Different ways of enforcing Love’s condition in determining equivalent currents from radiated field data

The main objective of this thesis is the study of three possible ways of determining equivalent currents from radiated field samples solving an inverse problem. The results obtained using the three different formulations are compared with reference results. As we work with synthetic data—simulations—we can access true values of the radiated field at an arbitrary location. From that, we can also evaluate true equivalent currents fulfilling Love’s null field condition. These constitute reference values. As currents fulfilling Love’s condition are directly related to the tangential components of the field at those locations, they are useful for diagnostic purposes. We consider three sets of equivalent electric and magnetic currents, each one obtained solving an inverse problem satisfying different equations. The first method enforces that the sought currents radiate a field that matches the field samples at the measurement surface. The second method enforces concurrently both the previous condition and the condition of having a vanishing field inside the reconstruction surface. The third method derives currents fulfilling Love’s condition applying a projection operator to the currents obtained with the first method. The results obtained during the work of the thesis show that the inverse currents obtained with the third method have the smallest error with respect to the reference currents. However, these currents radiate a field that differs from the reference one for an amount larger than in the cases of the other two methods. The currents obtained with the second method are the best trade-off between accuracy of the re-irradiated field and the adherence with the true equivalent currents fulfilling Love’s condition. These results hold for different values of Signal to Noise Ratio.