Tomographic Imaging of Crystalline Structures: Mathematics & Materials Science.

26^th November 2021, 14:00
Andreas Alpers
Mathematical Sciences

Abstract

Since the invention of the first CT scanner in the 1970s, tomography has evolved into a powerful imaging tool in modern medicine. By computer processing of scans acquired from multiple angles, tomography can provide 3D images of inner parts without having to cut the patient. Of course, tomography has also been found to be attractive in materials science. Here, however, new fundamental challenges arise as, for instance, crystalline objects are non-continuous, data is (or can be) acquired only from few angles, and data can be very noisy. It therefore becomes increasingly important to develop problem-specific reconstruction algorithms. As I will discuss in my talk, this can lead into areas of mathematics previously thought to be unrelated to materials science. And, vice versa, the materials science imaging tasks can motivate new developments in mathematics. I will focus in my talk on this interplay between mathematics and materials science, drawing on two examples from my research: the tomographic reconstruction of polycrystals from diffraction data and the reconstruction of nanowires from electron tomography data.