Field recovery over a sphere from a minimum number of data over a spiral

Electromagnetic field representations from a finite and non-redundant number of samples have been recently developed for arbitrary sources and observation surfaces having the same rotational symmetry [1]. In this framework, the field representation over a sphere [2] is a particularly interesting case, since it is relevant in the near field - far field (NF-FF) transformation with spherical scanning [3,4] and in the pattern recovery from measured or heavily computed data. When dealing with NF-FF transformations, a continuous movement of the robotic positioning systems makes the measurement set-up simpler and allows the reduction of the time required for the data acquisition. In particular a planar spiral arrangement of samples has been proposed in [5] and an efficient interpolation algorithm to reconstruct the near-field over a cylinder, from the data collected on a helix over it, has been developed in [6],