"3-2-1" PMP: Adding an Extra Pattern to Dual-Band Phase Shift Profilometry for Higher Precision 3-D Imaging

Phase measurement profilometry, or PMP, is undergoing rapid development at present. Combined with defocused projection and advanced multiband phase shift (PS) algorithms, such as heterodyne and number theory, PMP with over thousand framerates has shown great potential in 3-D dynamic scene monitoring, e.g., manufacturing process monitoring and industrial digital twins. PMP's outstanding advantages include a combination of high lateral resolution, axial precision, and speed; however, the widely used dual-band PS algorithms have limited axial precision compared to low-efficiency tri-band algorithms. In this article, we propose "3-2-1" PMP, which optimizes the existing dual-band approach by adding an extra fringe pattern for projection acquisition to achieve similar precision performance as tri-band PMP. Associated stabilization algorithms in dealing with fringe blur, nonlinear camera responses, phase-jump errors, and related impact factors have also been investigated. Comparative simulation and experiments show that the "3-2-1" approach produces higher precision performance, with a 42%-85% root-mean-square error lower than general dual-band PS methods and famous Fourier transform profilometry ( \mu FTP), but using an equivalent projection pattern number of 6 or less.