Precise and Fast Phase Wraps Reduction in Fringe Projection Profilometry
  The number of phase wraps in 2D wrapped phase map can be completely eliminated, or greatly reduced by frequency shifting. But the wraps usually cannot be optimally reduced using the conventional fast Fourier transform (FFT) because the spectrum can be shifted only by an integer number in the frequency domain. In order to completely eliminate the phase wraps or achieve a significant phase wrap reduction, in this paper, we propose a fast and precise two-step method for phase wraps reduction, which uses the iterative local discrete Fourier transform (DFT) to determine the sub-pixel spectral peak location and the frequency shifting algorithm that operates in spatial domain to reduce the number of phase wraps. Firstly, an initial estimate of the frequency peak is obtain by FFT, then the sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial spectral peak location, further the non-integer frequency shifting in spatial domain is realized to eliminate or reduce the number of phase wraps. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results demonstrate the proposed method's superb computing efficiency, high resolution and overall performance. 
Minmin Wang, Guangliang Du, Canlin Zhou, Shuchun Si, Zhenkun Lei,   XiaoLei Li, YanJie Li
physics.ins-det physics.optics