Penetrating power in radiography of high-Z materials as a function of bremsstrahlung spectrum endpoint energy
A modified radiographer’s equation is derived and fitted to simulation data so as to describe the increase in radiographic signal that comes with increasing bremsstrahlung spectrum endpoint energy. The dose contained in the incident spectrum follows an E28 power law, as often cited. However, the direct flux penetrating through a heavy, high-Z material, obeys a weaker scaling due to hardening of the radiation. The resultant expression depends on the thickness of the scene being radiographed, the composition of high-Z materials in the scene, and any filtering by other low-Z materials, such as Al or Be. The expression exhibits two asymptotic limits: a ‘thick’ limit at which radiation is extremely hardened and only a weak benefit to increasing endpoint energy is observed (also the most attenuating limit and therefore of dubious physical significance), and a ‘thin’ limit at which a minimum of high-Z material is present and the penetrating dose exhibits the 2.8 power scaling inherent in the incident spectrum. Behavior for intermediate thicknesses of W and Al are obtained by modeling incident and attenuated dose using the DOSECALC code and the Bayes’ Inference Engine (BIE). These data guide the optimization of MeV radiography over a wide range of energies where pair production plays a significant role in photon scattering.