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The role of the source geometry is investigated within the realm of inverse source problems. In order to examine the properties of the far zone radiation operator of some 2D curved sources its Singular Value Decomposition (SVD) is studied, either analytically, when possible, or numerically. This allows to evaluate the number of independent pieces of information, i.e., the number of degrees of freedom (NDF), of the source and to point out the set of far zone fields corresponding to stable solutions of the inverse problem. In particular, upper bounds for the NDF are obtained by exploiting Fourier series representations of the singular functions. Both curved (i.e., circumference and arc of circumference) and rectilinear geometries are considered, pointing out the role of limited angular observation domains. Moreover, in order to obtain some clues about the resolution achievable in the inverse source problem, a point-spread function analysis is performed. The latter reveals a spatially variant resolution for limited angular observation domains. The practical relevance of these results is highlighted with numerical examples of array diagnostics.

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The singular value decomposition of the far-zone scattering operator for weak strip-like scattering objects is studied under multiple view and/or multiple frequency illuminations. The aim is to highlight how such diversities impact the number of degrees of freedom (NDF) of the scattering problem. When the angles of incidence and/or frequencies vary within discrete finite sets, the singular values are analytically determined. It is shown that they exhibit a multistep behavior. For the continuous case, upper and lower bounds are found, which allows us to obtain estimations for the NDF dependending on the parameters of the configuration.

In this paper the inverse source problem in the presence of a reflecting plane is dealt with for a two-dimensional configuration and bounded rectilinear strip sources. The cases of both orthogonal and parallel (to the reflecting plane) sources are considered. Analytical arguments are developed to estimate the singular value decomposition of the pertinent radiation operator. This allows highlighting of the role played by the reflecting plane in the so-called number of degrees of freedom of the radiated field as well as in the achievable resolution while reconstructing the unknown sources.

The problem of studying how spatial diversity impacts on the spectrum (singular values) of the radiation operator is addressed. This topic is of great importance because of its connection with the so-called number of degrees of freedom concept which in turn is a key parameter in inverse source problems as well as to the problem of transmitting information by waves from a source domain to an observation domain. The case of a bounded rectilinear source with the radiated field observed over multiple bounded rectilinear domains parallel to the source is considered. Then, the analysis is generalized to two-dimensional extended observation domains. Analytical arguments are developed to estimate the pertinent singular value behavior. This allows highlighting the way observation domain features affect spectrum behavior. Numerical examples are shown to support the analytical results.

In this paper the problem of sampling the field radiated by a planar source observed over a finite planar aperture located in the near-field is addressed. The problem is cast as the determination of the spatial measurement positions which allow us to discretize the radiation problem so that the singular values of the radiation operator are well-approximated. More in detail, thanks to a suitably warping transformation of the observation variables, the kernel function of the relevant operator is approximated by a band-limited function and hence the sampling theorem applied to achieved discretization. It results in the sampling points having to be non-linearity arranged across the measurement aperture and their number can be considerably lowered as compared to more standard sampling approach. It is shown that the proposed sampling scheme works well for measurement apertures that are not too large as compared to the source’s size. As a consequence, the method appears better suited for broad-side large antenna whose radiated field is mainly concentrated in front of the antenna. A numerical analysis is included to check the theoretical findings and to study the trade-off between the field accuracy representation (over the measurement aperture) and the truncation error in the estimated far-field radiation pattern.