Calibration method for refracted rays passing through a transparent parallel plate in monocular vision

In specific measurement scenarios, a transparent parallel plate is placed between the vision measurement system and the measured object. This configuration not only reduces image quality but also alters the light-path, thereby necessitating precise calibration of the camera and the plate for the refractive parameters. Traditional monocular vision calibration methods are inadequate in addressing the air-plate-air condition induced by the plate. To address this, we propose a novel monocular refractive calibration method based on refractive coplanarity constraints and the geometric properties of the optical model. The calibration is optimized by forward projection and subsequently applied to monocular vision reconstruction. By relying on only a single refracted image, this method accurately determines the calibration parameters while eliminating the degradation issues typically caused by coplanar target points. Simulation and experimental results verify that the proposed approach is suitable for transparent parallel plates of various thicknesses. Notably, the mean plane distance error under refractive conditions is 0.031 mm, demonstrating the precision and robustness of the method.