An efficient phase error self-compensation algorithm for nonsinusoidal gating fringes in phase-shifting profilometry.

The phase-shifting method is widely used in fringe projection profilometry. Since both the digital light projector and camera used in a grating projection measurement system are nonlinear pieces of equipment, the grating fringes captured by using the camera do not have a good sinusoidal property, which leads to a three-dimensional measurement error. Although the double-step phase-shifting method has proved that the phase error can be reduced to a large extent, the number of grating fringes is doubled, which affects the measurement efficiency. In this paper, we present an efficient phase error self-compensation algorithm. It transforms the initial wrapped phase into a second wrapped phase and integrates the initial and second wrapped phases to reduce the phase error. The advantage is that the measurement accuracy is close to that of the double-step phase-shifting method without increasing the number of projection fringes; at the same time, the measurement time is shortened, and the measurement efficiency is improved. We have elaborated the proposed algorithm in detail and compared it with the traditional single-step phase-shifting method and the double-step phase-shifting method. Finally, we utilize the proposed algorithm to measure different objects. The results prove its effectiveness.