The design of reflectarray surface currents that satisfy both radiation and user-defined antenna feasibility constraints is addressed through a novel paradigm which takes advantage of the non-uniqueness of inverse source (IS) problems. To this end, the synthesis is formulated in the IS framework and its non-measurable solutions are employed as a design DoF. Thanks to the adopted framework, a closed-form expression for the design of reflectarray surface currents is derived which does not require any iterative local/global optimization procedure and which inherently satisfies both the radiation and the feasibility design constraints. The features and potentialities of the proposed strategy are assessed through selected numerical experiments dealing with different reflectarray aperture types/sizes and forbidden region definitions.

This thesis studies the use of the Source Reconstruction Method (SRM) to characterize antennas. The SRM calculates equivalent sources/currents on an arbitrarily shaped reconstruction surface to represent the original antenna. This is done by enforcing that the original antenna and equivalent currents radiate the same field at user selected measurement locations. These equivalent currents spatially characterize the original antenna because they can be used in direct radiation problems to obtain field estimates anywhere outside the reconstruction surface, including the far-field. First a spherical SRM algorithm is implemented and the diagnostic capabilities of the SRM are also synthetically shown through an example with an array of elementary dipoles. It is then shown that the SRM compares well to pre-existing commercial antenna software over different frequencies and can also be used successfully with a partial dataset. It is demonstrated that the equivalent currents can also provide meaningful information with experimental data. Next the hierarchical matrix framework is studied in conjunction with the SRM to decrease the algorithm's memory requirement and increase the speed of execution. It is shown that it is beneficial to use the hierarchical matrix framework with the SRM when using Love's condition or with measured data on a surface very close to the reconstruction surface. The SRM is then used to obtain incident field estimates in microwave imaging systems. Using a 2D transverse magnetic framework, we show that even with the limited data available in typical microwave tomography setups the SRM can produce incident field estimates in the imaging domain. These estimates are then used along with an MR-GNI algorithm to image synthetic and experimental objects with uncalibrated measured data. / October 2016