Quasi-Periodic Phase Coding for Long-Depth-Range 3-D Measurements of Moving Objects

Fringe projection profilometry (FPP) requires an auxiliary projection sequence or spatial landmark to remove phase ambiguity, thereby severely limiting the measurement speed or depth range for moving objects. In this article, we propose a novel quasi-periodic phase coding method for long-depth-range 3-D measurements of moving objects without temporal or spatial limitations. This article mainly focuses on the construction of the encoding schema for quasi-periodic fringe patterns and the execution of the phase decoding framework for long-depth-range 3-D measurements of moving surfaces. First, a set of stripes with similar periods is designed on the basis of a preset equivalent period, and the various combinations of these stripes constitute quasi-periodic fringe patterns. Second, we present a progressive phase recovery strategy for decoding quasi-periodic fringe images, in which the wrapped phase is converted first into a continuous phase distribution and then into the absolute phase. In this strategy, the absolute phase map is effectively screened via the piecewise linear transformation from the quasi-periodic phase to the equivalent phase. Compared with the existing FPP methods, the proposed method avoids the low-frame-rate constraint and the need for landmark configuration. Simulation and experimental results verify that the proposed method is applicable for dynamic 3-D measurements of moving objects over a large-depth range.