Improved roughness model of contact polishing for optical components based on self-affine

Roughness is an important indicator for evaluating the quality of optical components. Owing to the influence of the fabrication environment, it is difficult to obtain quantitative guidance from accurate models in contact polishing. As the classical model for contact removal, the Preston equation and its improved models mostly focus on describing macroscopic removal parameters and processes, while neglecting the description of rough surfaces that are closely related to microscopic removal and the consideration of influencing factors. By introducing the influence of various key components on the micro-removal of abrasive wear, a micro-removal model based on abrasive particles is established. As an extension of the model, the positive correlation between limited roughness and abrasive particle size was elucidated by calculating the cut-off line after integrating the abrasive particle size. Correspondingly, multiple sets of experiments validate the micro-removal model, and a limited roughness of slurry particle size and ultra-smooth surfaces with a roughness of 0.18 nm is achieved. The theoretical calculation shows that the best roughness for the CeO₂ polishing slurry with a median particle diameter of 50 nm is 0.176 nm, which shows good consistency. These models and promotion analysis provide an important theoretical basis and technical guidance for the fabrication of ultra-smooth optical surfaces.