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.
[1]
G. Franceschetti,et al.
On the spatial bandwidth of scattered fields
,
1987
.
[2]
G. Franceschetti,et al.
On the degrees of freedom of scattered fields
,
1989
.
[3]
O. Bucci,et al.
Optimal interpolation of radiated fields over a sphere
,
1991
.
[4]
Ovidio Mario Bucci,et al.
Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements
,
1991
.
[5]
O. Bucci,et al.
Fast and accurate far-field evaluation from a non redundant, finite number of plane polar measurements
,
1994,
Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting.
[7]
Ovidio Mario Bucci,et al.
Near-field-far-field transformation from nonredundant plane-polar data: effective modellings of the source
,
1998
.