Radiation Properties of Conformal Antennas: The Elliptical Source

Abstract

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.

On-Axis Resolution of a Circular Aperture

“…For this reason, we refer to it as on-axis resolution. Note that this a customary axicon geometry which has already been studied in [12][13][14][15]. However, it must be pointed out that although the references [12][13][14] concern the geometry addressed in this paper, their aim was different from the one proposed here.…”

“…Note that this a customary axicon geometry which has already been studied in [12][13][14][15]. However, it must be pointed out that although the references [12][13][14] concern the geometry addressed in this paper, their aim was different from the one proposed here. In fact, in [12][13][14], the focus is not on the resolution limits of the aperture, rather the aim was to study the diffraction by a circular aperture of a plane wave or other types of prescribed focused beam.…”

“…This practically entails that the number of well-connected communication modes is always bounded and dependent on the geometrical parameters of the two volumes. Such a number is known as Number of Degree of Freedom (NDF) [9] and it is linked to resolution because it gives a concise picture of which class of field profile the aperture can create [10,11]. In fact, in [6], it is shown that any field created by an aperture can consist of no finer details than those contained in the singular functions spanning the closure of the Range of radiation operator v n with n ≤ NDF.…”

Inverse Source on Conformal Conic Geometries

“…Leone, F. Munno, and R. Pierri T uncertainties on data, otherwise small noise on data can provide a large error on the reconstructed current. This problem may become particularly serious for the diagnostic of the faulty elements of an array, since if their number is too high it may occur that some excitations may not be diagnosed [24]. For this reason it is important to evaluate the Number of Degrees of Freedom (NDF) [25][26][27] of the source current in connection to its geometry, as the (finite) number (i.e.…”

“…By inserting (1) into (24) and resorting to the sifting property of the impulse, (21) becomes (25) with ( ) = ( ) and ( ) = ( ) . Let us, now, focus on the integral in (25).…”