Fast inverse equivalent current solutions with surface currents in complex space

Inverse equivalent current solutions for single-frequency field transformations of measured or computed field observations work commonly with electric and/or magnetic surface current densities. Often the field observation equations are augmented by a null-field condition in form of an integral equation for the region external to the Huygens surface. As an approximate and inexpensive alternative to the null-field condition, we propose to work with directive current sources, which are obtained by shifting the equivalent surface current densities into complex space. These sources are integrated into the fast irregular antenna field transformation algorithm which achieves low numerical solution complexity by utilizing multilevel fast multipole like principles. Field transformation results based on realistic measurement data are presented to demonstrate the functionality of the surface current densities in complex space.