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Proper field sampling strategies are important in antenna measurements and diagnostics applications to reduce the overall testing time. We investigate the role of the source dimension in determining the sampling points locations by referring to circumference geometries. An inverse problem approach is adopted, and the spectral decomposition of the relevant operator is considered for a two-dimensional geometry. First, we introduce and discuss an approximation of the resulting Point Spread Functions, on which we found our approach. Next, a numerical strategy to discretize the field observation domain is presented, which results in a nonuniform angular step depending, in turn, on the source extension. Some numerical examples of source characterization show the effectiveness of the approach in comparison with the uniform angular sampling.

An inverse problem approach is adopted to investigate the role of a limited observation domain in conformal source radiation both in the far and near zones. The spectral decomposition of the relevant operator drives the investigation, especially by the discussion of the singular values’ behavior and the point spread function (PSF). For a circular source geometry, accurate closed-form evaluations of the PSF allow to establish its angular variant behavior for limited observation angular domains. This leads to introducing a numerical procedure, based on the widths of the PSF main lobes, able to define an optimal source discretization, that is, the spacing of the array elements whose radiated field has the same number of degrees of freedom of the continuous conformal source. A nonuniform spacing is derived and the performances of the corresponding conformal arrays are compared with the uniform case, the number of elements being equal. Numerical results of pattern synthesis and array diagnostics of faulty elements support the improvement achieved by the approach when the same number of array elements are located in a nonuniform pattern.

In this paper, the question of how to efficiently sample the field radiated by a circumference arc source is addressed. Classical sampling strategies require the acquisition of a redundant number of field measurements that can make the acquisition time prohibitive. For such reason, the paper aims at finding the minimum number of basis functions representing the radiated field with good accuracy and at providing an interpolation formula of the radiated field that exploits a non-redundant number of field samples. To achieve the first task, the number of relevant singular values of the radiation operator is computed by exploiting a weighted adjoint operator. In particular, the kernel of the related eigenvalue problem is first evaluated asymptotically; then, a warping transformation and a proper choice of the weight function are employed to recast such a kernel as a convolution and bandlimited function of sinc type. Finally, the number of significant singular values of the radiation operator is found by invoking the Slepian–Pollak results. The second task is achieved by exploiting a Shannon sampling expansion of the reduced field. The analysis is developed for both the far and the near fields radiated by a 2D scalar arc source observed on a circumference arc.

Field sampling should be devised in order to preserve the information required for the knowledge of the radiation of an antenna. In this paper, we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

The inverse source problem has a number of applications in antenna analysis and synthesis. The properties of the radiation operator, connecting the source current to the far zone field, depends on the source geometry and can be analyzed by its Singular Value Decomposition. In this paper we examine point source reconstructions by considering the Point Spread Function. An approximate closed form evaluation for limited observation domains reveals a space variant behavior. It turns out that for a conformal array a non-uniform elements spacing accommodates definite advantages both for diagnostic and synthesis purposes. Numerical results are shown for a semi-circumference source observed in far zone over a semi-circumference.

Conformal arrays may be a viable solution in many antenna applications requiring a wide angular coverage with sufficiently high directivity values, so it is worth comparing different 2D conformal array geometries to satisfy these requirements. To this end, first, the singular value decomposition (SVD) of the radiation operator is exploited to determine the maximum directivity values an array can reach in the whole observation domain. A numerical study based on the maximum directivity and, hence, on the SVD is then proposed to select the array geometry complying with some given requirements. Therefore, the performances achievable by some array geometries (a semi-circumference, a trapezoidal, and an angle array) are analyzed, and the one assuring a better hemispherical coverage is suggested. Furthermore, such an SVD-based study is usefully exploited to determine which panels of a multi-faceted array must be fed to reach some assigned specifications.

The role of the source geometry in the the radiation of focusing beams by conformal antennas is examined by the comparison of their directivity functions at different maximum directions. An inverse source problem approach is adopted, where solutions stable with respect to data uncertainties are to be found by relying on the analysis of the pertinent operator by the Singular Values Decomposition. This general framework allows to connect the mean value of the mazimum directivity function to the Number of Degrees of Freedom of the conformal source, which depends only on its electrical length. For each source geometry the focusing far field ensuring the maximum directivity for every pointing direction and the corresponding source current are obtained. The comparison with the ones achieved by the usual phase compensation technique of the source current reveals their optimal behavior. The usefulness of the approach as a tool in antenna synthesis is shown by comparing different geometries for those applications where identical beams are required to be rdiated for the coverage of a larga angular domain.

