A radiation system includes a radiation generator to generate radiation, a source, and an illumination system configured to receive the radiation and provide a beam of radiation. The illumination system includes a beam measuring system configured measure at least one of position and tilt of the beam of radiation relative to the illumination system and a projecting device configured to redirect only a part of a cross section of the beam of radiation to the beam measuring system. The beam measuring system may include several position sensors, the readouts of which can be used to determine incorrect alignment of the radiation source with respect to the illumination system. Diaphragms are connected to the collector of the radiation generator, so that in addition to X, Y, and Z corrections, Rx, Ry and Rz corrections are possible.