Images of gas molecules by electron holography. I. Theory

Abstract

It is demonstrated that molecular images with an Abbe resolution limit as fine as 0.1 Å can, in principle, be reconstructed optically directly from appropriately recorded electron diffraction plates (holograms). Even when a sample of randomly oriented gas‐phase molecules is chosen as a subject, reconstructed images with a well‐defined physical interpretation can be made. If the molecules are selected to contain just one heavy atom—this atom to generate a strong ’’reference wave,’’ by scattering, so as to satisfy Gabor’s conditions for the production of a hologram—the reconstructed images correspond to rotational averages about the heavy atom. If no single atom dominates, the ’’image’’ is not as simple conceptually but the reconstruction is shown to display a series of rings, each of which corresponds to an interatomic distance in the molecule. The physical basis of the approach is reviewed, followed by a mathematical treatment of the electron scattered intensity and optical reconstruction.