Discrete Tomography and Imaging of Polycrystalline Structures

High resolution transmission electron microscopy is commonly considered as the standard application for discrete tomography. While this has yet to be technically realized, new applications with a similar flavor have emerged in materials science. In our group at Ris� DTU (Denmark's National Laboratory for Sustainable Energy), for instance, we study polycrystalline materials via synchrotron X-ray diffraction. Several reconstruction problems arise, most of them exhibit inherently discrete aspects. In this talk I want to give a concise mathematical introduction to some of these reconstruction problems. Special focus is on their relationship to classical discrete tomography. Several open mathematical questions will be mentioned along the way.