A ternary complementary Gray code phase unwrapping method in fringe projection profilometry

Abstract

This paper proposes a phase unwrapping method based on ternary Gray code in fringe projection profilometry. This method does not require additional projection images or any prior knowledge. It accurately determines the segmentation thresholds of the ternary Gray code using only the average intensity and intensity modulation calculated from phase-shifting fringes, effectively reducing projection costs and achieving lower codeword errors. Additionally, a segment selection strategy suitable for the ternary Gray code is proposed. By employing the complementary method, three sets of candidate orders with certain codeword shifts can be generated. The wrapped phase is then divided into three segments: upper, middle, and lower segments, and correspondingly matched with the central regions of the three sets of candidate orders, thus enabling the solution of the absolute phase. Through the segment selection strategy, error-prone areas at the edges of orders are effectively avoided, further enhancing the accuracy of measurement results. Compared to the binary Gray code, the ternary complementary Gray code can encode up to 3m−1 orders when the number of Gray code patterns is m; when the required number of encoding orders is K, only ⌈log3K⌉+1 Gray code patterns are needed. Its additional value capacity precisely enables it to encode more orders, thereby increasing the frequency of phase-shifting fringes and further enhancing measurement efficiency. A series of experiments validates the feasibility, robustness, and superiority of this method.