An apparatus and related method for processing image data supplied by a scanning phase contrast or dark-field imaging apparatus (MA). Beam hardening artifact in phase contrast and dark-field imaging can be reduced by applying a beam hardening processing operation by a beam hardening processing module (BHC) in respect of a plurality of detector readings that contribute signals to the same image pixel position or geometric ray of an imaging region of the apparatus (MA). In one embodiment, a phantom body (PB) is used to acquire calibration data on which the beam hardening processing is based.