The random process theory (RPT) has been widely applied to predict the joint
probability distribution functions (PDFs) of asperity heights and curvatures of
rough surfaces. A check of the predictions of RPT against the actual statistics
of numerically generated random fractal surfaces and of real rough surfaces has
been only partially undertaken. The present experimental and numerical study
provides a deep critical comparison on this matter, providing some insight into
the capabilities and limitations in applying RPT and fractal modeling to
antireflective and hydrophobic rough surfaces, two important types of textured
surfaces. A multi-resolution experimental campaign by using a confocal
profilometer with different lenses is carried out and a comprehensive software
for the statistical description of rough surfaces is developed. It is found
that the topology of the analyzed textured surfaces cannot be fully described
according to RPT and fractal modeling. The following complexities emerge: (i)
the presence of cut-offs or bi-fractality in the power-law power-spectral
density (PSD) functions; (ii) a more pronounced shift of the PSD by changing
resolution as compared to what expected from fractal modeling; (iii) inaccuracy
of the RPT in describing the joint PDFs of asperity heights and curvatures of
textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured
surfaces in case of special surface treatments, not accounted by fractal
modeling.Comment: 21 pages, 13 figure