A flexible and simplified calibration procedure for fringe projection profilometry

Fringe Projection Profilometry (FPP) is a widely used technique for optical three-dimensional (3D) shape measurement. Among the existing 3D shape measurement techniques, FPP provides a whole-field 3D reconstruction of objects in a non-contact manner, with high resolution, and fast data processing. The key to accurate 3D shape measurement is the proper calibration of the measurement system. Currently, most calibration procedures in FPP rely on phase-coordinate mapping (PCM) or back-projection stereo-vision (SV) methods. The PCM technique consists in mapping experimental metric XYZ coordinates to recovered phase values by fitting a predetermined function. However, it requires accurately placing 2D or 3D targets at different distances and orientations. Conversely, in the SV method, the projector is regarded as an inverse camera, and the system is modeled using triangulation principles. Therefore, the calibration process can be carried out using 2D targets placed in arbitrary positions and orientations, resulting in a more flexible procedure. In this work, we propose a hybrid calibration procedure that combines SV and PCM methods. The procedure is highly flexible, robust to lens distortions, and has a simple relationship between phase and coordinates. Experimental results show that the proposed method has advantages over the conventional SV model since it needs fewer acquired images for the reconstruction process, and due to its low computational complexity the reconstruction time decreases significantly.