Abstract

This Letter presents a novel, to the best of our knowledge, branch-cut algorithm for unwrapping phase maps acquired through fringe projection systems. The algorithm exposes second-order residues with vortex phase structures, computed from the original wrapped phase distribution using a second-order derivative that considers the wrap cycle. Remarkably, it reveals a consistent vorticity direction associated with these vortex structures, significantly facilitating branch-cut connections between residues, regardless of whether they carry the same or opposite charges. This innovative approach challenges a longstanding misconception in conventional branch-cut methods, which traditionally connected matched residues only when they had opposite charges. As a result, the algorithm provides a highly accurate methodology for explaining how phase behavior relates to surface characteristics. Its effectiveness is demonstrated through both computer simulations and practical experiments.

© 2024 Optica Publishing Group

Branch-cut algorithm for optical phase unwrapping

J. C. de Souza, M. E. Oliveira, and P. A. M. dos Santos
Opt. Lett. 40(15) 3456-3459 (2015)

Residue vector, an approach to branch-cut placement in phase unwrapping: theoretical study

Salah A. Karout, Munther A. Gdeisat, David R. Burton, and Michael J. Lalor
Appl. Opt. 46(21) 4712-4727 (2007)

Least-mean-squares phase unwrapping by use of an incomplete set of residue branch cuts

Igor V. Lyuboshenko, Henri Maı̂tre, and Alain Maruani
Appl. Opt. 41(11) 2129-2148 (2002)

Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms

Howard A. Zebker and Yanping Lu
J. Opt. Soc. Am. A 15(3) 586-598 (1998)

Phase unwrapping with the branch-cut method: role of phase-field direction

Bernd Gutmann and Herbert Weber
Appl. Opt. 39(26) 4802-4816 (2000)