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The random process theory (RPT) has been widely applied to predict the jointprobability distribution functions (PDFs) of asperity heights and curvatures ofrough surfaces. A check of the predictions of RPT against the actual statisticsof numerically generated random fractal surfaces and of real rough surfaces hasbeen only partially undertaken. The present experimental and numerical studyprovides a deep critical comparison on this matter, providing some insight intothe capabilities and limitations in applying RPT and fractal modeling toantireflective and hydrophobic rough surfaces, two important types of texturedsurfaces. A multi-resolution experimental campaign by using a confocalprofilometer with different lenses is carried out and a comprehensive softwarefor the statistical description of rough surfaces is developed. It is foundthat the topology of the analyzed textured surfaces cannot be fully describedaccording to RPT and fractal modeling. The following complexities emerge: (i)the presence of cut-offs or bi-fractality in the power-law power-spectraldensity (PSD) functions; (ii) a more pronounced shift of the PSD by changingresolution as compared to what expected from fractal modeling; (iii) inaccuracyof the RPT in describing the joint PDFs of asperity heights and curvatures oftextured surfaces; (iv) lack of resolution-invariance of joint PDFs of texturedsurfaces in case of special surface treatments, not accounted by fractalmodeling.

Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?