Estimation of roughness measurement bias originating from background subtraction

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Authors

NEČAS David KLAPETEK P. VALTR M.

Year of publication 2020
Type Article in Periodical
Magazine / Source MEASUREMENT SCIENCE & TECHNOLOGY
MU Faculty or unit

Central European Institute of Technology

Citation
Web https://iopscience.iop.org/article/10.1088/1361-6501/ab8993
Doi http://dx.doi.org/10.1088/1361-6501/ab8993
Keywords scanning probe microscopy; data processing; roughness; bias; levelling; autocorrelation
Description 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.
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