Practical Calibration of a Multi-View Telecentric Fringe Projection System for High-Dynamic-Range 3D Profilometry

Multi-view fringe projection profilometry systems that integrate a telecentric projector with multiple oblique-view cameras offer unique advantages for inspecting high dynamic-range surfaces featuring densely packed, intricate microstructures. Nevertheless, such systems encounter fundamental calibration challenges, namely, sign ambiguity in the rotation matrices and truncated extrinsic parameters inherent to telecentric projector models, as well as difficulties in multi-view point cloud registration. This paper introduces a novel calibration framework with three principal contributions. First, we resolve the sign ambiguity by calibrating the telecentric projector under a quasi pinhole model and directly transferring the extrinsic sign conventions, thereby obviating the need for costly precision displacement stages or elaborate virtual targets. Second, we fix the axial-gauge freedom by constraining the origin of the projector coordinate system to lie on the XY-plane of the camera coordinate system. Third, we establish precise relative poses between all cameras and a designated reference camera, enabling unified multi-view point cloud registration directly within the projector coordinate frame, which substantially reduces alignment errors and accelerates data processing. Experimental results demonstrate marked improvements in accuracy: reprojection root-mean-square errors of 0.084 pixels for the cameras and 0.106 pixels for the projector, corresponding to in-plane spatial resolutions of 0.21 µm and 0.26 µm, respectively. The proposed method offers a robust solution for micron-level inspection in semiconductor packaging and precision manufacturing.