Calibration method of the right-angle error of a hollow corner-cube retroreflector based on an independent autocollimator

Abstract

Hollow corner-cube retroreflectors (HCCRs) are an essential reflection component of next-generation lunar laser-ranging technology. The verticality among the three reflectors, known as the right-angle error, is a critical parameter that affects the emission performance, and thus, should be correctly measured and calibrated. However, conventional methods measure the three right-angle errors separately, which can induce error superposition during the measurement process. A one-time measurement method was developed for the three right-angle errors of the HCCR using a single autocollimator (AC). The method establishes a mathematical relationship between the right-angle error of the HCCR and the angle offset of the reflected beam, and it considers the observation coordinates of the AC simultaneously to perform the coordinate transformation of the relationship parameters. The corresponding measurement equation was derived to extract the three-plane right-angle error of the HCCR using the measured readings of a single AC. In addition, a HCCR was designed to freely adjust the angle of the two reflective surfaces and used to simulate the different states of the three right-angle errors in practice. The measurement results show that the root-mean-square error of the proposed method in all right-angle error states is smaller than 16′′.