Institut des
NanoSciences de Paris
Accueil > Evénements > Séminaires > Archives 2011 > Scale-sensitive fractal

Séminaire général

Scale-sensitive fractal analysis of surface topographies Physical interpretations and practical applications

Christopher Brown

The objective of applying fractal analysis to surface topographies is to characterize the geometry in some useful way. Useful characterization means that different kinds of surfaces can be discriminated and that correlations can be found between the topographic characterizations and topographically-related behaviour and processing of the surfaces. Of the many interesting kinds of fractal analysis that have appeared in the literature since the 1980s, when I was at the Swiss Federal Institute of Technology in Lausanne (EPFL), my students and I have developed area-scale analysis. Our method uses repeated virtual tiling exercises on a measured surface such that a range of tile sizes or scales are included. Area-scale analysis is particularly appealing because of the clear physical interpretations that can be associated with surface area. All the surfaces we have studied appear to have chaotic, or fractal, components to their topographies over some range of scales. The apparent area and the complexity of these chaotic components changes with the scale of observation. Geometrically the apparent area of a rough surface at a particular scale relates to the inclinations on the surface at that scale and therefore the area at some scale should correlate with the scattering from the surface. We have found that there can be particular scales where the area correlates well with some behaviour, such as adhesion. And, there are particular scales that work well for discrimination of surfaces based on their areas. These scales could provide insight for improving the understanding of topographically-related surface phenomena.