Determination of the electronic density in a medium by an inverse method based on double-Compton scattering in transmission imaging

We propose a new method for reconstructing defects in bulk materials, via the recovery of the electronic volume density ne in the material, using doubly Compton-scattered gamma photons in transmission imaging modality. We establish an integral relationship between the photon flux density after a double scattering and the product of electronic densities at two different sites. This photon flux density at different scattering angles can be measured by an energy-position detector in a fixed configuration. Thus the reconstruction of ne can be formulated as an inverse problem of the integral relation, which is bilinear in the electronic densities. This theoretical result opens the way for a new imaging principle, which exploits scattered radiation rather than discarding it as in most existing imaging procedures. In this new procedure, the motion of the detector is no longer necessary as it is the case of conventional tomography