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We present a theoretical background for heavy element quantification through the intensive analysis of beam hardening (cupping artifacts) in X-ray computed tomography (CT) images. Cupping artifacts resulting from X-ray CT using a polychromatic X-ray source are quantitatively analyzed with an analytical solution for a cylindrical sample of a homogeneous aqueous solution/suspension containing a heavy element. The theoretical solution reveals that the severity of cupping artifacts is strongly dependent on the sample chemistry and the acceleration voltage of the X-ray tube. Careful analysis of this dependency enabled simultaneous determination of the atomic number and molar concentration of the heavy element within a particular estimation error range. Significant improvement in terms of the accuracy of determining the atomic number was achieved by employing double-exposure X-ray CT.

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Nondestructive Quantification of Heavy Elements Through the Analysis of Beam Hardening Artifacts Using Double-Exposure X-ray Computed Tomography: A Theoretical Consideration