An apparatus and method for establishing a correction characteristic curve for a reduction of artefacts in a tomography are described. Projection data of the object is provided, wherein the projection data comprises transmission values for the object. A representation of the object is calculated from the projection data to obtain two or three-dimensional representation data for the object. A measure for the transmission length of the object is determined by using the representation data. A transmission value, which is associated to the determined measure for the transmission length, is determined and the correction characteristic curve of several determined measures is generated 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.