  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.
