Determination of equivalent x-ray spectra from attenuation data

A method is described whereby a polyenergetic x-ray spectrum, as produced by a typical x-ray tube used in radiographic imaging, is approximated by an equivalent spectrum consisting of a small number of discrete x-ray photon energies, i.e. a line spectrum. The equivalent spectrum is found by a least squares fit to attenuation data for three different attenuating materials. Computer simulation and experimental measurements show that a three-energy equivalent spectrum accurately predicts the attenuation properties of the polyenergetic spectrum. The accuracy is limited by the uncertainty in the known values of the x-ray linear attenuation coefficients.