Fourier-transform profilometry calibration based on an exhaustive geometric model of the system

In Fourier-transform profilometry (FTP), the height information is extracted from the phase distribution through triangulation; the relationship between the phase and height distribution depends on the system parameters such as the relative position of the projector and the camera, the fringe frequency and the reference plane position. In this paper, we propose a novel calibration approach for FTP that uses calibration planes to calculate the system parameters. The main innovation of this method is the application of an exhaustive geometric model of the FTP that expresses the phase-to-height relationship in the most general way with a camera and a projector not aligned; the aberration due to optics is also considered and compensated for. The obtained calibration data have a precise physic meaning and can be easily compared with the real system. Tests on both simulated and real data showed that the proposed method is robust, even in the case on non-negligible noise level.