Statistically representative estimators of multi-scale surface topography: example of aluminum blasted rough samples

The topography of a rough surface determines many of its physical properties, for instance, tribology, contact mechanics, optical properties etc. Nowadays, a deep understanding of such physical phenomena requires the knowledge of the topography at appropriate length scales. Apart from performing multi-scale measurements of the surface topography, it also requires the use of proper statistical estimators for the analysis of such topography maps. Moreover, when dealing with light scattering in the visible spectral range, the scale at which the estimators of local topography properties are defined is extremely important. Here we present a multi-scale and statistical study of the surface topography of blasted aluminum samples which all have rather different visual appearance. Various statistical estimators of surface topography are examined, including estimators related to the height distribution, the lateral correlation and local topology. The combination of these various estimators unveils a scale separation between a micro-scale roughness inherited from the initial cold-rolled aluminum surface and a large scale roughness fully controlled by the blasting process. A special emphasis is given to the crucial importance of length scales in the estimation of local slopes. The present analysis establishes a quantitative link between the statistical properties of the surface topography and the blasting process used to fabricate the samples.