Electron Spectroscopic Imaging (ESI) in an energy filtering TEM is a new analytical technique which allows one to obtain two-dimensional elemental distribution images. In the present paper the detection limits of the new technique will be discussed. Si3N4 ceramics with different thicknesses of the amorphous oxide grain boundary layers have been chosen as a model system. Quantitative results have been obtained on three different energy filtering instruments and will be compared with the results of theoretical calculations. The application of ESI for the mapping of near edge fine structure will be discussed.