The principles of proper placement of branch cut in phase unwrapping using combined and extended methods based on residue searching

Phase of backscattered signals is used in various systems such as digital elevation model and detecting topographic change. Phase of received signal is circular and varies only between 0 and 2π radians. Thus, an ambiguity emerges when phase exceeds 2π radians. In such cases, ambiguity needs to be corrected in a process known as phase unwrapping. The present study uses algorithms including Goldstein, quality-guided, mask cut and least squares for phase unwrapping and a systematic, combined and extended method is presented. We investigate the required conditions to have paired residues since these residues are highly useful for proper placement of branch cut. The main challenge for this study is the proper placement of branch cut which is used to prevent path dependence in phase unwrapping. To achieve this, the present work makes use of combined and extended method to investigate the principles of branch cuts.