Generalised Polarisation Tensors for Maxwell's Equations

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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.