以硅基板镀制单层HfO₂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(PSD_2D)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1 μm×1 μm、5 μm×5 μm、10 μm×10 μm、20 μm×20 μm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PSD_ISO，对这些PSD_ISO使用几何平均算法拼接得到具有足够大频率范围的PSD_ISO-Combined。结果显示，硅基板镀膜前后的PSD_ISO-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PSD_ISO在频域上积分得到表面均方根粗糙度σ_ISO，再同由定义式计算得到的σ_STD作对比的方法。计算得到的σ_ISO与σ_STD基本相同，验证了PSD_ISO计算方法的准确性。

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(PSD_1D), 2D power spectral density(PSD_2D) and isotropic power spectral density (PSD_ISO) 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, 1 μm×1 μm, 5 μm×5 μm, 10 μm×10 μm, 20 μm×20 μm. Using a MATLAB program, the PSD_ISOs of the different scan area were calculated. And the PSDISO-Combined over a larger spatial frequency range was given using the geometric mean of these PSD_ISOs. The result shows that the PSD_ISO-Combined of Si substrate before 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 is the main reason for the observed PSD difference between the Si substrate and the HfO₂ coating. The σ_ISO and σ_STD were calculated and compared. The results are quite similar, which proves the correctness of the proposed method for the PSD calculation.