On the Formulation and Implementation of the Love's Constraint for the Source Reconstruction Method

The formulation and implementation of the Love's condition constraint for the source reconstruction method (SRM) in near-field antenna measurements is analyzed in the context of inverse problems. To this end, the SRM is first analyzed to identify the non-unique or non-radiating current sources which may be present. Next, the advantages and disadvantages of general regularization techniques, which may address the non-radiating currents, are presented which serve to motivate the use of the Love's condition constraint. The main methods of formulating the constraint are then presented, one of which is a novel technique developed for this paper. Following this, the formulation methods are analyzed in order to predict the similarities and differences of the methods in the context of addressing the non-radiating currents of the SRM. This analysis is reinforced by simulated antenna measurements. In particular, the novel formulation method is demonstrated to provide greater reconstruction accuracy (in the examples considered), at the cost of computational complexity.