Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Baré, Jonathan (2012) Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Ingegneria energetica, nucleare e del controllo ambientale, 24 Ciclo. DOI 10.6092/unibo/amsdottorato/4892.
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Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

Tipologia del documento
Tesi di dottorato
Baré, Jonathan
Dottorato di ricerca
Scuola di dottorato
Ingegneria industriale
Settore disciplinare
Settore concorsuale
Parole chiave
Inverse problems; X-ray spectrum; Boltzmann equation; Adjoint transport; Rayleigh scattering; Compton scattering;
Data di discussione
11 Maggio 2012

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