中文摘要：

以硅基板镀制单层Hf O2薄膜前后的表面微观形貌的变化为例,开展了光学表面功率谱密度的计算及表征研究。首先给出了一维功率谱密度（PSD（1D））、二维功率谱密度（PSD2D）以及各向同性功率谱密度（PSDISO）的计算方法和具体步骤。然后使用原子力显微镜测量了硅基板镀膜前后在1μm×1μm、5μm×5μm、10μm×10μm、20μm×20μm四种扫描尺寸下的表面轮廓。在此基础上使用MATLAB编程计算得到这四种扫描尺寸下的（PSDISO）,对这些（PSDISO）使用几何平均算法拼接得到具有足够大频率范围的（PSDISO-Combined）。结果显示,硅基板镀膜前后的PSDISO-Combined在低频段基本相同,中高频段出现了明显差异。分析指出这是由镀膜后表面柱状晶体结构引起的。提出了对PSDISO在频域上积分得到表面均方根粗糙度σISO,再同由定义式计算得到的σSTD作对比的方法。计算得到的σISO与σSTD基本相同,验证了PSDISO计算方法的准确性。

英文摘要：

Using the Si substrate and the HfO2 single layer as the examples, the power spectral density （PSD） of the optical surface was calculated and characterized. First, the method that calculates the 1D power spectral density （PSD1D）, 2D power spectral density （PSD~） and isotropic power spectral density （PSDIso） was introduced. Then, the surface morphologies of the Si substrate and the; HfO2 single layer were measured using atomic force microscopy with four scan areas, for example, 1μm×1μm、5μm×5μm、10μm×10μm、20μm×20μm. Using a MATLAB program, the PSDIOSS of the different scan area were calculated. And the PSD-Comioned over a larger spatial frequency range was given using the geometric mean of these PSDISOS. The result shows that the PSDISO-Comitined of Si substrate bef9re and after HfO2 coating were similar for the low spatial frequency region but quite different for the middle and high frequency region. The poly-crystallized microstructure of the HfO2 coating observed PSD difference between the Si substrate and the HfO2 coating. The and compared. The results are quite similar, which proves the correctness of PSD calculation. is the σISO and main reason for the σSTD were calculated the proposed method for the frequency region. The poly-crystallized microstructure of the HfO2 coating is the main reason for the observed PSD difference between the Si substrate and the HfO2 coating. The σISO and σSTD were calculated and compared. The results are quite similar, which proves the correctness of the proposed method for the PSD calculation.