Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry

In phase-shifting fringe projection profilometry, the luminance nonlinearity of the used projector has been recognized as one of the most crucial factors decreasing the measurement accuracy. To solve this problem, this paper presents a self-correcting technique that allows us to suppress the effect of the projector nonlinearity in the absence of any calibration data regarding the projector intensities or regarding the phase errors. In its first step, the standard phase-shifting algorithm is used to recover the phases, as well as the background intensities and the modulations. Using these results enables normalizing the fringe patterns, for ridding them of the effects of the background and modulations. Second, we smooth the calculated phase map by use of a low-pass filter in order to remove the ripple-like phase errors induced by the projector nonlinearity. Third, we determine a polynomial representing the projector nonlinearity by fitting the curve of the normalized fringe intensities against the cosine values of the smoothed phases. Finally, we correct the phase errors using the curve just obtained. Doing these steps in an iterative way eventually results in a phase map and, further, a 3D shape with their artifacts induced by the projector nonlinearity suppressed significantly. Experimental results demonstrate that this technique offers some advantages over others. It does not require a prior calibration of the projector, thus being suitable for dealing with a time-variant nonlinearity; its pointwise operation protects the edges and details of the measurement results from being blurred; and it works well with very few fringe patterns and is efficient in image capturing.