## 4 Results and Discussion  
Figure 6a shows the theoretically calculated surface topography of a 40 \(\times\) 40 mm polishing pad. Figure 6b presents a partial schematic diagram of the distribution of micropores on the pad surface (5 mm \(\times\) 5 mm), with micropores of different sizes being evenly distributed on the pad surface. The surface porosity of the polishing pad obtained by simulation was 35.8%, and the error between the simulated distribution and the measurement results was within the allowable range. The surface of the actual polishing pad had a 2 \(\times\) 1.5 mm diversion groove and a slurry supply hole with a diameter of 4 mm in the center, so the simulated pad surface morphology is shown in Figure 6c. Figure 6d presents a photograph of a 40 mm diameter porous polyurethane polishing pad, showing that the pore distribution characteristics of the simulated surface were basically consistent with the real structure.  
Figure 4: Discretization of polishing path and illustration of tool normal error for corresponding machining tracks.  
Figure 5: Normal-error distribution of polishing tools used in group (**a**) B and (**b**) C polishing experiments.  
Figure 7 shows the three-dimensional material removal characteristics of planetary-motion polishing with different normal errors. The simulation results showed that when the normal error was 0, the removal topography of the material presented a perfect axisymmetric distribution. However, when the normal error increased to 0.5\({}^{\circ}\), the material removal topography was skewed, and the maximum removal depth increased. When the normal phase error continued to increase to 1\({}^{\circ}\), the material removal profile exhibited a severe unilateral collapse, and the material removal along the inclined side increased significantly. The reason for this was that the force on the material surface in the single-spot removal was uneven due to the error of the normal accuracy, resulting in the uneven removal of the material, which eventually increased the error of the actual machined surface relative to the ideal surface.  
Figure 6: Simulation of surface morphology of polishing pad: (**a**) surface pore distribution, (**b**) micropore characteristics, (**c**) surface morphology of polishing pad with diameter of 40 mm, (**d**) actual photo of polishing pad.  
of the surface error of the experimental and simulated polishing surface, the higher the normal error of the polishing robot, the greater the reduction in the contour accuracy of the surface after polishing and the larger the decrease in the surface convergence efficiency in the practical polishing process.  
Figure 9 shows the PSD distribution of the polished surface for three different polishing-tool normal errors. The results showed that the motion accuracy of the polishing robot had a substantial influence on the medium- and high-frequency errors after polishing. As the normal error of the polishing robot gradually increased, the relative changes in the medium- and high-frequency errors before and after polishing gradually decreased, because the random change in the normal error of the polishing robot caused an uneven force to be exerted on each point of the polishing pad as the polishing process progressed, resulting in an uneven material removal rate and the suppression of medium- and high-frequency errors. Therefore, the higher the motion accuracy of the polishing robot, the higher the convergence efficiency of the optical element surface. Additionally, the mid- and high-frequency errors of the optical element could be reduced to a certain extent.  
Figure 8: Experimental and simulated form error distribution for different motion accuracies.