Amorphous carbon and amorphous materials in general are of particular importance for high resolution electron microscopy, either for bulk materials, generally covered with an amorphous layer when prepared by ion milling techniques, or for nanoscale objects deposited on amorphous substrates. In order to quantify the information of the high resolution images at the atomic scale, a structural modeling of the sample is necessary prior to the calculation of the electron wave function propagation. It is thus essential to be able to reproduce the carbon structure as close as possible to the real one. The approach we propose here is to simulate a realistic carbon from an energetic model based on the tight-binding approximation in order to reproduce the important structural properties of amorphous carbon. At first, we compare this carbon with the carbon obtained by randomly generating the carbon atom positions. In both cases, we discuss the limit thickness of the phase object approximation. In a second step, we show the influence of both carbons models on (i) the contrast of Cu, Ag, and Au single atoms deposited on carbon and (ii) the determination of the long-range order parameter in CoPt bimetallic nanoalloys.