Application of Inverse Source Reconstruction to Conformal Antennas Synthesis

The inverse source problem for a 2-D geometry is considered in the circular geometry. The mathematical relationship between the radiated pattern and the source current is investigated by the appropriate singular value decomposition for different 2-D planar and curved shapes. The spectral analysis allows discussing the number of degrees of freedom of each geometry and reveals a peculiar common passband behavior of the radiation operator. For some geometries, this can significantly affect the inverse source reconstruction problem by reducing the class of sources that can be stably reconstructed, and therefore, it can impact the achievable resolution. In addition, when the source is made of an arc of circumference, the number of degrees of freedom is reduced. The numerical results show how this affects the class of patterns that can be radiated and, consequently, be of interest in conformal sources antenna synthesis problems.