论文标题
源自背景减法的粗糙度测量偏差的估计
Estimation of roughness measurement bias originating from background subtraction
论文作者
论文摘要
在测量粗糙表面的粗糙度时，扫描区域的有限尺寸会导致其系统的低估。多项式和其他用于原子力显微镜数据实际处理中使用的过滤的升级大大增加了这一偏见。在这里，开发了一个框架，为在平整的情况下，通过使用线性最小二乘拟合模型背景函数来为平方均方根的偏置提供明确的表达式。然后将该框架应用于一维数据处理以及表面自相关功能（高斯和指数）的基本模型的多项式级别。还涵盖了其他几种常见的情况，包括中位平台，中间高斯 - 指数自相关模型和频率空间过滤。讨论了结果将结果应用于其他数量，例如RQ，SQ，RA和〜SA。结果总结在涵盖一系列自相关函数和多项式程度的概述图中，这些函数允许对偏差的图形估计。
When measuring the roughness of rough surfaces, the limited sizes of scanned areas lead to its systematic underestimation. Levelling by polynomials and other filtering used in real-world processing of atomic force microscopy data increases this bias considerably. Here a framework is developed providing explicit expressions for the bias of squared mean square roughness in the case of levelling by fitting a model background function using linear least squares. The framework is then applied to polynomial levelling, for both one-dimensional and two-dimensional data processing, and basic models of surface autocorrelation function, Gaussian and exponential. Several other common scenarios are covered as well, including median levelling, intermediate Gaussian--exponential autocorrelation model and frequency space filtering. Application of the results to other quantities, such as Rq, Sq, Ra and~Sa is discussed. The results are summarized in overview plots covering a range of autocorrelation functions and polynomial degrees, which allow graphical estimation of the bias.
