光学表面的分形特点与模拟表征算法

根据光学表面在微观结构呈现出的自相似性,利用尺度无关的分形模型描述了其结构特征;采用结构函数法对抛光表面的分形维数进行计算,分析了粗糙度参数RMS值、误差波长、测量尺度、采样长度和采样点数对分形维数的影响规律。在此基础上,提出了采用一阶自回归分形模型对抛光表面进行模拟的新方法,分析了界定尺度、模型参数对分形特征和分形维数的影响规律。利用分形维数描述光学表面的微观结构具有评价方法简单、在一定范围内与测量尺度无关等优点。

Fractal Characteristic and Simulation Arithmetic of Optical Surface

According to the self-similar nature of the optical surface in microstructure, its structure feature is described with fractal model independent of the scale. Fractal dimension of the polished surface is calculated by structure function. The influences of roughness RMS, error wavelength, measure scale, sampling length and the number of sampling points on fractal dimension are analyzed. On this basis, a new method which applies the first-order autoregressive fractal model to simulating the optical surface is presented. The influences of the definition scale and model parameter on fractal feature and fractal dimension are analyzed. The research indicates that the evaluation method is simple and independent of the scale in certain range when the microstructure of the optical surface is described by fractal dimension.