Lab-based X-ray computed tomography (XCT) systems use X-ray sources that emit a polychromatic X-ray spectrum and detectors that do not detect all X-ray photons with the same efficiency. A consequence of using a polychromatic X-ray source is that beam hardening artefacts may be present in the reconstructed data, and the presence of such artefacts can degrade XCT image quality and affect quantitative analysis. If the product of the X-ray spectrum and the quantum detection efficiency (QDE) of the detector are known, alongside the material of the scanned object, then beam hardening artefacts can be corrected algorithmically. In this work, a method for estimating the product of the X-ray spectrum and the detector's QDE is offered. The method approximates the product of the X-ray spectrum and the QDE as a Bézier curve, which requires only eight fitting parameters to be estimated. It is shown experimentally and through simulation that Bézier curves can be used to accurately simulate polychromatic attenuation and hence be used to correct beam hardening artefacts. The proposed method is tested using measured attenuation data and then used to calculate a beam hardening correction for an aluminium workpiece; the beam hardening correction leads to an increase in the contrast-to-noise ratio of the XCT data by 41% and the removal of cupping artefacts. Deriving beam hardening corrections in this manner is more versatile than using conventional material-specific step wedges.
Keywords: Bézier curve; X-ray spectrum; beam hardening; linearisation; quantum detection efficiency.