Feasibility study for a novel method of dual energy x-ray analysis

Dual energy x-ray analysis (DEXA) is investigated using a nonlinear model for the x-ray linear attenuation coefficient μ that is expressed as a function of electron density N(e) and the fourth compositional ratio R₄. Nonlinear simultaneous equations are solved using a least-squares algorithm based upon the method of Levenberg and Marquardt. Measurements of μ for low atomic number materials (containing elements hydrogen to calcium) at energies 32-66 keV are used to study DEXA accuracy as a function of sample composition, photon energy and their separation ΔE. Results are presented for ΔE = 5-30 keV, for 2% measurement precision, and the doses involved are quantified. The model is subject to propagation of error analysis and results are presented for the relationship between measurement uncertainties and those for N(e) and R₄. The analysis shows how DEXA accuracy is controlled by the fractional compositional cross-product, which represents the contribution of composition to μ, and how this can be optimized by careful selection of beam energies according to the compositional range of interest. Accurate DEXA is achieved over restricted energy and compositional ranges: soft tissues only at approximately 15-25 keV, all tissues at approximately 30-80 keV and, for situations where a higher dose can be tolerated, all tissues at approximately 4-8 MeV.