Rich Nonlinear Tomography for advanced materials (LEAD)

层析成像技术使科学家和工程师能够利用X射线、中子和电子形成三维图像，看到材料和部件的内部。这些技术已经帮助开发先进的材料，测试制造的组件和开发新的电子设备。3D图像中的每个小立方体（体素）都被分配了一个灰度值。在新的丰富的层析成像方法中，收集更多的数据，例如频谱或衍射图案，这导致恢复每个体素中更复杂的属性的可能性。通过衍射方法，我们可以成像固体材料中的应变，这有助于了解组件是否会断裂，并帮助我们设计更好的硅芯片，因为应变会影响电子器件。我们还可以测量微观结构，例如材料中的小晶体或纤维在某个方向上排列。利用旋转的中子，我们可以对既有方向又有大小的磁场成像。这将有助于开发更好的磁性材料，例如电力供应中的变压器铁芯，或电池中的小规模电流成像。虽然所有这些方法的测量技术都在开发中，但数学却落后于人，并且了解相关理论的数学家和实验科学家之间存在脱节。数学方法将显示哪些数据是需要明确的所需的图像。我们还可以产生有效的算法来从数据中重建图像。目前，丰富的层析成像系统产生了大量的数据，淹没了他们的存储和计算设施。收集正确的数据和寻找更好的算法是取得进展的关键。在这个项目中，数学团队将与领先的实验小组密切合作，开发测量方法和实用的重建技术，并确保科学和工程用户从我们的工作中受益。

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.