[@veeco], between a sphere with a diameter of $100\;\mu m$ attached on a $240\;\mu m$ long cantilever of stiffness $k=4\; N/m$ (as given by the manufacture), and an $Au$ coated silicon plate. Both sphere and plate are coated with $100\; nm$ of $Au$, and afterwards their root-mean-square (rms) roughness was measured by AFM (see Figs. \[fig1\] and \[fig2\]). Analysis of the area on the sphere where the contact with the substrate occurs was performed by inverse imaging (Fig. \[fig1\]) [@Pal08; @Zwo08c]. The histograms in Fig. \[fig1\] and \[fig2\] show the number of pixels corresponding to a given height.

![(a) Reverse AFM scan of a sphere that has been used for measurement. (b) Surface scan and and height distribution with large spots. (c) Surface scan and and height distribution without large spots. The full width of the roughness distribution of the sphere without the spots in (c) is about $6\;
nm$. (d) Grid used for the inverse AFM scans of the contact area.[]{data-label="fig1"}](fig1.eps){width="45.00000%"}

Notably the sphere roughness of $1.8\pm 0.2\; nm$ rms [@Zwo08b] is an average over a large area where relatively high spots are observed (see Fig. \[fig1\]a,b), which increase the rms roughness value. For plates surfaces (Fig. \[fig2\]) these 