基于分形维数的光学表面质量评价及响应曲面模型

Abstract

针对光学元件表面的微观形貌结构呈现出随机性、无序性和多尺度性,反映出一种非平稳的随机过程.针对这一问题,利用光学元件表面具有微观结构上的统计自相似性特征,首先通过结构函数法计算光学表面的分形维数,分析了分形维数与表面传统评价参数峰谷(PV)值近似线性的关系,验证了可以利用分形维数来评价光学元件表面精度;其次,建立了分形维数与抛光参数的响应曲面回归模型,为了通过控制显著性较强的抛光参数来获取更好的光学元件表面质量,评价了各抛光参数对分形维数的影响权重.

In view of the traditional evaluation method on the optical element surface which depend on the sampling length,the instrument resolution and so on many issues,in this paper,the optical element surface which has statistical self-similarity of microstructure characteristics is used.First,the fractal dimension of the optical surface is calculated through the structure function method,the approximate linear relationship is analyzed between fractal dimension and the traditional evaluation parameters—PV of the surface,the fractal dimension is proved which can be used to evaluate the optical element surface accuracy;moreover,the establishment of fractal dimension and the polishing parameters of response surface regression model,each polishing parameter is evaluated on the influence of fractal dimension weight,in order to control significantly stronger polishing parameters to obtain better surface quality of the optical element.