High-frequency average phase compensation method for gamma nonlinearity based on optimal-frequency strategy

Abstract The accuracy of fringe projection phase-shifting profilometry (PSP) is affected by gamma nonlinearity greatly, and the average phase compensation method is an effective technique to reduce the nonlinear error. However, double fringe patterns are commonly required, especially combined with the multi-frequency phase unwrapping method (MFPU), using 6 × 3 images in three-frequency method, which limits the measurement efficiency. To reduce the number of required images, this paper presents an efficient average phase compensation method using 6 f h +3 f l +3 f u algorithm based on an optimal-frequency strategy. Six high-frequency standard and π /3 shifted 3-step phase-shifting fringe patterns are used together to generate high-accuracy wrapped phase. Three unit-frequency and three low-frequency fringe patterns are used to obtain coarse unit-frequency wrapped phase and a coarse low-frequency wrapped phase, respectively. To ensure the robust phase unwrapping for high-frequency phase, the mathematical model of the optimal frequency is derived and determined by phase error amplitude calculation. Simulation and experimental results verified that only applying average phase compensation under the guidance of optimal-frequency selection strategy could achieve robust phase unwrapping and high-accurate measurement by reducing the nonlinear error substantially.