<div>This manuscript has been accepted for publication on IEEE Transactions
on Antennas and Propagation.</div>


<div>Abstract:
<br>The paper adopts an inverse problem approach to investigate the far zone
radiation of a collection of 2D linear sources. By the evaluation of the
number of independent pieces of information, i.e. the number of degrees
of freedom (NDF), and the analysis of the reconstruction of a focusing
beam, the role of the geometry can be examined in determining the set of
possible radiation patterns. The results are relevant to the radiation
pattern synthesis problem, since they allow to define the optimal source
geometry for the hemispherical coverage with identical radiation
patterns.</div>