Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

Fringe projection profilometry (FPP) using a digital video projector is widely used for three-dimensional shape measurement. However, the gamma nonlinearity, system vibration, and noise cause the captured fringe patterns to be nonsinusoidal waveforms and have a grayscale deflection from their true value. This leads to an additional phase measurement error for a general phase-shifting algorithm. Based on the theoretical analysis, we propose a method to eliminate the phase error considering two factors. In this method, four-step phase-shifting is done four times with an initial phase offset of 22.5 deg and the average of these four phase maps precisely results in the real phase. As a result, phase error caused by gamma nonlinearity can be effectively suppressed. In addition, every image in phase shifting is replaced by the average of 20 fringe images continuously captured at the same state to avoid the phase error caused by system vibration and noise. Experimental results show that this method is effective in eliminating the phase error in practical phase-shifting FPP. In general, more than 90% of the phase error can be reduced.