the intrusions are only 2 to 4 C-C bond lengths wide, it appears likely that they are capped in the production process thus stabilizing the structure. The intrusions are then left as voids in the film. The effective potential is strongly reduced at the position of the voids leading to the observed phase modulation. At the same time the cap yields a rather smooth surface consistent with the observed island formation. The C atoms surrounding the voids have less nearest neighbor atoms,[@DD98] which is consistent with the measured EELS spectra[@RFG04] indicating largely trivalent coordination. In the absence of methods for a more precise determination of the local structure of the substrate we use this scenario as a working hypothesis.

Finally, the histogram in Fig. \[SubstrateHologram\](c) shows the normalized phase shift distribution of the a-C substrate film [ *with*]{} the Au adsorbate, albeit at positions without any of the observed islands. (The latter are discussed in Sec.\[sectionFilmChar\]). The Gaussian fit from Eq. \[Gauss\] as shown by the full line has a width of $\sigma_{\rm subs} = 0.164$ rad which is 25% larger than $\sigma_{\rm a-C}$. The difference is readily interpreted as induced by small Au clusters pinned at small intrusions of 