Branch-cut algorithm for optical phase unwrapping

In this Letter, a proposal addressing the problem of two-dimensional phase unwrapping based on the theory of residues is presented. Here, wrapped phase maps with shifted phase jumps are used to balance residue charges. With this approach, we seek to minimize processing time and residue connection, which is essential in the development of branch-cut algorithms. Finally, a phase-unwrapping algorithm is applied to these wrapped maps, generated by Fourier transform profilometry to obtain three-dimensional profiles of objects illuminated by photorefractive moiré-like patterns generated in an experiment of real-time dynamic holography, and by fringe patterns generated with a Michelson interferometer.