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.

在条纹投影轮廓仪（FPP）中，投影仪的几何校准主要基于反相机模型的假设。但该模型不适用于非相机模型照明设备，例如基于 MEMS 的无透镜激光投影仪，从而导致测量结果出现错误。在这里，我们提出了这个问题的解决方案：一种射线模型方法，用于参数化测量空间中投影仪照明的分布，而不是确定其内在参数。依靠相位的连续分布，我们根据分辨率要求将条纹结构光照明离散为具有可变下采样率的光线集。根据这个原理，设计了一种灵活的校准策略来确定具有度量空间角度参数的每条照明光线。基于射线参数方程，我们进一步推导了3D映射，从而可以直接从射线的相应截断图像点映射空间坐标。实验结果表明，所提出的方法为配备了一种非反相机模型照明装置的 FPP 系统提供了合适的校准策略。此外，通过该技术，与投影仪亮度非线性相关的误差被显着抑制。