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.