parameters for MC simulations which reproduce the experimental observations.

Holography {#SubstrateHolography}
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When imaging vacuum with TEM off-axis holography the phase shift observed is slightly fluctuating due to imperfections of the biprism wire, aperture, and noise induced by the CCD camera.[@LL02] We analyzed these vacuum fluctuations in order to distinguish them from the sample signal. The inset in Fig. \[SubstrateHologram\](a) shows a typical image of the vacuum phase shift $\phi_{\rm vac}$ after subtraction of its mean value. The main graph of Fig.\[SubstrateHologram\](a) shows the normalized distribution $w_{\rm
  vac}(\Delta\phi_{\rm vac})$ of the vacuum fluctuations $\Delta\phi_{\rm vac} = \phi_{\rm vac}$. The full line is a Gaussian fit $$\label{Gauss} 
w(\Delta\phi) = \frac{1}{\sqrt{2\pi}\sigma}\ 
\exp\left\{-\frac{(\Delta\phi)^2}{2\sigma^2}\right\}$$ from which we obtain a width of the vacuum fluctuations of $\sigma =
\sigma_{\rm vac} = 0.052$ rad.

![\[SubstrateHologram\]*(Color online) Phase shift distributions as a measure of fluctuations of the phase. Panel (a) shows the result for the vacuum, panel (b) shows the substrate film without adsorbate, and panel (c) shows the distribution for the substrate film with Au adsorbate albeit at positions without islands. Please note the different scales of the $x$ axes. Histograms are obtained by binning and normalization of the shifted raw data, full lines are Gaussian 