Design of temporal phase unwrapping algorithms

Phase unwrapping is an inevitable process in modern phase-evaluation based fringe analysis because the arctangent functions used in phase extraction only return phase module 2 pi. In recent years, several temporal phase unwrapping methods have been proposed, which use a couple of phase maps with different sensitivities for the unique determination of the unwrapped phase on a pixel-by-pixel basis. We have found that, however, some of them are not effectively designed, probably due to the lack of proper philosophy for guidance. In this paper; we present a generalized mathematical excess fraction method, which is more complete and general in nature and can be used to re-interpreted those temporal phase unwrapping algorithms in a unifying perspective. It is also demonstrated that more efficient and flexible algorithms can be designed-based on the principle of the generalized excess fraction method.