3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography: prospects of atomic resolution electron tomography.

A novel reconstruction procedure is proposed to achieve atomic resolution in electron tomography. The method exploits the fact that crystals are discrete assemblies of atoms (atomicity). This constraint enables us to obtain a three-dimensional (3-D) reconstruction of test structures from less than 10 projections even in the presence of noise and defects. Phase contrast transmission electron microscopy (TEM) images of a gold nanocrystal were simulated in six different zone axes. The discrete number of atoms in every column is determined by application of the channelling theory to reconstructed electron exit waves. The procedure is experimentally validated by experiments with gold samples. Our results show that discrete tomography recovers the shape of the particle as well as the position of its 309 atoms from only three projections. Experiments on a nanocrystal that contains several missing atoms, both on the surface and in the core of the nanocrystal, while considering a high noise level in each simulated image were performed to prove the stability of the approach to reconstruct defects. The algorithm is well capable of handling structural defects in a highly noisy environment, even if this causes atom count "errors" in the projection data.