Linear arrays have been well studied for their widespread applications, but they suffer from severe limitations in the scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its singular value decomposition and the number of degrees of freedom of the source according to its geometry. Then, a connection with the known closed-form results of the single line case is established. Next, for an angle geometry, the discussion of the point spread function reveals the condition to be achieved for an angle source to radiate identical beams with a coverage larger than the one of a single linear source with the same total length. Finally, we consider the power synthesis of identical focusing beams by linear arrays, arranged in an angle geometry, also including the effect of the element factor, without excitation constraints, so to show how possibly to drive the design of electrically large arrays by such an analytical approach.

The inverse source problem has a number of applications in antenna analysis and synthesis. The properties of the radiation operator, connecting the source current to the far zone field, depends on the source geometry and can be analyzed by its singular value decomposition. Here, first, we present useful upper bounds about the number of degrees of freedom for some 2D source geometries (i.e. for elliptical and parabolic arc sources) and examine the role of two different representation variables. These results were obtained from asymptotic arguments and allow to define the maximum number of independent sources and patterns that can be radiated by each geometry. They are verified to fit the numerically computed ones, too. Next, we examine the point source reconstructions by considering the point spread function. An approximate closed form evaluation reveals that the arc length representation variable leads to a space invariant behavior. The role of the source electrical length in determining the number of degrees of freedom is pointed out, too. Finally, the radiation properties of different source geometries are compared by means of a synthetic index and examples of radiation pattern synthesis and array diagnostics confirm the need to investigate the role of the source geometry.

In this paper, the inverse source problem for different source support 2D geometries is considered, when assuming that the radiated field is observed on a circumference in far zone. The Singular Value Decomposition (SVD) of the relevant linear operator is examined and an estimation of the Number of Degrees of Freedom (NDF) is recalled for some conic curves. In addition, a 2D source geometry made up by two lines is considered. Then, the reconstruction and radiation properties of some conic curves are compared to those ones of less bulky angle sources with the same aspect ratio.

In this work we investigate the effect of the source shape and of the representation variables choice on the eigendecomposition of the radiation operator and on the Point Spread Function (PSF) in a 2D geometry, when the radiated field is observed over a semi-circumference in far zone. The considered sources evolve from a line to a semi-ellipse and, finally, to a semicircumference. The main conclusions concern with an estimate of the number of degrees of freedom in connection with the source geometry and the fact that the PSF exhibits the same variant behavior along the source domain, independently on the observation variable.

The solution of inverse source problems by numerical procedures requires the investigation of the number of independent pieces of information that can be reconstructed stably. To this end, the mathematical properties of the relevant operators are to be examined in connection with the source shape. The aim of this work is to investigate the effect of the source shape on the eigendecomposition of the radiation operator in a 2D geometry, when the radiated field is observed over a semi-circumference in the far zone. We examine both the behavior of the eigenvalues and the effect of the choice of the representation variables on the point spread function (PSF). In particular, the effect of the choice of the representation variables is considered since operator properties may depend on it. We analyze different source shapes evolving from a line to a semi-ellipse and, finally, to a semi-circumference, in order to understand how the increase of the source aspect ratio affects the results. The main conclusions concern an estimate of the number of degrees of freedom in connection with the source geometry and the fact that the PSF exhibits the same variant behavior along the considered domain, independently of the observation variable. The practical relevance of the result is illustrated by two numerical examples. The first one deals with the conformal array diagnostics for the reliable reconstruction of the excitation of the array elements. The second one concerns the array synthesis problem, and a comparison between the radiating performances of the source geometries is presented.

The aim of this work is to present a useful estimation for the Number of Degrees of Freedom (NDF) when both the source of the electromagnetic field and the observation domain are arcs of circumferences and when the source is a modulated circumference observed over a circumference. Then, it is shown that for the circumference arc and the elliptical source the use of different source variables does not affect the NDF, but only the shape of the eigenvalues/singular values trend. In all the cases, the observation is in far zone.

The aim of this paper is to investigate the role of multiple views and multiple frequencies in linear inverse scattering problems. The study was performed assuming the Fresnel-zone approximation on the scattering operator. Due to the crucial role played by singular values into analysing the linear inverse scattering problems, the impact of view and frequency diversities on singular values behaviour was established. In fact, the singular values were related to the most common metrics used to quantify the achievable performances in inverse scattering problems, such as the number of degrees of freedom (NDF), the information content and the resolution.