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Accuracy of roughness exponent measurement methods.

Jan Øystein Haavig Bakke1, Alex Hansen

  • 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Jan.Bakke@ntnu.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
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Summary

This study evaluates methods for measuring profile roughness, identifying power spectrum density analysis and averaged wavelet coefficients as best for estimating the self-affine roughness exponent. These methods offer accurate, unbiased results for profiles longer than 256 units.

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Area of Science:

  • Surface science
  • Statistical physics
  • Signal processing

Background:

  • Characterizing rough profiles is crucial in various scientific fields.
  • Accurate measurement of the self-affine roughness exponent is essential for understanding surface properties.
  • Distinguishing between different sources of roughness, such as long-range correlations and Lévy distributions, remains a challenge.

Purpose of the Study:

  • To evaluate and compare methods for measuring and characterizing rough profiles.
  • To determine the most effective methods for estimating the self-affine roughness exponent.
  • To develop a method for distinguishing between different origins of roughness exponents.

Main Methods:

  • Testing various measurement techniques on profiles with known roughness exponents.
  • Utilizing power spectrum density analysis and averaged wavelet coefficients.
  • Developing a simple test to differentiate between roughness exponents from long-range correlations and Lévy distributions.

Main Results:

  • Power spectrum density analysis and averaged wavelet coefficients provide the best estimates for roughness exponents (0.1-0.9).
  • Error bars are less than 0.03 for profile lengths > 256, with no systematic bias.
  • Quantitative estimates of error bars and systematic errors are provided, showing dependence on roughness exponent and profile length.

Conclusions:

  • Power spectrum density analysis and averaged wavelet coefficients are reliable methods for roughness exponent estimation.
  • The proposed test effectively distinguishes between different sources of profile roughness.
  • Understanding error sources and their dependence on parameters is key for accurate surface characterization.