Three-dimensional measurements based on multivariate gray code phase encoding

To address the problems of low efficiency, large error and high bit error rate in the phase unwrapping of high-frequency fringes by the traditional time-phase unwrapping method, in this paper we propose a phase coding method that quantizes the multivariate gray code in the phase domain. Instead of embedding the stepped phase into a sinusoidal pattern, we embed the multivariate gray code pattern into a sinusoidal pattern, which reduces the gray levels in the phase coding pattern to a larger extent and widens the longitudinal phase width between each step in the coding pattern. After the camera captures the deformed coding pattern, the deformed multivariate gray code is dequantified by the phase difference and the gray level, and the high-quality high-frequency ladder code word is obtained by decoding the quantized multivariate gray code. In addition, the step code word is superimposed with the binary wrapped phase and then filtered to obtain a correction code word for correcting the phase error. Through simulations and experiments, we comprehensively compare the proposed method with various classical phase unwrapping methods. The effectiveness of the proposed method is verified in terms of the decoding error, the measurement effect, and the projection pattern.