Probability-distribution-based Gamma correction method in fringe projection profilometry

This paper proposed a Gamma effect correction method based on the probability distribution function (PDF) for suppressing phase nonlinearity error in fringe projection profilometry. In this work, the periodicity of phase with Gamma effect is first analyzed, and nonlinear wrapped phase is modeled as superposition of normal wrapped phase with a sinusoidal function. Afterwards, a series of reference phases with Gamma factors ranging from 1 to 3 is constructed and the corresponding PDF is calculated. Then the optimal precoding factor γp of projected fringe is obtained by applying Jensen-Shannon (JS) divergence matching between the PDF of measured phase and constructed reference phases. In simulations, the availability of proposed method is investigated, where RMSE decreases from 0.218rad to 0.016rad. In experiments, the turbine blade is tested and compared with calibrated values where RMS of measured deviations after correction has decreased from 0.269mm to 0.095mm. All the investigations have proved the high reliability of proposed method.