Correction for beam hardening artefacts in computerised tomography

Conventional computerised tomography systems (CT) are usually equipped with polyenergetic X-ray sources, which prevents accurate density measurements because of the general CT-image artefact called beam hardening (BH). BH results in false gradients of the linear attenuation coefficient in the CT cross section images, indicating a non-existent density or composition gradient in the imaged object. A number of methods have been proposed to correct for, or limit the effect of, beam hardening. One of these is called linearisation of the CT-data, in which the polyenergetic CT-data are transformed to monoenergetic CT-data. This requires knowledge of the CT-data as a function of object thickness. Data points to derive this function are usually measured using a set of samples of different object material thicknesses at the imaging parameter settings used and fitted with a polynomial. However, the sample preparation makes this method tedious to use. In this work a simulation method has been developed, which can accurately simulate the polyenergetic CT-data for any arbitrary object material and thickness if a priori information of the object material density and composition exists. The simulation method requires detailed knowledge of the imaging system, that is, X-ray energy spectra, detector response and information transfer from detector to digitised data. Besides developing the simulation tool, it has been shown that one of the major difficulties with this BH-correction method is to accurately determine the curvature of the function representing the polyenergetic CT-data. Earlier proposed endorsements to fit a second-degree polynomial to the polyenergetic CT-data are not sufficient to describe its curvature, at least a polynomial of degree eight or higher is required. Here cubic-spine interpolation is used, which avoids the problem.