Real-space formulation of the quantum-mechanical inelastic scattering under complex-valued n-fold axially symmetric potentials.

A numerical technique is presented which enables the propagation of wave functions in a three-dimensional complex potential-energy distribution, as required for modelling electron `absorption'. The technique is implemented in a transfer-matrix and Green's-function general procedure to simulate field-emission and electronic projection microscopy. In particular, simulated observations of a small carbon fibre by projection microscopy reveal the effects of absorption on the final images. In the situation considered, absorption is responsible for the reinforcement of the external fringes compared to those located well inside the geometrical projection. In agreement with experimental figures and two-dimensional simulations, it turns out that absorption has to be accounted for to explain the shape of projected images, even if the sample has a low level of opacity.