Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation

For three-dimensional shape measurement, phase-shifting techniques are widely used to recover the objective phase containing height information from images of projected fringes. Although such techniques can provide an accurate result in theory, there might be considerable error in practice. One main cause of such an error is distortion of fringes due to nonlinear responses of a measurement system. In this paper, a postprocessing method for compensating distortion is proposed. Compared to other compensation methods, the proposed method is flexible in two senses: (1) no specific model of nonlinearity (such as the gamma model) is needed, and (2) no special calibration data are needed (only the observed image of the fringe is required). Experiments using simulated and real data confirmed that the proposed method can compensate multiple types of nonlinearity without being concerned about the model.