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

A numerical technique is presented which enables the propagation of wave fu nctions in a three-dimensional complex potential-energy distribution, as re quired 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 ob servations of a small carbon fibre by projection microscopy reveal the effe cts of absorption on the final images. In the situation considered, absorpt ion is responsible for the reinforcement of the external fringes compared t o those located well inside the geometrical projection. In agreement with e xperimental figures and two-dimensional simulations, it turns out that abso rption has to be accounted fur to explain the shape of projected images, ev en if the sample has a low level of opacity.