Research on Calibration Method of off-axis Closed-loop Detection System for Multi-target Spectral Telescope

The LAMOST telescope has been operating steadily for more than 10 yr and is currently undergoing an upgrade to its fiber-optic positioning system on the telescope's focal plane. By adding a vision detection system to accurately measure the current position of the optical fibres and carry out closed-loop feedback control, the positioning accuracy of the original optical fiber system is greatly improved. Due to the limitation of the existing optical path of the telescope, to avoid blocking the optical path, the detection system camera cannot be placed on the optical axis of the telescope, which makes the camera and the optical fiber end face at a relatively inclined position. However, the angle between the camera and an object will introduce errors to the polynomial calibration method used in the visual detection system. To address this problem, by analyzing the relationship between the camera imaging principle and the polynomial calibration method, this paper studies the influence of distortion and imaging angle on polynomial calibration results under different angle conditions and proposes an improved high-precision polynomial calibration method. First, the distortion parameters are calculated using Zhang's method, and the image distortion is removed. Then, a mapping model between oblique plane image and nonoblique plane image is established through a homography matrix. The coordinates of all oblique plane feature points are mapped one by one to the nonoblique plane positions on the image space, and a good correction effect is obtained. Finally, the calibration images from different angles are calculated and analyzed through simulation experiments and compared with Zhang's method. The results show that this method has a 10%-40% improvement over Zhang's method.