Nonlinear phase error compensation for fringe deflectometry measuring system

Fringe deflectometry technique (FDT) plays a more and more important role in specular surface measurement due to its large slope measurement range. However, its accuracy is heavily dependent on the quality of the extracted phase. The gamma effect of liquid crystal display (LCD) and CCD introduces significant phase distortion, resulting in a periodical phase error and measurement error. A mathematical model is established to illustrate phase error introduced by gamma effect, and an optimal algorithm based on four-time four-step phase-shifting (FFPS) is proposed to retrieve phase. Simulation results prove that FFPS phase retrieval method can compensate for the phase error caused by the nonlinearity of the LCD and CCD point-by-point, thus it is immune not only to calibration error, but also to the non-unitary of the gamma effect spatially and temporally. Experimental results are also presented to verify the performance of the proposed method.