The problem of computing the singular system of the radiation operator pertaining to the case of strip currents is dealt with. The associate eigenvalue problem involves a space-variant operator whose kernel is not band-limited. As a consequence, the sampling approach, which has been recently introduced for computing the eigenwavefronts of some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it is shown that the kernel function can be recast as a varying band-limited function. This allows exploiting the pseudo-sampling series theory from which a sampling approximation of the kernel function is derived and eventually used to set the discrete eigenvalue problem. In particular, unlike the classical sampling approach, the sampling points turn out to be non-uniformly distributed. Some numerical examples are used to check the theory. It is shown that the most significant part of the singular system can be very accurately computed by using a number of samples slightly greater than the Shannon number.

The inverse source problem for a 2D geometry is considered in the circular geometry. The mathematical relationship between the radiated pattern and the source current is investigated by the appropriate Singular Value Decomposition (SVD) for different 2D planar and curved shapes. The spectral analysis allows discussing the number of degrees of freedom of each geometry and reveals a peculiar common pass-band behavior of the radiation operator. For some geometries, this can significantly affect the inverse source reconstruction problem by reducing the class of sources that can be stably reconstructed and therefore it can impact the achievable resolution. In addition, when the source is made of an arc of circumference the number of degrees of freedom is reduced. The numerical results show how this affects the class of patterns that can be radiated and, as a result, be of interest in conformal sources antenna synthesis problems.

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.

This article deals with the classical question of estimating the achievable resolution in terms of the configuration parameters in inverse source problems. In particular, the study focuses on the case of a planar surface magnetic current which is to be reconstructed from near-field observed over a bounded rectangular aperture parallel to the source domain. Resolution formulas are well known for far-field or Fresnel-zone configurations, and also for near-field cases, when data are full-view or a measurement aperture is an unbounded plane. For the case of bounded near-field observations, the resolution estimations mainly rely on some asymptotic arguments in order to mimic far-field reasoning. Here, the plan is to improve these results and to work out a resolution estimation that precisely captures the spatially varying behavior entailed by the near-field and aspect-limited configuration. To this end, the pertinent radiation operator is inverted by an adjoint inversion scheme (a back-propagation-like method) and the corresponding point-spread function is analytically estimated. Numerical examples show that the derived resolution estimation clearly points out the role of the geometrical parameters of the configuration and it is more accurate than other literature results.

The reconstruction of the field radiated by a source from square amplitude only data falls into the realm of phase retrieval. In this paper we tackle phase retrieval with two different approaches. The first one is based on a convex optimization problem called Phaselift. The latter exploits the lifting technique to recast phase retrieval as a linear problem with an increased number of unknowns and then, because the linear problem is highly undetermined, it adds further constraints (based on the mathematical properties of the solution) to estimate it. The second approach formulates phase retrieval as a least squares problem therefore it requires to tackle the minimization of a quartic functional which will be carried out by applying a gradient descent method. In the second part of the paper, in order to corroborate the effectiveness of both approaches, we present numerical results. Afterwards, we provide a comparison between the two methods and finally we emphasize how the ratio between the number of independent data and the number of unknowns impacts on the performance in both approaches.

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.