Ref. [@Ben66], where the authors checked the validity of the Drude theory by measuring reflectivity of carefully prepared gold films in ultrahigh vacuum in the spectral range $0.04<\omega<0.6$ eV. Therefore, this value is good if one disposes of well prepared samples.

The Drude parameters from Kramers-Kronig analysis\[Sec5\]
=========================================================

Because the values of the Drude parameters are crucial for a reliable prediction of the Casimir force, it is important to assess that different methods to determine the parameters give the same results. Alternatively to the extrapolation procedure of the previous section we will now discuss a procedure based on a Kramers-Kronig analysis. To this aim we will extrapolate only the imaginary part of the dielectric function to low frequencies $\omega<\omega_{\rm c}$. The dispersion relation between $\varepsilon^{\prime}$ and $\varepsilon^{\prime\prime}$

$$\label{KKrel}
    \varepsilon^{\prime}(\omega)-1=\frac{2}{\pi
}P\int\limits_{0}^{\infty }dx\frac{x\varepsilon ^{\prime \prime
}\left( x\right) }{x^{2}-\omega ^{2}}$$

can then be used to predict the behavior of $\varepsilon^{\prime}(\omega)$ and compare it with the one observed in the experiments. From this comparison the Drude parameters can be extracted.

The low-frequency behavior of $\varepsilon^{\prime\prime}(\omega)$ is important for the prediction of $\varepsilon^{\prime}$ because for metals $\varepsilon^{\prime\prime}(\omega)\gg1$ in the low frequency range. Therefore, at $\omega<\omega_{\rm c}$ we are using $\varepsilon^{\prime\prime}(\omega)$ from Eq. (\[ImDrude\]). At higher 