title: Relativistic calculations of intensity distributions in elemental maps using contrast transfer functions.
abstract: The interpretation of highly resolved elemental maps is not straightforward: one has to consider the quantum mechanical nature of the scattering process as well as the influence of the microscope. Existing calculations of the contrast in elemental maps are based on a non-relativistic approach, while in most of the currently installed electron microscopes, the electrons penetrate the specimen with relativistic energies >/= 200 keV. Therefore, we have recalculated the intensity distribution in elemental maps based on a fully relativistic theory. Using the concept of contrast transfer functions, the simulations account for lens aberrations as well as the defocus. Surprisingly, the results exhibit considerable deviations between the relativistic and non-relativistic calculations even in the region of low acceleration voltages such as 100 kV. These differences increase with increasing acceleration voltage and are strongly dependent on aperture and energy loss. Quantitative simulations and evaluations of highly resolved elemental maps should therefore make use of a fully relativistic theory.