All-telecentric multi-camera microscopic FPP: Scheimpflug calibration and reprojection-based multi-view fusion

Microscopic fringe projection profilometry (MFPP) is a key technique for recovering 3D structure at the microscopic scale. However, conventional single-view setups perform poorly on complex specimens, where self-occlusion and specular saturation compromise measurement completeness and accuracy. This article presents an all-telecentric multi-camera MFPP system comprising a vertical telecentric projector and four oblique Scheimpflug telecentric cameras arranged at 90^∘ intervals. To calibrate the system, we introduce a pipeline that 1) fits the full projection matrix from multi-pose images, 2) decomposes it into intrinsic and extrinsic parameters, and 3) performs bundle-adjusted joint calibration to align all devices in a common reference coordinate frame. This approach mitigates the ill-conditioning and scale drift typical of methods that separate intrinsics and extrinsics prematurely. For reconstruction, we establish cross-view correspondences using phase-consistent reprojection and perform modulation-weighted fusion with adaptive mismatch rejection. This strategy preserves high-quality observations, suppresses redundancy-induced bias, and fills visibility gaps while maintaining boundary fidelity. Experiments on standard targets and complex specimens show higher completeness and consistency relative to single-view and conventional multi-view baselines, demonstrating that an all-telecentric design coupled with the proposed calibration and fusion methods enables accurate and robust microscopic 3D measurement.