An improved gray-level coding method for absolute phase measurement based on half-period correction

Abstract Absolute phase retrieval is important for three-dimensional (3D) shape measurement in fringe projection technique. Numerous phase unwrapping methods have been proposed for addressing this issue, and gray-level is one such technique employed to determine fringe orders for wrapped phase. However, the codeword detection can fail due to random noise or cameras/projectors defocus. We propose an improved method to determine the codewords in this paper. Specifically, three sinusoidal fringe patterns are used to obtain the wrapped phase and three n-ary gray-level (nGL) patterns are employed to obtain the fringe order. Two opposite masks can be calculated through wrapped phase binarization. The masks and the nGL patterns are roughly used to obtain codewords. After half-period correction, the codeword is accurately reconstructed, and the fringe order is also determined. Simulations and experiments demonstrated the robustness and effectiveness of the proposed algorithm to measure isolated objects with complex surfaces.