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We present energy filtered holography experiments on a thin foil of Al. By propagating the reduced density matrix of the probe electron through the microscope, we quantitatively predict the fringe contrast as a function of energy loss. Fringe contrast simulations include the effect of Fresnel fringes created at the edges of the defocused biprism, the effect of partial coherence in combination with inelastic scattering, and the effect of a finite energy distribution of the incoming beam.

We present an ab initio calculation of the electron energy loss spectrum of rutile TiO2 in the energy range of 0 to 60 eV, focusing our interest on the excitation from the titanium 3p semicore levels. The results are compared to our measurements. Local field effects turn out to be crucial at those energies, and their inclusion in the calculation yields excellent agreement between theory and experiment. We show how in rutile these effects induce an anisotropy in the otherwise isotropic transitions from quasispherical 3p semicore states to 3d states of almost cubic symmetry.

We show that the mixed dynamic form factor for inelastic scattering of fast electrons in crystals is closely related to the density matrix of the probe electron and to that of the scatterer. With this insight it is possible to calculate both energy filtered diffraction patterns and energy spectroscopic high-resolution images. As an example we discuss the Si-K and -L edges.