Gray-code fringe order jump error self-correction based on shifted phase encoding for phase measuring profilometry

Temporal phase unwrapping based on Gray-code method (TPU-GC) has prospective application in three-dimensional (3D) shape measurement due to its high-speed measurement and high-efficiency code. Currently, it is still an essential task to remove jump error that may be caused by edge ambiguity of Gray-code pattern or uneven reflectivity of the measured object. So, a Gray-code fringe order jump error self-correction method based on shifted phase encoding (FOSC-SP) is proposed. By changing the calculating sequences of N-step phase-shifting patterns, a series of wrapped phases with a shifted phase of 2π/N can be obtained to identify the 2π discontinuities uniquely. The fringe order error caused by the misalignment between the edges of fringe order and the 2π discontinuities can be located and then corrected accurately. Subsequently, the fringe order caused by uneven reflectivity can be identified by the difference map of wrapped phase and the primary unwrapped phase without edge fringe order error, and then eliminated by a statistical method. Experimental results demonstrate the feasibility and validity of the proposed method. It performs good anti-noise capability and robustness to correct the above two kinds of jump errors in TPU-GC and it is also a generalized correct method that can be used to others TPU, such as multi-frequency and phase-coded methods.