A primary electron beam is generated with the aid of an electrode cathode and acceleration towards the anode, and then focused as finely as possible on the surface of the sample to be examined by means of subsequent electromagnetic lenses. In the probe, secondary electrons (SE), backscattering electrons (BSE) and X-rays are generated in an interaction volume dependent on the acceleration voltage and the material composition. The energy of the X-ray radiation depends on the atomic number of the emitting atom and is therefore "characteristic" of the element in question. All these signals can be registered with appropriate detectors. Corresponding topography, material and/or element contrasts can thus be imaged.