Gamma Calibration and Phase Error Compensation for Phase Shifting Profilometry

Phase Shifting Profilometry is a method of structured light whose three-dimensional reconstructions are susceptible to error from Gamma distortion. In practice, the luminance nonlinearity caused by the Gamma distortion effect of a digital video projector and a digital camera yields undesired fringe intensity changes, which substantially reduce the measurement accuracy, and while the effects of the Gamma distortion diminish with an increasing number of employed phase-shifting patterns. A Gamma calibration method expressed as Fourier series and binomial series theorem is proposed to reduce the measurement error caused by the Gamma distortion. After Gamma calibration, the Gamma distortion effect is attenuated and the accuracy is enhanced. The linear least square is compensated the phase error of absolute phase still existing after Gamma calibration. To verify the presented method in this paper, a profilometry experimental system is constructed using digital video projector and CCD camera. The experiment results shown that, the Gamma calibration reduce the maximum phase error of absolute phase by 75.0%. After the linear least square compensation, the maximum phase error is only 5.9% of without any Gamma calibration or phase compensation. The reconstruction surface of a complex curve surface is hardly any waviness, which is clearly noted in the reconstruction of the same tested object without any correction or compensation.