spots were absent leading to the rms roughness $1.3\pm 0.2\; nm$ [@Zwo08b]. Although the high spots within the contact area may increase the contact separation between bodies, $d_0$, they deform fast when pushing surfaces into contact to determine the deflection sensitivity. This is demonstrated by inverse imaging (see [@Zwo08d] for detailed explanations) and mechanics calculations also confirm it [@Stress]. Locally without the spots or with the deformed spots the roughness obtained by inverse imaging was $0.8-1.2\; nm$ rms or $w_{sph}=1\pm 0.2\; nm$ within the contact area of size $1\; \mu m$ (Fig. \[fig1\]c).

![Scan areas and height distributions of the $Au$ films deposited on $Si$ substrate used for the force measurements.[]{data-label="fig2"}](fig2.ps){width="45.00000%"}

Stiff cantilevers used in this experiment do not allow low voltage electrostatic calibration ($<0.5\; V$) at small separations. To obtain the contact separation due to roughness $d_0$ we used a different procedure. One can define the distance between rough bodies as the distance between zero roughness levels. From the histograms in Figs. \[fig1\], \[fig2\] it is clear that the zero roughness level corresponds to the maximum of the distribution. Without the spots mentioned above these distributions are approximately symmetric. Two rough surfaces in contact are separated by the distance 