Inverse Source on Conformal Conic Geometries

The inverse source problem has a number of applications in antenna analysis and synthesis. The properties of the radiation operator, connecting the source current to the far zone field, depend on the source geometry and can be analyzed by its singular value decomposition. Here, first, we present useful upper bounds about the number of degrees of freedom (NDF) for some 2-D source geometries (i.e., for elliptical and parabolic arc sources) and examine the role of two different representation variables. These results were obtained from asymptotic arguments and allow to define the maximum number of independent sources and patterns that can be radiated by each geometry. They are verified to fit the numerically computed ones, too. Next, we examine the point source reconstructions by considering the point spread function. An approximate closed form evaluation reveals that the arc length representation variable leads to a space invariant behavior. The role of the source electrical length in determining the NDF is pointed out, too. Finally, the radiation properties of different source geometries are compared by means of a synthetic index and examples of radiation pattern synthesis and array diagnostics confirm the need to investigate the role of the source geometry.