Evaluation method to obtain a fiducial fiber metrology benchmark for the Large Sky Area Multi-Object Fiber Spectroscopic Telescope

Realizing accurate positioning with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) closed-loop system depends on accurate high-precision calibration of the visual measurement system, which has a great impact on collision avoidance and accurate positioning. We designed fiducial fibers for the calibration of the LAMOST closed-loop system to provide accurate fiducial positions for visual measurement. The benchmark position accuracy of the fiducial fibers is a key factor affecting the accuracy of the visual measurement system; the more accurate the fiducial fiber positions are, the higher the visual measurement correction accuracy. In this study, three measurement methods were used to obtain the fiducial fiber positions, namely, measuring the hole positions using a coordinate measuring machine, imaging the fiducial fibers using a calibrated photographic system, and directly measuring the fiducial fiber spatial positions using a laser tracker. By evaluating the fiber positions obtained via the three methods, we can obtain a stable and reliable fiducial fiber position benchmark. A fiducial fiber positions evaluation method based on an optimal residual criterion is proposed, and the optimal residual solution for a small calibration target (SCT) is used to evaluate the optimal fiducial fiber measurement method. Specifically, the fiducial positions obtained via each of the three methods are used to invert the camera calibration parameters, which are then used to calculate the physical position of an SCT. Finally, the residual value between the calculated and theoretical positions is taken as the standard for evaluating the fiducial fiber measurement benchmark performance. The results show that the fiducial fiber positions measured using the laser tracker can be applied to effectively calibrate the photographic system, enabling the LAMOST vision measurement system to achieve a positioning accuracy of nearly 10 (mu)m with the camera 20 m from the focal surface, whereas the accuracy is within 20 (mu)m for similar to 95% of the measurement points.