Aiding phase unwrapping by increasing the number of residues in two-dimensional wrapped-phase distributions

In phase unwrapping residues are points of locally inconsistent phase that occur within a wrapped-phase map, which are usually regarded as being problematic for phase-unwrapping algorithms. Real phase maps typically contain a number of residues that are approximately proportional to the subsequent difficulty in unwrapping the phase distribution. This paper suggests the radical use of the discrete Fourier transform to actually increase the number of residues in 2D phase-wrapped images that contain discontinuities. Many of the additional residues that are artificially generated by this method are located on these discontinuities. For example, in fringe projection systems, such phase discontinuities may come from physical discontinuity between different parts of the object, or by shadows cast by the object. The suggested technique can improve the performance of path independent phase-unwrapping algorithms because these extra residues simplify the process of setting the branch cuts in the wrapped image based on the distance to the nearest residue. The generated residues can also be used to construct more reliable quality maps and masks. The paper includes an initial analysis upon simulated phase maps and goes on to verify the results on a real experimental wrapped-phase distribution.