Fringe contrast in inelastic LACBED holography.

We discuss diffraction holography in a scattering geometry reported by Herring [Ultramicroscopy 104 (2005) 261, Ultramicroscopy 106 (2006) 960] and interpreted in terms of the density matrix of the fast electrons. Whereas the previous description used an approximation replacing the LACBED by a CBED geometry and consequently left some doubts about the conclusions (namely the non-detectability of the MDFF) we now fully include the Fresnel propagator and the biprism operator in order to calculate the density matrix of the inelastically scattered electrons in LACBED geometry. We show that a defocus on the biprism with respect to the sample does not cause a significant effect on the fringe patterns that are formed when the discs are exactly overlapping. An important difference to the CBED geometry is however that the fringe contrast decreases when the shear deviates from a reciprocal lattice vector. This should enable to measure the spatial coherence for smaller shears than is possible in image holography.