Calculation of 3D sensitivity matrix for electromagnetic tomography system using boundary elements and the perturbative approach

Electromagnetic tomography (EMT) is a non-invasive imaging technique capable of mapping the conductivity and permeability of an object. In EMT, eddy currents are induced in the object by the activation coils, and the receiving coils can measure the EMT voltages. When the activation frequency is significantly large, we can treat the metallic targets as electrically perfect conductors (EPCs). In this situation, a thin skin approximation is reasonable and this type of scattering problem can be effectively treated by the boundary element method (BEM) formulated through integration equations. In this study, we compute three-dimensional (3D) sensitivity matrix between the sensors due to an EPC perturbation. Efficiency improvement is achieved through the utility of scalar magnetic potential. Two EPC objects, one sphere and one cube shaped, are simulated. The results agree well with the H dot H formula. Overall, we conclude that BEM can be used to calculate the 3D sensitivity matrix of an EMT system efficiently. This method is a general one for any shaped objects while the H dot H solution is only capable of producing the response for a small ball.