The KATRIN experiment is going to search for the average mass of the electron antineutrino with a sensitivity of 0.2 eV/c2. It uses a retardation spectrometer of MAC-E filter type to accurately measure the shape of the electron spectrum at the endpoint of tritium beta decay. In order to achieve the planned sensitivity the transmission properties of the spectrometer have to be understood with high precision for all initial conditions. For this purpose an electron source has been developed that emits single electrons at adjustable total energy and adjustable emission angle. The emission is pointlike and can be moved across the full flux tube that is imaged onto the detector. Here, we demonstrate that this novel type of electron source can be used to investigate the transmission properties of a MAC-E filter in detail.