Monotonic phase coding with dynamic boundary alignment for high-speed 3D profilometry

This study explores the important balance between efficiency and robustness in temporal phase unwrapping (TPU) for fringe projection profilometry (FPP). Traditional phase-coding techniques require multiple coded patterns to accurately determine fringe orders, which limits their use in high-speed dynamic measurements. We introduce a robust framework that employs three phase-shifting patterns alongside a single coded pattern to achieve accurate absolute phase retrieval. Initially, a monotonic encoding strategy reorganizes the phase sequences, dividing the projected field into complementary regions with monotonicity of the phase, thus broadening the coding range to cover the entire domain. Next, a gradient-constrained local search (GCLS) algorithm dynamically aligns codeword edges with phase discontinuities by utilizing localized boundary detection and making specific adjustments for each region. Our experimental findings indicate a 66% reduction in the number of projected patterns compared to traditional phase-coding methods, all while maintaining submillimeter accuracy.