With scanning probe experiments, it became possible to visualize electron flow in a two-dimensional electron gas. In this paper, a Green's function technique for efficient simulation of such experiments is presented. Interpretation of the experiments is further facilitated by a calculation of the current distribution. Furthermore, an alternative imaging method is put forward for measuring the local chemical potential. As an application, electron flow through a quantum point contact is studied. All features seen in experiments are reproduced and an interference effect is predicted resulting from the crossing of coherent beams of electron flow.