Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Leone, Giovanni; Maisto, Maria Antonia; Pierri, and Rocco

doi:10.2528/pierm18062102

Cited by 30 publications

(39 citation statements)

References 16 publications

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“…A relevant result is that the eigenvalues are almost constant for n , where λ is the wavelength, and [•] stands for the nearest integer; after this index they abruptly decay [29]. Moreover, although the singular values/eigenvalues are not the same for operators (6) and 7, the NDF is the same for both cases and the only difference is in the shape of their behavior [27]. For the PSF analysis, as mentioned above, in this case we focus only on the variables ξ.…”

Section: Linear Sourcementioning

confidence: 99%

“…It can be expected that the PSF is narrower towards the end points of the domain when we use the variable ξ instead of the variable ϕ. In fact, the ξ variable is not linearly linked to ϕ, and this For this case, an upper bound to the NDF is provided by [27] as…”

Section: Semi-circumference Sourcementioning

confidence: 99%

“…Moreover, the step occurs approximately for an index equal to (13). For this case, an upper bound to the NDF is provided by [27] as…”

Section: Semi-circumference Sourcementioning

confidence: 99%

“…In a 2D setting, that is, when sources and fields are independent on one Cartesian variable, circumference sources observed over a whole 2π observation range in the far zone have been considered in [25][26][27] with both analytical (whenever possible) and numerical approaches. Hereafter, we mean to investigate a different source geometry, that is, a semi-elliptical one, whose far field is observed over a π angle.…”

Section: Introductionmentioning

confidence: 99%

“…Equation 17returns a more accurate estimation for the NDF of a semi-circumference source with respect to the upper bound (13) provided by [27].…”

mentioning

confidence: 99%

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Radiation Properties of Conformal Antennas: The Elliptical Source

2019

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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.

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Section: Linear Sourcementioning

confidence: 99%

Section: Semi-circumference Sourcementioning

confidence: 99%

“…Moreover, the step occurs approximately for an index equal to (13). For this case, an upper bound to the NDF is provided by [27] as…”

Section: Semi-circumference Sourcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Equation 17returns a more accurate estimation for the NDF of a semi-circumference source with respect to the upper bound (13) provided by [27].…”

mentioning

confidence: 99%

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Radiation Properties of Conformal Antennas: The Elliptical Source

2019

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NDF of the Near-Zone Field on a Line Perpendicular to the Source

Pierri

Moretta

2021

IEEE Access

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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 behavior of the singular values. 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.INDEX TERMS dimension of data, eigenvalue problem, inverse source problem, integral equation, radiation operator, singular values, NDF.

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The Effect of a Reflecting Cylinder in Two-Dimensional Inverse Source Problem for Circumference Geometries

Jiang

Xiao

2022

2022 International Applied Computational Electromagnetics Society Symposium (ACES-China)

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Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Cited by 30 publications

References 16 publications

Radiation Properties of Conformal Antennas: The Elliptical Source

Radiation Properties of Conformal Antennas: The Elliptical Source

NDF of the Near-Zone Field on a Line Perpendicular to the Source

The Effect of a Reflecting Cylinder in Two-Dimensional Inverse Source Problem for Circumference Geometries

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