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.

In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.

We consider the evaluation of the Number of Degrees of Freedom (NDF) of the field radiated by square sources in the far zone. The analysis is performed by employing a Singular-Value Decomposition (SVD) of the radiation operator in the two-dimensional scalar case. To this end, we start the analysis from simple geometries like two parallel strips and angle strips where analytical results can be established. For sufficiently spaced strip sources, the NDF depends only on their total electrical length. Then results for square sources follow on the same line. Finally, the numerical investigation of the case of concentric square sources, leading to an NDF independent on the inner source, opens the way to the discussion of the NDF of a full square source. In this case, it results that it depends only on the source perimeter.

In this paper, the problem of computing the number of degrees of freedom (NDF) of the field radiated by a strip current along all the possible lines orthogonal to the source is addressed. As well known, the NDF is equal to the number of singular values of the radiation operator that are before a critical index at which they abrupt decay. Unfortunately, in the considered case, the solution of the associate eigenvalue problem is not known in closed-form, and this prevents us from directly evaluating the singular values of the radiation operator. To overcome this drawback, a weighted adjoint operator is exploited. The latter allows obtaining an eigenvalue problem whose solution is known in closed-form but, at the same time, it modifies the singular values behavior. However, since the change affects only the dynamics of the singular values but not the critical index at which they abrupt decay, the NDF of the radiated field can be analytically estimated by resorting to the weighted adjoint operator.

Conformal antennas lack of general analysis methods of their radiation properties. For a circumference source, we examine the role of the angular width of the observation domain both in far and near zone in determining the set of radiated fields. By an inverse problem approach, the evaluation of the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), and the analysis of the reconstructions of point-like sources allow to introduce optimal array configurations. The results are relevant to the radiation pattern synthesis problem and to array diagnostics applications.

This paper deals with microwave subsurface imaging obtained by a migration-like inversion scheme, for a 2D monostatic scalar configuration and a two-layered background medium. The focus is on the determination of a data sampling strategy which allows to reduce the number of required measurements and at the same time keep the same performance in the reconstructions. To this end, the measurement points are determined in order to approximate the point-spread function corresponding to the ideal continuous case (i.e., the case in which the data space is not sampled at all). Basically, thanks to suitable variable transformations the point-spread functions is recast as a Fourier-like operator and this provides insight to devise the sampling scheme. It is shown that resulting measurement spatial positions are non-uniformly arranged across the measurement domain and their number can be much lower than the one provided by some literature standard sampling criteria. The study also contains a comparison with the free space case so as to highlight the role played by the half-space that schematized the subsurface scattering scenario on the number and the locations of the measurement points. Numerical examples are also included to check the theoretical arguments.

This paper 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. Here, the plan is to work out a resolution estimation that precisely captures the spatially varying behaviour entailed by the near-field and aspect-limited configuration. To this end, the pertinent radiation operator is inverted by an adjoint inversion scheme (a backpropagation- 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.

This manuscript has been accepted for publication on IEEE Transactions on Antennas and Propagation. Abstract: The paper adopts an inverse problem approach to investigate the far zone radiation of a collection of 2D linear sources. By the evaluation of the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), and the analysis of the reconstruction of a focusing beam, the role of the geometry can be examined in determining the set of possible radiation patterns. The results are relevant to the radiation pattern synthesis problem, since they allow to define the optimal source geometry for the hemispherical coverage with identical radiation patterns.

This manuscript has been accepted for publication on IEEE Transactions on Antennas and Propagation. Abstract: The paper adopts an inverse problem approach to examine the role of some 2D geometries in the source reconstruction from far zone data. It aims at evaluating the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), of the source and pointing out the set of far zone fields corresponding to stable solutions of the inverse problem. Some of the results are relevant to the synthesis problem of conformal antennas, since a general comparison of different source geometries in providing radiation pattern specifications is proposed.