The lateral resolution of three-dimensional atom probes is mainly controlled by the aberrations of the ion trajectories near the specimen surface. For the first time, a simulation program has been developed to reconstruct the ion trajectories near a sharp hemispherical electrode defined at the atomic scale. Surface atoms submitted to the highest field were removed one by one. The consecutive gradual change of the surface topology was taken into account in the calculation of ion trajectories. As the tip was 'field evaporated', the initial spherical shape of the emitter was observed to transform gradually into a polygonal shape. When the tip reached its equilibrium shape, the field distribution at the tip surface was found to be much more uniform compared to the initial distribution. The calculated distribution of ion impacts on the detector exhibits the presence of depleted zones both at the centre of low index poles and along <001> zone axes. These predictions are in excellent agreement with experiments.