An apparatus for establishing a correction characteristic curve for a reduction of artefacts in a tomography comprises a means for providing projection data of the object, wherein the projection data comprise transmission values for the object, a means for calculating a representation of the object from the projection data, to obtain two or three-dimensional representation data for the object, a means for determining a measure for the transmission length of the object by using the representation data, a means for determining a transmission value, which is associated to the determined measure for the transmission length, and a means for generating the correction characteristic curve of several determined measures for transmission lengths and associated transmission values, wherein a precorrection of the projection data can be performed by using the determined correction characteristic curve, to iteratively determine the correction characteristic curve by using the precorrected transmission values. This concept for establishing a correction characteristic curve requires no reference object measurements or other information about the condition of the radiation source, the object, etc.