Surface roughness evolution model of discrete-precession polishing

Abstract

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.

Keywords

Wheel polishing / X-ray mirror / Roughness evolution / Discrete precession polishing

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Funding

National Natural Science Foundation of China(12305365)

RIGHTS & PERMISSIONS

Shanghai University and Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature