Gamma correction for two step phase shifting fringe projection profilometry

In this paper, for two step phase shifting fringe projection profilometry (PSP), we analyze the nonlinear intensity response caused by the gamma distortion effect of a digital projector and a digital camera which leads the captured fringe patterns to be non-sinusoidal waveforms, therefore for the three-dimensional measurement an error will be introduced. Then we combine the two step PSP with a pre-coding gamma correction method to attenuate the gamma distortion effect. The traditional pre-coding gamma correction method proposed for three step PSP is based on a simplified one-order gamma model to find an appropriate pre-coding gamma value, but the result is not so reliable like many previous works show. We propose a simple and robust way to calculate an appropriate pre-coding gamma value for the two step PSP. The resolved value is very close to experiment result. When applying the appropriate pre-coding gamma value to the projected sinusoidal fringe patterns, the measurement error of the two step PSP can be significantly reduced.