In this paper, it is shown that the electromagnetic (EM) field, radiated or scattered by bounded sources, can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded. The number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field. This result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain. It is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry. The case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered. For these geometries, precise and fast sampling algorithms of central type are presented, which allow an efficient recovery of EM fields from a nonredundant finite number of samples. Such algorithms are stable with respect to random errors affecting the data.

Abstract-In this paper, the theoretical foundations of near-field-farfield transformations with spiral scannings are revisited and a unified theory is provided. This is accomplished by introducing a sampling representation of the radiated electromagnetic field on a rotational surface from the knowledge of a nonredundant number of its samples on a spiral wrapping the surface. The obtained results are general, since they are valid for spirals wrapping on quite arbitrary rotational surfaces, and can be directly applied to the pattern reconstruction via near-field-far-field transformation techniques. Numerical tests are reported for demonstrating the accuracy of the approach and its stability with respect to random errors affecting the data.

No abstract

No abstract

No abstract