Robust phase-coding method for absolute phase retrieval

Phase-coding method has been widely used for absolute phase retrieval in fringe projection profilometry (FPP). However, the robustness and the accuracy is severely affected by the gamma nonlinearity of FPP system. The wrapped phase extracted from distorted fringe patterns will deviate from the actual phase, which cannot be directly employed to retrieve the absolute phase. To address this problem, a robust phase-coding method based on an effective nonlinear correction strategy was proposed. First, the distorted wrapped phase could be adjusted by the phase histogram equalization (PHE) method to obtain the corrected wrapped phase. Theoretical studies demonstrated that the frequency of the nonlinear phase error is thrice that of the ideal phase. Therefore, the nonlinear phase error was further reduced by shifted-phase histogram equalization (SHE) method. Then, the continuous function was fitted by the Hermite interpolation algorithm, which could reduce the discretization error introduced by the SHE method. Both the simulation and experimental results show that the proposed method is more robust than the traditional method under gamma nonlinearity.