Compton scattering tomography

When a fan beam of monoenergetic γ rays is emitted from a point source into a plane and the scattered photons are recorded by a point detector, the locus of points over which singly Compton-scattered photons suffer the same energy loss is a circle passing through the source and detector points. Thus, the number of scattered photons recorded at a particular detector and energy can be expressed as a weighted line integral of the electron density over a circular path uniquely determined by the energy and the detector location. This defines a novel tomographic reconstruction problem in which, by recording the number of scattered photons as a function of energy and detector position, an image of electron density can be reconstructed from measurements of its line integrals over many overlapping circular paths. It is shown here that this image reconstruction problem has an analytical solution which bears some resemblance to the filtered-backprojection algorithm used in conventional (transmission) computed tomography (CT). A tomographic imaging scheme based on this idea would have several potential advantages over conventional CT systems in the field of industrial nondestructive evaluation, e.g., the ability to image from one side of the object, and the absence of moving parts.