Are Residues of Primary Importance in Phase Unwrapping?

Conclusions

In discrete phase maps, phase inclusions and residues are inseparably linked with phase inclusions being of primary importance and residues indicating where phase inclusions lie. Phase inclusions result when noise in the phase measurement combines with the gradient of the phase being measured to create steps greater than π that must not be unwrapped. Phase inclusions, unlike residues, cannot be used to guide phase unwrapping; however, residues are inadequate because they do not clearly define the locations of phase inclusions. In general, then, it is better to use methods that do not rely on residues for phase unwrapping. To date, it would appear that there are only two such methods, which are cited in refs. 2 and 3. Of these, we recommend the method of ref. 2, which calculates unwrap regions based upon the idea that the locations of phase wraps depend upon the phase reference used in the arctangent calculation whereas the locations of phase inclusions do not. These unwrap regions are then used to guide the unwrapping process in a way that guarantees that phase inclusions will be ignored.