A computer tomography apparatus has a circular anode and a circular radiation detector in which a patient to be examined is disposed. An electron beam from an electron gun is deflected by a beam deflection system, fed by a line voltage, so that the focus of the electron beam on the anode orbits the patient, thereby irradiating the patient from different angular positions. The radiation attenuated by the patient is recorded by the radiation detector, and corresponding electrical signals are read-out from the radiation detector by a data acquisition system, from which an image of the patient is constructed. To avoid image artifacts due to fluctuations such as ripples in the line voltage which supplies the tomography apparatus, the beam deflection system and the data acquisition system are synchronized so that, at each of n revolutions of the focus, the focus movement and the read-out of the measured values ensue slightly phase-shifted compared to the preceding revolution relative to the ripple period of the line voltage.