The Influence of Fixed Errors of a Detector Array on the Reconstruction of Objects from Their Projections

A two-dimensional layer of a three-dimensional object is reconstructed from projection data generated with a fan-beam geometry and a detector array. The expection value of the amplitude of ring artefacts is given which are caused by fixed errors of the detector array. Simple analytic approximations of the amplitude are given. The amplitude increases near the center of rotation. For an application in X-ray scanners the uniformity of the detector array has to be very high to avoid ring artefacts.