Fast X-Ray Diffraction (XRD) Tomography for Enhanced Identification of Materials

X-ray computed tomography (CT) can provide 3D images of density, and possibly the atomic number, for large objects like passenger luggage. This information, while generally very useful, is often insufficient to identify threats like explosives and narcotics, which can have a similar average composition as benign everyday materials such as plastics, glass, light metals, etc. A much more specific material signature can be measured with X-ray diffraction (XRD). Unfortunately, XRD signal is very faint compared to the transmitted one, and also challenging to reconstruct for objects larger than a small laboratory sample. In this article we analyze a novel low-cost scanner design which captures CT and XRD signals simultaneously, and uses the least possible collimation to maximize the flux. To simulate a realistic instrument, we derive a formula for the resolution of any diffraction pathway, taking into account the polychromatic spectrum, and the finite size of the source, detector, and each voxel. We then show how to reconstruct XRD patterns from a large phantom with multiple diffracting objects. Our approach includes a reasonable amount of photon counting noise (Poisson statistics), as well as measurement bias, in particular incoherent Compton scattering. The resolution of our reconstruction is sufficient to provide significantly more information than standard CT, thus increasing the accuracy of threat detection. Our theoretical model is implemented in GPU (Graphics Processing Unit) accelerated software which can be used to assess and further optimize scanner designs for specific applications in security, healthcare, and manufacturing quality control.