Motion-induced error reduction for binary defocusing profilometry via additional temporal sampling

The recently proposed binary defocusing technique has brought speed breakthroughs for three-dimensional (3D) shape measurement with a digital fringe projection system. Despite this, motion-induced phase error is still inevitable due to the multi-shot nature of the phase-shifting algorithm. To alleviate this problem, this paper proposes a motion-induced error reduction method by taking advantage of additional temporal sampling. Particularly, each illuminated fringe pattern will be captured twice in one projection cycle, resulting in two sets of phase shifted fringe images being obtained. Due to the mechanism of binary defocusing projection, the motion-induced phase error could be effectively separated from the fixed phase shift value by evaluating the difference between the two phase maps. Based on this, an iterative compensation strategy is further applied to compensate the phase error until high-quality phase maps are generated. Meanwhile, different synchronization schemes are also proposed and tested to evaluate the error compensation effects. Both simulation and experiments demonstrated that the proposed methods can substantially reduce motion-introduced measurement errors. Since defocused 1-bit binary patterns are utilized to bypass rigid camera-projector synchronization, this method has potential for high-speed applications.