Key concepts for phase-to-coordinate conversion in fringe projection systems

Fringe projection systems encode the scanned object shape as a phase distribution according to the system parameters. However, to obtain the object shape in physical units of length, the demodulated phase must be converted to the coordinates of the observed points on the object surface. The design of a phase-to-coordinate conversion algorithm is straightforward when the following key concepts are considered: cameras and projectors as direction sensors, gratings as coordinate-encoding devices, absolute phase, and triangulation. In this paper, the theoretical principles of these concepts are formalized. Then, an efficient and generalized phase-to-coordinate conversion method, which supports systems with multiple cameras and projectors arranged arbitrarily, is proposed. The usefulness of this approach is illustrated by a 3D surface imaging experiment.