Detail publikace

Estimation of roughness measurement bias originating from background subtraction

NEČAS, D. KLAPETEK, P. VALTR, M.

Originální název

Estimation of roughness measurement bias originating from background subtraction

Anglický název

Estimation of roughness measurement bias originating from background subtraction

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Dokumenty

BibTex


@article{BUT169006,
  author="David {Nečas} and Petr {Klapetek} and Miroslav {Valtr}",
  title="Estimation of roughness measurement bias originating from background subtraction",
  annote="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.",
  address="IOP PUBLISHING LTD",
  chapter="169006",
  doi="10.1088/1361-6501/ab8993",
  howpublished="online",
  institution="IOP PUBLISHING LTD",
  number="9",
  volume="31",
  year="2020",
  month="september",
  pages="094010-1--094010-15",
  publisher="IOP PUBLISHING LTD",
  type="journal article in Web of Science"
}