Iterative reconstruction of in-line electron holograms.

In low energy electron point source (LEEPS) microscopy, electrons emerge from a point source, propagate as spherical waves, and arrive at a screen. Some electrons scatter off an object, i.e. a cluster of atoms, placed between the source and the screen; others arrive at the screen without scattering. The interference pattern on the screen, an electron hologram, is used to reconstruct the object by calculating and analyzing a function K(r) in the region occupied by the object. We present an iterative method that uses the original reconstruction K(o)(r) to determine the atomic configuration of the object. No knowledge of the object, except for the vicinity in which the object is located, is used in the iterative scheme. In particular, no knowledge of the atomic structure is used. The method uses K(o)(r) to make a test object that in turn gives another reconstruction K(1)(r); K(1)(r) and K(o)(r) are used to modify the test object and obtain K(2)(r). The iteration is repeated until it converges on a final object that gives a reconstruction K(f)(r) that is very similar to K(o)(r). The final object gives an atomic structure that is close to the atomic structure of the original object. Results for several idealized objects are presented and discussed.

Tomographic reconstruction of multiple in-line electron holograms of realistic objects.

In theoretical low energy electron point source microscopy, simulated holograms are made and used to reconstruct atomic clusters. In previous investigations, simple test clusters were used for convenience. In this paper we explore more realistic structures composed of a single type of atom such as diamond, graphite and Buckminsterfullerene--all of which consist of carbon atoms. We also examine clusters with two or more distinct atom types, including TiO(2), CuO, Pt(3)O(4), Ga(3)Pt(5), WC, MgCO(3), and MgO. Reconstructions from a single hologram do not give atomic resolution, and consist instead of 'spurious peaks' that are not located at atomic sites, as well as 'atomic peaks' close to atomic sites. Here we apply methods we developed previously to remove all spurious peaks. We show final reconstructions that consist only of atomic peaks located very close to atomic sites.

Reconstruction of composite in-line electron holograms using a small emission cone.

We report a new method that gives atomic resolution in the reconstruction of simulated holograms in theoretical low energy electron point source (LEEPS) microscopy, and that uses a screen size that is commensurate with screen sizes used in experimental LEEPS. The method exploits the spherical symmetry in the electron waves emerging from the source. We compare holograms obtained by rotating the screen about an axis passing through the point source as opposed to rotating the atomic cluster in the opposite sense about the same axis. We show that, by generating and combining simulated holograms obtained by rotating the cluster, with the screen held fixed, a composite hologram, comprised of the individual holograms, captures enough information that atomic resolution in the reconstructions is obtained. A key feature is to choose the rotations to optimize the collective interference pattern on the composite hologram. This results in sharper resolution while using a considerably smaller screen size; results are reported for a screen size about ten times smaller than screen sizes typically used in theoretical LEEPS. The method used gives commensurate or better resolution on comparison to results obtained using the larger screen size. Possible implications for experimental LEEPS are briefly discussed.