On the Formulation and Implementation of the Love’s Condition 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 are analyzed in the context of inverse problems. To this end, the SRM is first analyzed to identify the nonunique or nonradiating (NR) current sources which may be present. Next, the advantages and disadvantages of general regularization techniques, which may address the NR 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 article. Following this, the formulation methods are analyzed in order to predict the similarities and differences of the methods in the context of addressing the NR currents of the SRM. This analysis is reinforced by simulated antenna measurements. In particular, the novel formulation method is demonstrated to provide a greater regularizing effect (in the examples considered), at the cost of computational complexity.