Generalised Polarisation Tensors for Maxwell's Equations

The detection of hidden targets from measurements of electromagnetic fields has many important applications, which include improving food safety by locating foreign objects, using medical imaging to find cancerous tumours, detecting landmines and weapons as well as in the application of geological surveys to find new aquifers. Depending on the application, the measured electromagnetic fields might relate to low frequency magnetic induction, medium frequency radio wave propagation, microwave radiation or higher frequency visible light, ultraviolet and x-rays. To determine the shape, location and material properties of hidden target from the measured electromagnetic fields requires the solution of the "Maxwell inverse problem". This process is mathematically and computationally challenging.

In this project, we will assemble a team of international scientists, mathematicians and engineers who will develop new mathematical results that describe how electromagnetic fields behave at different distances from the target across a range of frequencies. This, in turn, will lead to the individual classification of targets using a mathematical construction called a "generalised polarisation tensor". These results will open up possibilities for the next generation of inverse solution algorithms, which are capable of the rapid and accurate detection of hidden targets from electromagnetic field measurements.

Our proposed feasibility study has, in the longer term, the possibility to bring benefits to a range of beneficiaries in the UK and beyond.

In the short term, our project will bring academic benefits to applied mathematicians, physicists and engineers, working in the field of computational and theoretical electromagnetism and inverse problems, in the form of new theoretical developments. These theoretical developments will lead to possibilities for new forms of low-cost imaging that can be exploited by engineers, medical physicists and geophysicists involved in the design and development of new and improved forms of metal detectors, medical imaging equipment and geophysical survey equipment. We will ensure that the academic beneficiaries benefit from our research by the publication of papers and paying any publication costs to make these freely available to all Universities and other Research Organisations.

Our feasibility study will also bring rapid societal and economic benefits. It will bring immediate benefits to the "Find a Better Way" Charity, which is devoted to accelerating the detection and safe removal of landmines. This will be achieved by providing a more complete theoretical basis to the practical studies they are funding as part of the Scanning Electromagnetic Mine Imaging System (SEMIS) being developed by Professor Petyon at The University of Manchester. It will bring immediate benefits to companies specialising in the development of scanning equipment, for ensuring safety and security at public events and airports, companies developing metal detectors for food safety applications, organisations involved in the development of novel medical imaging modularities as well as those developing geophysical survey equipment. We will ensure they benefit from our research by engaging representatives from the groups in future proposals that will build on the success of this feasibility study.

In the medium term, this feasibility study, together with our proposed future research projects, will help to inform members of the public sector, such as policy makers, making decision over investments in new technologies for security and anti-terrorism measures at public events and airports, and health care managers, making decisions over investments in new medical technologies for medical technologies. It will also assist managers of companies involved in food production and preparation making decisions over new technologies for improving food safety and managers of water companies making decisions over new technologies for the prospecting of ground water aquifers.

In the longer term, the general public will benefit from the research initiated in this feasibility study. Examples of potential benefits include new techniques for the accelerated detection and safe removal of land mines, improvements to screening techniques that lead to greater safety and security from acts of violence and terrorism at public events and airports, improvements to medical diagnosis, through new technological developments, improvements to food safety, by reducing the risk of foreign objects through better detection techniques, and reductions in water shortages, through the improved prospecting of ground water aquifers.