# A Polishing Processes Optimization Method for Ring-Pendulum Double-Sided Polisher
## 1 Introduction  
The ring-pendulum double-sided polisher (RDP) is a high-precision optical processing machine. It is designed for processing large-aperture planar optical components. These components are widely used in various essential scientific and technological fields, including space telescopes [1; 2; 3], high-energy laser weapons [4; 5; 6], laser nuclear fusion systems [7], and other essential scientific and technological fields [8; 9; 10]. In order to improve the precision optical element processing, numerous amounts of research have been carried out. Numerous studies have been conducted to enhance precision optical element processing. [PERSON] et al. [11] systematically investigated the effects of four crucial process factors, namely polish pressure, pad rotational speed, polish head rotational speed, and slurry supply velocity, on chemically mechanically polished optical silicon substrates. Through meticulous CMP experiments, they successfully identified the optimal combination of these factors, resulting in a significant improvement in polishing efficiency. [PERSON] et al. [12] introduced an advanced conditioning method called subaperture conditioning. By strategically removing and controlling specific regions of the pad surface using a smaller-sizedconditioner tool, this method achieves a more uniform surface shape and higher polishing accuracy. [PERSON] et al. [13] investigated a polished trajectory interpolation scheme to ensure accuracy in trajectory runtime. The NURBS interpolation approach demonstrated a remarkable improvement in both interpolation and runtime error compared to linear interpolation. Moreover, the convergence rate of surface error for elements improved from 37.59% to 44.44%. [PERSON] et al. [14] examined the influence of slurry pH on the size of silica abrasives and their colloidal stability, and how these factors ultimately impacted the polish rate. Their findings provided strong evidence supporting the significant effects of slurry pH, abrasive concentration, and grain size on the polish rate. Notably, smaller abrasive particles with higher surface area showed improved performance in terms of polish rate. [PERSON] et al. [15] investigated the impact of robot motion accuracy on element surface topography during polishing. They developed a material removal model that considers the normal error of the polishing tool, enabling predictions of surface morphology and form accuracy under varying normal-error conditions. This model offers guidance for achieving uniform material removal and improving polishing accuracy. [PERSON] et al. [16] proposed a material removal model to reduce surface roughness of optical elements. Through systematic analysis, they established a uniform polishing method that efficiently enhanced the surface roughness of hard-polished spherical optics. [PERSON] et al. [17] developed a material-removing model to analyze the effects of rotary table run-out error on polishing efficiency and accuracy at any given point on the element. Through an analysis and a series of polishing experiments using the KPJ1700 and KPJ1200 CMP machines, they obtained definitive evidence that reducing the run-out error leads to improved polishing efficiency and accuracy. [PERSON] et al. [18] introduced an interpolation process for polishing trajectory using the equal proportional feed rate adjustment strategy. This approach significantly improved the accuracy of implementing dwell time in optical polishing. Simulations and experiments demonstrated that their proposed dwell time algorithm and spline interpolation method had a notable impact on enhancing the solution accuracy of dwell time and improving the convergence rate of form error during the polishing process. These studies have led to significant advances in improving the accuracy and efficiency of the polishing process through the optimization of the process and the construction of material removal models from various perspectives.