  It has been argued that in atomic-resolution transmission electron microscopy
(TEM) of sparse weakly scattering structures, such as small biological
molecules, multiple electron scattering usually has only a small effect, while
the in-molecule Fresnel diffraction can be significant due to the intrinsically
shallow depth of focus. These facts suggest that the three-dimensional
reconstruction of such structures from defocus image series collected at
multiple rotational orientations of a molecule can be effectively performed for
each atom separately, using the incoherent first Born approximation. The
corresponding reconstruction method, termed here Differential Holographic
Tomography, is developed theoretically and demonstrated computationally on
several numerical models of biological molecules. It is shown that the method
is capable of accurate reconstruction of the locations of atoms in a molecule
from TEM data collected at a small number of random orientations of the
molecule, with one or more defocus images per orientation. Possible
applications to cryogenic electron microscopy and other areas are briefly
discussed.
