Rich Nonlinear Tomography for advanced materials (LEAD)

Tomographic imaging allows scientists and engineers to see inside material and components, using x-rays, neutrons and electrons to form three dimensional images. These techniques already help develop advanced materials, test manufactured components and develop new electronic devices. Each little cube in the 3D image (voxel) is assigned a grey scale value. In new rich tomography methods more data is collected, for example frequency spectra or diffraction patterns and this leads to the possibility to recover more complicated properties in each voxel. With diffraction methods we can image the strain in a solid material, which helps understand if a component will break, and helps us design better silicon chips as the strain affects the electronics. We can also measure the microstructure, for example where small crystals or fibres are are aligned in a certain direction in a materials. Using spinning neutrons we can image magnetic fields which have direction as well as magnitude. This will help develop better magnetic materials, for example the cores of transformers in electricity supply, or image the currents on a small scale in batteries.

While measurement techniques are under developed for all these methods, the mathematics is lagging behind, and there has been a disconnect between mathematicians who know relevant theory and experimental scientists. Mathematical methods will show which data is needed to unambiguously for the required image. We can also produce efficient algorithms to reconstruct images from data. Currently rich tomography systems produce huge amounts of data, swamping their storage and computational facilities. Collecting the right data and finding better algorithms is now essential for progress.

In this project the mathematical team will work closely with leading experimental groups to develop both the measurement methods and practical reconstruction techniques, and make sure science and engineering users benefit from our work.