Field reconstruction over a cylinder from a non-redundant number of samples over a non-uniform circular helix

Field representations from a finite and non-redundant number of samples have been developed for arbitrary sources and observation geometries with the same rotational symmetry. In this context the field reconstruction over a cylindrical surface is a particularly interesting case. In fact, this problem is relevant not only in the near field far field (NP-FF) transformation with cylindrical scanning, but also whenever an efficient reconstruction of the electromagnetic field over a cylinder is wanted. This work is devoted to the development of an efficient sampling interpolation scheme for an accurate reconstruction of the field over a cylindrical surface from the knowledge of a finite and non-redundant number of samples lying on a non-uniform circular helix. To do this, a sampling representation of the field over such an unconventional curve is developed starting from the theoretical results obtained by Bucci, Gennarelli and Savarese (see IEEE Trans. Antennas Propagat., vol.46, p.351-9, 1998).