the effectiveness of the proposed method.