Though AFM is capable of obtaining sub-angstrom resolution in z-direction, the accurate height measurement of protruding particles is hindered by raster nature of this technique. In this work using Monte Carlo simulations we have quantified the influence of pixelization on the mean AFM apparent height (hmean) of spheres and cylinders. We have demonstrated that for a zero size AFM probe hmean may be increasing, decreasing function of a pixel size, or has more complex character depending on the standard deviation of a particle size. Therefore, AFM pixelization effects may induce both under- and overestimation of the true diameter. The observed complex behavior of hmean is explained by interplay of two opposing factors: the mismatch of the position of the "highest" pixel to the real topographical maximum and higher registration probabilities of larger particles. Consideration of the AFM probe size results in even bigger pixelization induced drops of hmean, which may amount to ∼50% of the true value. The obtained results contribute to AFM data interpretation and methodological aspects of AFM operation in many fields of nanoscience. In particular, they may be used for estimation of true height of nanoparticles from their AFM images obtained with different (even low) pixel resolution.

中文翻译：

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像素化对原子力显微镜高度测量的影响

尽管 AFM 能够在 z 方向获得亚埃分辨率，但这种技术的光栅特性阻碍了对突出颗粒的准确高度测量。在这项使用蒙特卡罗模拟的工作中，我们量化了像素化对球体和圆柱体的平均 AFM 表观高度 (hmean) 的影响。我们已经证明，对于零尺寸的 AFM 探针，hmean 可能是像素尺寸的增减函数，或者根据粒度的标准偏差具有更复杂的特征。因此，AFM 像素化效应可能会导致对真实直径的低估和高估。观察到的 hmean 的复杂行为可以通过两个相反因素的相互作用来解释：“最高”位置的不匹配 像素到真实地形最大值和较大粒子的更高配准概率。考虑 AFM 探针尺寸会导致更大的像素化引起的 hmean 下降，这可能相当于真实值的 50%。获得的结果有助于在纳米科学的许多领域进行 AFM 数据解释和 AFM 操作的方法学方面。特别是，它们可用于从以不同（甚至低）像素分辨率获得的 AFM 图像中估计纳米粒子的真实高度。