Abstract: A positron source with high intensity and low energy bandwidth and small spatial dimensions, has a positron emitter of high specific activity and, following the positron emitter, a reflection moderator with a hole. The hole diameter on the emitter side of the reflection moderator is smaller than 0.4 mm, preferably below 0.1 mm. Because of the small hole diameter and the small energy spread, the phase space of the positrons coming from the positron source corresponds to the phase space of the electrons emitted by a conventional thermionic cathode. The positron source can therefore be used in a conventional scanning electron microscope, which can be selectively changed over between positron operation and electron operation. Two adjusting units and are provided for adjustment of the positron source.