Non-iterative distortion correction for Scheimpflug multi-view microscopic fringe projection profilometry

Microscopic fringe projection profilometry (MFPP) has become an essential technique for precisely inspecting intricate microscale industrial parts, where Scheimpflug multi-view imaging is commonly used to extend the depth of field (DOF). However, lens distortion significantly reduces measurement accuracy, creating a major challenge for seamlessly fusing data from different views. In this Letter, we introduce a non-iterative distortion correction method for Scheimpflug multi-view MFPP that directly remaps camera and projector pixels using pre-calibrated parameters. The undistorted position for unidirectional fringes is calculated by intersecting undistorted camera sight lines with a sub-pixel-interpolated DMD grid, thereby eliminating the need for pattern reloading or iterative optimization. Experiments with a dual Scheimpflug camera MFPP system show that the proposed approach decreases the root-mean-square error (RMSE) of 3D measurements for planes and standard spheres by 43.5% and 21.1%, respectively. Additionally, reconstructing a complex aircraft model demonstrates the method's ability for seamless multi-view fusion, providing a computationally efficient and accurate solution for micro-scale 3D metrology.