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.

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Abstract. With reference to inverse scattering from an unlmown object of limited extension embedded in a homogeneous background at a fixed frequency, we show that only a fmitedimensional representation of the unknown contrast can be hopefully retrieved. Exploiting the quasi-band-limitedness property of scattered fields, an accurate upper bound to the dimension of such a space is evaluated in both the single incidence and multiview cases. Moreover, effective schemes are given to collect all the information available from the scattering experiments in a nonredundant manner. As a by-product, an optimal (minimally redundant) sampling strategy for the monostatic radar cross section is also provided. Finally, we briefly discuss how the requirement for a globally effective and reliable solution scheme can lead to a reduction of the actually retrievable information.

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