## 4 Experiments
### Aspheric Surface Processing Experiment  
To further verify the polishing performance of the optimized TIF, we selected a piece of JGS2 glass with a diameter of 230 mm and carried out aspheric surface processing experiments. The objective of the experiment is to process the spherical surface with a curvature radius of 4000 mm on the quartz into an off-axis parabolic surface with an off-axis amount of 170 mm, as well as to make the RMS value of the surface error converge to below 10 nm. The processing steps are as follows: (1) Mark the direction of the spherical surface and use an interferometer to detect the error compared with that of the target off-axis parabolic surface, which will be taken as the initial form error. (2) Use the dwell time algorithm based on the matrix method to calculate the polishing dwell time. (3) Calculate the running speed of the robot according to the processing path and the dwell time, and then carry out the processing. (4) Detect the error between the processed surface and the target off-axis parabolic surface. If the RMS of the error is less than 10 nm, the processing is completed. If it fails to meet the requirements, continue with the next round of processing. In order to exclude the influence of the edge effect, only the error within the area with a diameter of 200 mm is detected. The processing parameters are shown in Table 4, and the processing status is shown in Figure 12. The selection of parameters remains consistent with that in TIF modeling and experiments. The polishing trajectory is of the type commonly used in polishing engineering. During the experiment, the temperature was maintained at 24 \(\pm\) 0.5 \({}^{\circ}\)C, and the humidity was controlled within 50 \(\pm\) 5%. The surface shape measurement equipment used was the Zygo Verifire interferometer, and  
Figure 11: Comparison between the experimental TIF and the theoretical TIF. (**a**) Section profile in the X-direction, (**b**) section profile cross-peak point and parallel to the y-direction. the detection method was the null point interferometry. We used the Zygo Mx analysis software version 6.3.0.4 to display the surface shape data of the initial surface and that was measured after three rounds of processing. The results of the aspheric surface processing experiment are as follows: After three rounds of processing, the value of PV of the surface error converged from 1861.180 nm to 64.875 nm, and the value of RMS converged from 299.857 nm to 6.043 nm, achieving the goal. The initial form error and the error after three rounds of processing are shown in Figure 13. The convergence efficiencies of PV and RMS values after each round of processing are shown in Table 5. In order to exclude the influence of the edge effect, only the error within the area with a diameter of 200 mm is detected. The processing parameters are shown in Table 4, and the processing status is shown in Figure 12.  
It can be seen from Figure 13 and Table 5 that the initial surface form is of a low-frequency type. For low-frequency surface form error when processed using the eccentric pressured small tool polishing device, the actual convergence efficiencies of PV and RMS have reached over 80%. For the medium-frequency surface form error remaining after the first and second rounds of processing, the actual convergence efficiency of PV is higher \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Diameter of polishing disc (mm) & 30 \\ Eccentric distance (mm) & 5 \\ Eccentric direction & \(\chi\)+ \\ Polishing pressure (N) & 20 \\ Rotating speed (rps) & 3 \\ Polishing powder & Cerium oxide \\ Workpiece material & JGS2 \\ The type of trajectory & Raster type \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the processing experiment. Figure 12: Processing status of Eccentric pressured small tool polishing device. than 55%, and that of RMS is higher than 60%, which is very close to the performance in the simulation experiment.