Reconstruction of the X-ray tube spectrum from a scattering measurement.

An inverse technique has been designed to unfold the x-ray tube spectrum from the measurement of the photons scattered by a target interposed in the path of the beam. A special strategy is necessary to circumvent the ill-conditioning of the forward transport algebraic problem. The proposed method is based on the calculation of both, the forward and adjoint analytical solutions of the Boltzmann transport equation. After testing the method with numerical simulations, a simple prototype built at the Operational Unit of Health Physics of the University of Bologna was used to test the method experimentally. The reconstructed spectrum was validated by comparison with a straightforward measurement of the X-ray beam. The influence of the detector was corrected in both cases using standard unfolding techniques. The method is capable to accurately characterize the intensity distribution of an X-ray tube spectrum, even at low energies where other methods fail.