Monte-Carlo evaluation of bias and variance in Hurst exponents computed from power spectral analysis of atomic force microscopy topographic images
Monte-Carlo evaluation of bias and variance in Hurst exponents computed from power spectral analysis of atomic force microscopy topographic images
复制标题
蒙特卡洛评估根据原子力显微镜地形图像的功率谱分析计算出的赫斯特指数的偏差和方差
DOI：
10.1016/j.apsusc.2021.152092
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发表时间：
2022
影响因子：
6.7
通讯作者：
Mangolini, Filippo
中科院分区：
文献类型：
--
作者：
Chrostowski, Robert;Li, Zixuan;Smith, James;Mangolini, Filippo
表面形貌影响多种表面特性，包括摩擦力和粘附力。虽然表面形貌的统计描述可以通过原子力显微镜 (AFM) 高度图的功率谱密度 (PSD) 分析获得，并拟合 PSD 的自仿射区域以确定赫斯特指数 (H)，但这种方法的准确性尚未经过严格评估。在这里，我们使用傅立叶滤波算法与一种新颖的方法相结合来模拟典型的 AFM 扫描线各向异性，以生成具有已知输入 Hurst 指数的合成 AFM 形貌图像。这些合成的 AFM 图像用作蒙特卡罗实验，以评估不同假设实验方法中 PSD 的 H 估计的方差和偏差，包括以一种扫描尺寸（尺度）收集的一组图像的情况和以不同尺度收集的一组图像的情况。我们的分析表明，尽管方差收敛具有误导性，但以单一尺度收集的图像对赫斯特指数的估计仍然以依赖于尺度的方式存在偏差。通过组合在 AFM 可访问的尺度范围内至少三个不同尺度收集的图像，可以减少这种偏差。
Surface topography influences several surface properties, including friction and adhesion. While a statistical description of surface topography can be obtained from a power spectral density (PSD) analysis of atomic force microscopy (AFM) height maps and fitting the self-affine region of the PSD to determine the Hurst exponent (H), the accuracy of this approach has not been rigorously evaluated yet. Here, we use a Fourier filtering algorithm combined with a novel approach to simulate typical AFM scan-line anisotropy to generate synthetic AFM topography images with known input Hurst exponent. These synthetic AFM images are used as a Monte Carlo experiment to evaluate the variance and bias in H estimation from PSDs across different hypothetical experimental approaches, including the case of a cluster of images collected at one scan size (scale) and the case of a cluster of images collected at different scales. Our analysis reveals that estimates of the Hurst exponent from images collected at a single scale are persistently biased in a scale-dependent fashion despite misleading convergence in variance. This bias can be reduced by combining images collected at least at three different scales across the range of scales accessible to AFM.