Novel four-step phase shifting algorithm based on the products of sines and cosines

Wrapped phase extraction is an essential process for the retrieval of absolute phase and even the computation of object height information in fringe projection profilometry. Over the past few decades, tremendous efforts have been devoted to developing various techniques for computing wrapped phase. By comparison, four-step phase-shifting techniques play an important vehicle for obtaining the wrapped phase of 3D objects. At present, a variety of four-step phase-shifting algorithms show the comprehensive mathematical deduction and their theories are very clear. Analysis from the perspective of theoretical integrity, however, the phase-shifting techniques lack the exploration of arbitrary phase shift. In view of this, inspired by the prosthaphaeresis in trigonometric, we present a novel four-step phase-shifting algorithm. The proposed method includes 16 kinds of four-step phase-shifting fringe combination and corresponding calculation formula of wrapped phase, which are deduced with two frames fringe images of sines and two ones of cosines. Furthermore, simulations and experiments have been carried out to reveal the influence law of variable phase shift on the performance of these approaches.