Effect of beam splitter thickness on angle measurement accuracy of dual-arm Tolansky interferometric autocollimator
Authors: FANG Zhenyuan , ZHANG Baowu , CUI Jianjun , ZHANG Bin , CHEN Kai , XU Zijie , ZHU Ling , SUN Yi , LUO Xianhuan ,   College of Measurement Testing and Instrumentation, China Jiliang University , Hangzhou 310018, China,   National Institute of Metrology, Beijing 100013, China
Published: January 2025

In order to solve the problem that the measurement arm length needs to be obtained in real time when calculating the measurement angle in the process of Tolansky interference small angle measurement, a dual-arm Tolansky interference autocollimation angle measurement scheme is proposed, which not only maintains the function of Tolansky interference, but also integrates the principle of optical leverage. In the simulation study, it is found that the splitter with thickness in the scheme will lead to the lateral offset of the optical axis of the emitted light, which will change the position of the virtual point light source, and finally change the position of the center of the interference circle on the detector. In this work, in order to reduce the influence of the thickness of the beam splitter on the angle measurement accuracy of the angle measurement scheme, the optical path structure of the angle measurement scheme is redrawn, and the relationship between the center offset of the interference ring and the deflection angle, which contains the thickness factor and can accurately describe the optical path, is deduced. Therefore, the corresponding method is adopted as follows. Firstly, the measurement optical path of the splitter with a thickness factor is redrawn, the splitter is partially enlarged, and the original beam is replaced with the center line of the laser beam to draw the optical path. Then, the position of the virtual point light source under the influence of the thickness of the splitter is analyzed by using the single refraction spherical formula and the transition formula of geometric optics, and the relationship between the offset of the interference center and the deflection angle with the thickness of the splitter is established. Secondly, the coordinate information of the center of the interference ring under different thickness parameters of the splitter is obtained by using the virtual simulation experiment, which proves the correctness of the theoretical analysis. Then, simulation experiments such as simulation measurement of multiple sets of setting angles and angle measurement under different splitter thickness conditions are carried out, and the accuracy of the relationship including the splitter thickness factor deduced above is cross-validated. Finally, combined with the actual experiment, measurements are taken on the guide rail and calibrated autocollimator, and the influence of beam splitter thickness on angle measurement accuracy is investigated in detail. The research results are obtained below. Experiments show that the thickness of the splitter will affect the position of the initial center of the circle; with the increase of the thickness of the splitter, the error between the simulation measurement results and the relationship including the thickness factor is within ± 0.5 % at different angles, and the experimental data and theoretical results are in good agreement. At the same angle, as the thickness of the beam splitter increases, the difference between the established relationship and the approximate relationship gradually increases. With 1-mm-thick beam splitter, the relative error between the established relationship and the calculated value of the approximate relationship is only 0.22 % based on the data of the guide rail measured by the calibrated autocollimator. From these results, a conclusion can be drawn below. The utilizing a thinner spectroscope can effectively reduce the calculation and measurement errors, providing an important guidance for carrying out the in-depth research and development of this new autocollimator.