Generalized Technique for Separating Nonsinusoidal Errors in Fringe Projection Profilometry With Arbitrary Phase Shifts

In phase-shifting fringe projection profilometry, the nonsinusoidal profile of fringes is one of the most crucial error-inducing factors. Especially, when using nonuniform phase shifts, the complex response of the phase-shifting algorithm to fringe harmonics makes the nonsinusoidal errors difficult to eliminate. To overcome this problem, this article analytically deduced a general phase error function related to the fringe harmonics when using arbitrary phase shifts and then exploited this function to derive a blind method for separating the nonsinusoidal errors from the measured phase maps. In implementation, this method calculates a coarse phase map first by using the least-squares algorithm from captured fringe patterns and then filters this calculated phase map to isolate its artifacts caused by the nonsinusoidal errors. By fitting these isolated artifacts to the phase error function with the outliers excluded using the three-sigma criterion, the coefficients related to the fringe harmonics are estimated. Using these coefficients allows one to compensate for the nonsinusoidal errors at each pixel through fixed-point iterations or, more efficiently, by using a postestablished look-up table. This proposed method offers several merits over others. First, by taking advantage of the model with arbitrary phase shifts, this method is flexible in practical measurements that may use various types of light sources and phase-shifters. Meanwhile, it has generality in principle, making it easy to derive a simplified error-suppressing algorithm adaptive to a special case of using uniform or selected nonuniform phase shifts. Second, it is a purely blind method that allows users to eliminate the effects of fringe harmonics depending on very few (e.g., 3 or 4) fringe patterns without a calibration or a priori knowledge of the light source. Third, it effectively preserves edges and detailed features of the measured surface from being blurred. The effectiveness and feasibility of this suggested method have been demonstrated through simulation and experimental results.