A novel projector ray-model for 3D measurement in fringe projection profilometry

In fringe projection profilometry (FPP), the geometric calibration of the projector is based mainly on the assumption of the anti-camera model. But that model is not adequate for the non-camera model illumination devices, such as the lens-less laser projector based on MEMS, thus inducing errors in measurement results. Here we present a solution to this problem: A ray-model method to parameterize the distribution of projector illumination in the measurement space instead of determining its intrinsic parameters. Relying on the continuous distribution of phase, we discretize the fringe structured light illumination into a ray set with a variable down-sampling rate according to resolution requirements. On this principle, a flexible calibration strategy was designed to determine each illumination ray with metric spatio-angular parameters. Based on the ray parametric equation, we further derived 3D mapping so that spatial coordinates can be directly mapped from the corresponding truncated image point of the ray. Experimental results demonstrated that the proposed method provided a suitable calibration strategy for FPP systems equipped with a type of non-anti-camera model illumination device. Further, with this technique, errors associated with the projector's luminance nonlinearity are significantly suppressed.