Conformal antennas lack of general analysis methods of their radiation properties. For a circumference source, we examine the role of the angular width of the observation domain both in far and near zone in determining the set of radiated fields. By an inverse problem approach, the evaluation of the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), and the analysis of the reconstructions of point-like sources allow to introduce optimal array configurations. The results are relevant to the radiation pattern synthesis problem and to array diagnostics applications.