A Normalized Metric for Effective Atomic Number Estimation in Dual-Energy X-Ray Imaging

Dual-energy X-ray imaging generates Z-images to classify materials and estimates the effective atomic number (Z_eff) to identify specific organic substances such as explosives or narcotics. Conventional methods relying on the attenuation ratio R =  µ₁/µ₂ exhibit limited sensitivity for distinguishing materials with close Z_eff values, such as TNT and water. This study introduces a normalized metric M=(µ₁−µ₂)/(µ₁+µ₂), transposed from the Michelson contrast index used in satellite remote sensing, and evaluates its performance through analytical simulation on 15 organic materials (Z_eff ranging from 5.4 to 8). Simulated spectra centered at 60keV and 120keV with 10⁴ events per spectrum are based on Jia Hao et al. (2013). Results show a relative error of ±3.51 % for M compared to ±4.56 % for R, a 23 % reduction in estimation error, demonstrating M's enhanced sensitivity to Z_eff variations in the organic domain. Error propagation analysis confirms that ΔM < ΔR for R ∈ [0.7, 0.9]. These findings illustrate that elementary transformations of existing dual-energy measurements remain underexplored, and that meaningful gains in material discrimination are accessible without modifying acquisition hardware or resorting to iterative reconstruction methods.