Analysis of the quality values of the residues in branch cut phase unwrapping algorithm

Identifying the residues is the most significant process in Goldstein's Branch Cut algorithm. The path-independent-integral criterion is a sufficient and unnecessary condition of residue identification. To overcome this shortcoming, this essay aims to analyze the phase quality of the residues. We find that on the aspect of position, the positions of the residues can typically show the distribution of the phase quality of the graph generally. We also find that on the aspect of the quality value, the quality values of the residues can help us figure out the phase quality of local regions. In a nutshell, analyzing the quality values of the residues can guide us to unwrap phases in a completely correct way.