Structured-light three-dimensional measurement based on the Scheimpflug condition and telecentric imaging

Abstract With the development of precision manufacturing and micro-assembly, miniature components with complex geometries require three-dimensional measurement systems with a small field of view, high accuracy and non-contact operation. Conventional structured-light systems are sensitive to perspective distortion, limited common depth of field and calibration errors in micrometre-level measurements, making it difficult to achieve both high accuracy and flexible calibration. This work develops a small-field structured-light three-dimensional measurement system that combines the Scheimpflug condition with telecentric imaging, focusing on calibration of individual components and the complete system. First, a stage-free telecentric-camera calibration method based on orthographic affine homography and target-normal invariance is proposed, enabling planar-target calibration without metric depth constraints, a displacement stage or a three-dimensional calibration target. Second, an oblique projector model with two-dimensional tilt parameters is established to address the mismatch between the conventional pinhole model and Scheimpflug projection geometry. Phase mapping treats the oblique projector as an inverse camera for calibration. Finally, a virtual-plane-based phase-to-three-dimensional mapping (P3DM) calibration method is proposed. Only two reference planes are used to generate virtual-plane data covering the measurement depth of field, and global parameter optimization is introduced to improve parameter consistency. Experiments show that the calibration root-mean-square errors of the telecentric camera and the Scheimpflug projector are 0.087 pixels and 0.124 pixels, respectively. In a 20 mm × 20 mm field of view, the measured RMSE of a standard plane is 7.66 μm, the sphere-centre-distance error of a standard ball plate is 10.9 μm and effective measurement depth of field is approximately 5 mm, about 25% of the lateral field size. A supplementary measurement of a miniature metal component further demonstrates the applicability of the proposed system to practical miniature-part measurement. These results demonstrate the feasibility of the proposed Scheimpflug-telecentric structured-light system for micrometre-level three-dimensional measurement within a small field of view.