Density and atomic number measurements with spectral x-ray attenuation method

Abstract

X-ray attenuation measurements are widely used in medical and industrial applications. The usual results are one- to three-dimensional representations of the attenuation coefficient μ(r). In this paper, we present the ρZ projection algorithm for obtaining the density ρ(r) and atomic number Z(r) with an energy-resolving x-ray method. As input data the algorithm uses at least two measurements μ1,μ2,… with different spectral weightings of the source spectrum S(E) and/or detector sensitivity D(E). Analytically, ρ is a function of μ1−cμ2, c=const, and Z is a function of μ1/μ2. The full numerical treatment yields ρ(μ1,μ2) and Z(μ1,μ2) with S(E) and D(E) as commutative parametric functions. We tested the method with dual-energy computed tomography measurements of an organic sample and a set of chemical solutions with predefined ρ and Z. The resulting images show ρ and Z as complementary information: The density ρ reflects the morphology of the objects, whereas the atomic number Z=number of electrons/atom describes the material distribution. For our experimental setup we obtain an absolute precision of 0.1 for Z and 20 mg/cm3 for ρ. The ρZ projection can potentially lead to these classes of quantitative information for various scientific, industrial, and medical applications.