Non-central refractive camera calibration using co-planarity constraints for a photogrammetric system with an optical sphere cover

Abstract

Optical sphere covers are widely used in photogrammetric systems to protect camera systems from external conditions. The spherical refraction can cause severe non-linear distortion, resulting in imprecise and unreliable measurements. In particular the cameras with a relatively thick optical sphere cover (e.g. underground or underwater cameras). However, the conventional perspective camera model are not suitable for such spherical refraction calibration problem. This study presents a novel non-central refractive calibration technique for cameras with an optical sphere cover. Considering the general situation in which the camera optical axis could not pass through the spherical center, a universal spherical refraction geometric model was established with coplanarity constraints. The model introduces modified perspective center and enables the spherical refraction can be integrated into the equivalent collinearity equations, which make it possible to describe explicitly the correspondences between the image points and object coordinates. Moreover, a calibration technique is proposed to estimate relative orientation parameters. With no need to gain explicit knowledge of object space coordinates, the spherical refraction calibration can be performed with known refractive index as well as the radius of sphere cover. Numerical and experimental results demonstrated the proposed spherical refraction calibration model to be both effective and robust, which can achieve high levels of calibration accuracy.