## 4 Measurement Experiment  
In order to verify the proposed measurement method and error model, an experimental device was designed and built. As shown in Figure 4, all components were installed on the optical platform. The target rotary axis was an SKQ-12200 numerically controlled rotary table made by Yiliya Company. The angular positioning accuracy is about 40\" and repeatability precision is about 20\". The polyhedral prism adopted the 0-level 12-face prism from Hongce Company. The manufacturing error of the working surface was \(\leq\)\(\pm\)1\", and the perpendicularity between the working face and the datum plane was \(\leq\)\(\pm\)5\". The Collapex-EXP photoelectric autocollimator was used as the rotation angular error measurement unit. An ILD2300-2 LL laser displacement sensor from Micro-Epsilon, Germany, was used as the measurement unit of the radial and axial motional errors of the target rotary axis. The specific parameters of the autocollimator and laser displacement sensor are shown in Table 2.  
Figure 3: (**a**) The difference between the simulation compensation results of the angular positioning error and the tilt motion errors around the X and Y axes and the set value. (**b**) The difference between simulation compensation results of radial and axial motion errors and the set value. The laboratory environment temperature was about 25 \(\pm\) 1 \({}^{\circ}\)C. The measurement angle interval was 30\({}^{\circ}\) (determined by the number of polygon faces), and the rotation speed of the target rotary axis was 0.57\({}^{\circ}\)/s. Limited by laboratory conditions, one laser displacement sensor and one autocollimator were used to carry out the experiment step by step. The specific steps were as follows: Firstly, the autocollimator was installed in the X direction of the target rotary axis to measure the angular positioning error and the tilt motion error around the Y axis. The laser displacement sensor was installed in the Y direction to measure the radial motion error of the rotary axis along the Y axis, as shown in Figure 4. The second step was to install the autocollimator in the Y direction to measure the tilt error of the target rotary axis around the X axis. The laser displacement sensor was installed in the X direction to measure the radial motion error of the target rotary axis along the X direction. Finally, the axial motion error along the Z direction was measured by a laser displacement sensor placed on the target rotary axis through a fixed device. The SKQ-12200 numerically controlled rotary table was measured ten times with the above measuring device, and errors were compensated by the proposed model. The measurement results before and after the compensation of the six DOF motion errors of the rotary axis are shown in Table 3. The motion error of a certain DOF is the maximum absolute value of the motion errors of all measurement points. According to the compensation results, \(\varepsilon_{x}\), \(\varepsilon_{y}\), \(\delta_{x}\) and \(\delta_{y}\) are significantly reduced after compensation. The maximum reduction is 79.1%. According to Equation (9), \(\varepsilon_{z}\) is only affected by the manufacturing errors of the polyhedral prism's working surface, and the values of manufacturing errors of the polyhedral prism is small (\(\leq\)\(\pm\)1\"). It can be seen that the other error terms have small influence on the measurement of \(\delta_{z}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Autocollimator**} & **Range** & **Maximum Error** & **System Accuracy** & **Resolution** \\ \cline{2-5}  & \(\pm\)300\({}^{\prime\prime}\) & \(\pm\)0.05\({}^{\prime\prime}\) & \(\pm\)0.2\({}^{\prime\prime}\) & \(\pm\)0.01\({}^{\prime\prime}\) \\ \hline \multirow{2}{*}{**laser displacement sensor**} & **Wavelength** & **range** & **absolute error** & **resolution** \\ \cline{2-5}  & 670 nm & 2 mm & 0.6 μm & 0.03 μm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The specific parameters of the autocollimator and laser displacement sensor.