Variable-Frequency Phase Unwrapping for High-Speed 3-D Shape Measurement

Phase unwrapping plays a critical role in digital fringe projection (DFP) 3-D measurements. The phase unwrapping methods based on geometric constraints require no additional patterns, achieving superior efficiency and accuracy. However, our study reveals that existing methods suffer from a depth range imbalance (DRI) problem, leading to unwrapping failure and measurement error. This article presents a variable-frequency fringe pattern to address this problem. Unlike artificially defined constant-frequency fringes, we quantify the measurement depth range and theoretically determine the optimal fringe frequency according to the system parameters. Based on this, we propose a variable-frequency phase unwrapping (VFPU) method for high-speed 3-D shape measurement. The proposed method overcomes the DRI problem and maximizes the measurement accuracy and robustness. Extensive experimental results demonstrate the superiority of the proposed method in high-speed 3-D shape measurements.