Estimation of a photon energy spectrum for a computed tomography scanner

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Abstract
Estimated photon energy spectra are derived from transmission measurements using aluminum, copper, and sodium iodide absorbers. Two spectral models are proposed. One is based on a previously published model that analyzes the electron's penetration into the anode, and the production and attenuation of bremsstrahlung photons. The second model does not include details regarding the underlying physics, but treats the spectrum as a sum of delta functions. A nonlinear regularization method is used to overcome ill conditioning in the second model. Both models fit the transmission data to an accuracy of 0.30%, which is consistent with the experimental error. A quantitative comparison of the models is made by calculating the average and variance (over the derived energy spectra) of several relevant mass attenuation coefficients. The maximum variation in the average and variance was 1.5% and 3.2%, respectively, indicating that the spectra exhibit similar attenuation and beam hardening properties. The spectra were tested with a simulation that predicts scanner CT numbers for phantom measurements consisting of dilutions of sodium iodide in a water equivalent background. The agreement between simulation and experiment ranged from 1.5% at 220 HU to 4.4% at 1700 HU.