r=\frac{r_{01}-r_{21}e^{2ik_1h}}{1-r_{01}r_{21}e^{2ik_1h}},$$ where the reflection coefficients $r_{ij}$ on the border between media $i$ and $j$ are defined as $$\label{rij}
    r_{s,ij}=\frac{k_i-k_j}{k_i+k_j},\ \ \ r_{p,ij}=
    \frac{\varepsilon_jk_i-\varepsilon_ik_j}
    {\varepsilon_jk_i+\varepsilon_ik_j}.$$ Since we expect that the thickness of the water layer is small ($\sim 1\; nm$) then the phase factor $k_1h$ will be small $|k_1h|\ll 1$ at all frequencies covered by the ellipsometers. This is true because in the investigated frequency range $|\varepsilon_1(\omega)|\lesssim 2$. For this reason the measured “pseudodielectric” function $\langle\varepsilon\rangle$ only slightly deviates form the dielectric function of gold $\varepsilon_2$: $$\label{de}
    \langle\varepsilon\rangle=\varepsilon_2+
    \delta\varepsilon,\ \ \
    \left|\frac{\delta\varepsilon}{\varepsilon_2}\right|\ll 1.$$ Using the perturbation theory in $\delta\varepsilon$ one can find from (\[ps\_diel\])-(\[rij\]) the expression for the relative correction to the dielectric function of $Au$: $$\label{deps}
    \frac{\delta\varepsilon}{\varepsilon_2}=i\frac{4\pi h}{\lambda}
    \sqrt{\langle \varepsilon\rangle-\sin^2\vartheta}\;
    \frac{ \langle \varepsilon \rangle - \varepsilon_1 }
    {\langle \varepsilon \rangle-1}\cdot
    \frac{\varepsilon_1-1}{\varepsilon_1}.$$ This equation precisely coincides with that presented by Aspnes in Ref. [@Asp82].

If the dielectric functions of gold $\varepsilon_2$ and water $\varepsilon_1$ are known, then using Eqs. (\[de\]) and (\[deps\]) one could find the film thickness $h$. This can be performed by the best fit of the known $\varepsilon_2$ with the calculated $\langle \varepsilon\rangle-\delta\varepsilon$. However, as it was demonstrated [@Sve08] the optical properties of opaque $Au$ films depend on 