Reconstruction of Compton scatterers in the plane with a polychromatic source

James Webber (University of Manchester)

Frank Adams 2, School of Mathematics, Alan Turing Building,

Here we investigate the scattering problem for a polychromatic source and detectors collimated to the plane. We apply this to a system with a single rotating source and a fixed ring of detectors. Although more applications may be possible. We see after differentiating the data that we have a full set of circular arc integrals over the electron density, a curve which is closely related to a straight line through an inversion in the unit disk.

The problem for scattering has previously been investigated in a number of publications, where a monoenergetic source is typically assumed. However in many applications (e.g threat detection and baggage scanning) a type of x-ray tube is often used and the physics suggests a whole spectrum of initial photon energies is produced. Here we aim to address this complication in the continuos case, assuming Compton scattering to be the dominant process.

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