In a tomography apparatus and operating method, at least two acquisition systems are respectively each disposed in the azimuthal direction at respective specific system angles around a common rotation axis. Both system angles can be determined for a substantially constant rotation angle speed of the two acquisition systems on the basis of measurement values, which are calculated at a rotation angle position of a reference object that can be introduced into both measurement planes. The tomography apparatus in this manner enables artifact-free reconstruction of a slice or volume image using the system angles determined in this manner.