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.
In this paper we are concerned with a microwave imaging problem for a non-magnetic two-layered background medium, where objects are buried in the lower half-space, and the scattered field is collected in the upper one according to a multi-monostatic configuration. In particular, we are interested in estimating the achievable transverse resolution. As well known, range resolution mainly depends on the working frequency band whereas transverse resolution depends on the geometrical parameters of the configuration and is usually computed in correspondence to the highest (or even the average) adopted frequency. Determining transverse resolution is much more difficult, and closed form estimations have been actually found only for the case of unbounded observation domain. However, in real scattering scenarios, measurements have to be necessarily collected under an aspect limited setup. Therefore, in order to fill such a theoretical gap, here the focus is on the estimation of transverse resolution for bounded observation domains. To this end, we consider a single-frequency 2D scalar prototype configuration where the buried scattering object domain is represented by a strip parallel to the half-space interface. More in detail, we succeed in finding an analytical estimation of the transverse resolution which highlights the role of the configuration parameters as well as the dielectric permittivity of the lower half-space.
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