A model for multi-energy x-ray analysis

Multi-energy x-ray analysis (MEXA) uses measurements of the x-ray linear attenuation coefficient μ, obtained at different photon energies to determine parameters that characterize the density and composition of materials. The key to achieving this goal is an accurate parameterization for μ, allowing measurements to be written as simultaneous equations and then solved. This author has reported such a model where mixtures are characterized by four or more statistical moments that describe the distribution of atomic number. These can be re-expressed as the product of the electron density N(e) and four or more compositional ratios R(k) with the same 'units' as atomic number (i.e. dimensionless). The model was turned to MEXA where it delivered reliable estimates for N(e) and R(4) and not the intermediate compositional ratios. This report studies the relationships between compositional ratios for tissues and tissue substitute materials. Correlations are identified leading to a new parameterization that is expressed as a nonlinear function of N(e), R(4) and other coefficients. The properties of the transformed parameterizations for μ and the energy absorption coefficient μ(en) are considered for low atomic number materials at energies 15-100 keV, and for a broader range of materials at energies 5 keV to 20 MeV. The interpretation of the parameters N(e) and R(4) is explored in terms of basis materials. The general case of three basis materials cannot be solved for all contributions, but the special case of just two basis materials can be fully solved.