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<p>Bonnet and wheel polishing techniques have been widely adopted to fabricate ultrasmooth surfaces for extreme ultraviolet and X-ray optical systems. However, conventional methods inevitably generate undesirable anisotropic textures aligned along the polishing direction. Discrete precession polishing offers a promising solution for eliminating these textures; however, the accurate prediction of surface roughness evolution during this process remains a significant challenge. This paper presents a mathematical model and numerical simulation framework for surface texture evolution in discrete precession polishing using root-mean-square (RMS) roughness as the surface quality indicator. Unlike the conventional assumption of a monotonic decrease in the surface roughness, our model reveals a three-stage evolution pattern: initial reduction, subsequent increase, and eventual convergence to a fixed RMS roughness value. The parametric analysis indicates that reducing the polishing tool profile roughness and increasing the number of precession angles can effectively improve the final surface quality. Experimental validation confirmed the accuracy and reliability of the model. Through model-guided optimization, we successfully achieved a surface with 0.41&#xa0;nm RMS roughness over a measurement area of 640&#xa0;μm × 480&#xa0;μm, demonstrating the practical applicability of this model for high-precision optical surface fabrication.</p>

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Surface roughness evolution model of discrete-precession polishing

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Peng-Feng Sheng,
  • Yi-Fan Zhu,
  • Jing-Jing Xia,
  • Kun Wang,
  • Zhan-Shan Wang

摘要

Bonnet and wheel polishing techniques have been widely adopted to fabricate ultrasmooth surfaces for extreme ultraviolet and X-ray optical systems. However, conventional methods inevitably generate undesirable anisotropic textures aligned along the polishing direction. Discrete precession polishing offers a promising solution for eliminating these textures; however, the accurate prediction of surface roughness evolution during this process remains a significant challenge. This paper presents a mathematical model and numerical simulation framework for surface texture evolution in discrete precession polishing using root-mean-square (RMS) roughness as the surface quality indicator. Unlike the conventional assumption of a monotonic decrease in the surface roughness, our model reveals a three-stage evolution pattern: initial reduction, subsequent increase, and eventual convergence to a fixed RMS roughness value. The parametric analysis indicates that reducing the polishing tool profile roughness and increasing the number of precession angles can effectively improve the final surface quality. Experimental validation confirmed the accuracy and reliability of the model. Through model-guided optimization, we successfully achieved a surface with 0.41 nm RMS roughness over a measurement area of 640 μm × 480 μm, demonstrating the practical applicability of this model for high-precision optical surface fabrication.