Reliability of self-affine measurements

Abstract

Reliability and accuracy of the determination of self-affine exponents are studied and quantified from the analysis of synthetic self-affine profiles and surfaces. The self-affine exponent is measured using different methods either relying on the determination of a ‘‘fractal dimension’’ (i.e., box counting and divider methods) or directly analyzing the self-affine exponent. The second group of methods includes the variable bandwidth, the first return and the multireturn probability distribution, and the power spectrum. The accuracy of all these methods is assessed in terms of the difference between an ‘‘input’’ self-affine exponent used for the synthetic construction and the ‘‘output’’ exponent measured by those different methods. The statistical results of this study provide a quantitative estimate of the dependence of the accuracy with the system size and the value of the self-affine exponent. Artifacts in the measurement of self-affine profiles or surfaces, misorientation, signal amplification, and local geometric filtering, which lead to biased estimates of the self-affine exponent, are also discussed.