Quantitative characterization of hierarchical multiscale surfaces of micro and nanostructured materials

Hierarchical surfaces have recently attracted a lot of interest, mainly due to their ability to exhibit multifunctionality combining different properties. However, despite the extensive experimental and technological appeal of hierarchical surfaces, a systematic and thorough quantitative characterization of their features is still missing. The aim of this paper is to fill this gap and build a theoretical framework for the classification, identification and quantitative characterization of hierarchical surfaces. The main questions addressed in the paper are the following: given a measured experimental surface how can we detect the presence of hierarchy, identify the different levels comprising it and quantify their characteristics? Special emphasis will be given on the interaction of different levels and the detection of the information flow between them. To this end, we first use a modeling methodology to generate hierarchical surfaces of a wide spectrum of characteristics with controlled features of hierarchy. Then we applied the analysis methods based on Fourier transform, correlation functions and multifractal (MF) spectrum properly designed to this aim. The results of our analysis reveal the importance of the hybrid use of Fourier and correlation analysis in the detection and characterization of different types of surface hierarchy as well as the critical role of MF spectrum and higher moment analysis, in the detection and quantification of the interaction between hierarchy levels.