Objective  In laser communication and photoelectric tracking systems, the pointing, acquisition and tracking (PAT) mechanism based on optional grating or wedge has been used to adjust the angle of the optical axis. This structure is light in weight and small in size, which is very beneficial to the lightweight and miniaturization of the system. Since the coaxiality error of the two rotating axes of the structure seriously affect the performance of the PAT mechanism, it is necessary to strictly ensure the parallelism of the two axes during mechanical assembly. For the cross-tracking frame gimbal, the precision of shafting angle position depends on the verticality of two axes, which can be measured by autocollimator with optical mirror. But in optional grating or wedge PAT system, the gimbal is characterized by two rotating axes coaxially arranged to drive two gratings to rotate respectively, and the test method for cross-tracking frame gimbal is not applicable. The existing parallelism measurement methods, such as contact measurement and non-contact measurement, are straight-line measurements, contact measurement includes micrometer measurement and three-coordinate measurement, and the required angular deviation between two rotating axes of a coaxial turntable can be obtained only after data conversion. When the diameter of the distribution circle is small, its accuracy is low, and there are problems such as inconsistent conversion standards, poor conversion data accuracy, and low confidence. Therefore, it is necessary to establish the methods for angle parallelism measurement of grating or wedge PAT system with high precision, high reliability and high convenience to solve the engineering problems in the process of gimbal test and assembly.

  Methods  A non-contact optical measurement method is proposed, and it uses an autocollimator as the only reference to measure the axis angle of two coaxial shafting without moving the autocollimator and the test gimbal in the test （Fig.4）. Data processing is used to eliminate the influence of shafting sloshing to get the spatial position of the rotating axes. By comparing the angular deviation of the two axes, the parallelism of the two rotating axes can be measured. A semi-reverse semi-transparent reference mirror is designed in order to solve the problem of mutual occlusion of mirrors （Fig.4）. The semi-reflection semi-transmission reference mirror can reflect collimating laser when testing its own shafting and project self-collimating light when testing another shafting （Fig.5）. The spatial position of the axis of the rotating shafting is obtained by fitting the measured data with a least squares. Then the influences of the number of data points （Fig.6）, the uniformity of data distribution （Fig.7）, the dispersion of data distribution （Fig.8） and the accuracy of test points on the accuracy of test results are analyzed.

  Results and Discussions   The fitting program is compiled by MATLAB , and a double-grating PAT mechanism is tested, the required coaxiality is better than 10″. In the test, 16 measuring points data are measured by TAHS 300-57 autocollimator whose measuring accuracy is 0.75′, and the distribution error of measuring points is less than 10°. Then the uncertainty of the measurement result is 0.8″, and the measuring precision of this method fully meets the requirement. In the test the error of comprehensive parallelism is 5.1″, and the sloshing error of two shafting is 3.96″ and 3.12″ （Fig.9). The two-axis combined swing error caused by unparallelism and shafting sloshing is calculated as the square root of two-axis parallelism error and two-axis sloshing error respectively (6.5″, 5.8″). After the alignment of the liquid crystal grating, the performance of the system axis is calibrated by optical method. In the two tests, the maximum value of the swing error of the synthetic shafting on the x-axis and y-axis is about 5.82″ and 5.48″, and the maximum value of the swing error on the x-axis and y-axis is about 6.01″ and 5.66″ （Fig.10). The deviation between the assembly period and the test results is (10%, 5.5%, 7.6% and 2.4%) respectively.

  Conclusions  In this study, a parallelism testing method based on auto-collimation principle is proposed, and a testing device is designed. It innovatively realizes that the angle and parallelism of two parallel shafting axes can be measured under the same reference without adjusting the test and the tested equipment. This method only needs one test equipment, which eliminates the measurement and transformation errors in the benchmark conduction and transformation when the traditional multiple test equipment is used for joint measurement, and improves the test accuracy and efficiency. Then the error link in the test is studied, and the uncertainty of the test method is analyzed. The method of the paper can solve the problem of high precision and high reliability parallelism measurement of PAT mechanism. It is used in an coaxial PAT gimbal with grating. Through the experiment and test, it is proved that the deviation between the test result and the final-state test result is less than 10%. It is proved that the testing precision is good and the parallelism between coaxial rotors can be effectively measured.