The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution

Marengo, Edwin A.; Devaney, Anthony J.

doi:10.1109/8.761085

Cited by 68 publications

(84 citation statements)

References 6 publications

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“…The arbitrariness of the limiting enforcement surface Σ − R can be removed with a more general formulation [5]; it can be shown [5, 21, Eqs. (6), (29)] that the equations above are equivalent to the following boundary integral identities:…”

Section: Integral Equation Setup and Uniquenessmentioning

confidence: 99%

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Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Quijano¹,

Vecchi²

2010

PIER

147

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Abstract-This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that singleequation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

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Section: Integral Equation Setup and Uniquenessmentioning

confidence: 99%

“…A different, more theoretically-oriented line of research exists, e.g., [28][29][30], but apparently these works have not been considered in most of the previously cited literature (some of these results will be employed here).…”

Section: Introductionmentioning

confidence: 99%

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Quijano¹,

Vecchi²

2010

PIER

147

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“…Modal expansion coefficients α i u decay exponentially fast for |u| > ka [47], enabling us to approximate the far-zone scattered field pattern using ∼ (2 [ka] + 1) terms, where [ka] is the greatest integer less than ka:…”

Section: Far-zone Scattered Field Patternmentioning

confidence: 99%

“…is decomposed into its corresponding ∆α i u coefficients, from which one can calculate the minimum-energy (i.e., minimum L 2 norm) current density distribution ∆J i min within the object support which radiates ∆f i (φ), as explained in [47]. The field radiated by ∆J i min into the support radius is then computed via various variants of the Lommel integral formulae [50].…”

Section: Iterative Use Of the Techniquementioning

confidence: 99%

Modal-based tomographic imaging from far-zone observations

Karbeyaz

Rappaport

2008

J. Opt. Soc. Am. A

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A novel method of optical diffraction tomography (ODT) to image weakly scattering, electrically large two dimensional (2D) objects using the far-zone scattered field data is presented. The proposed technique is based on the expansion of the target object function in terms of Fourier-Bessel basis functions, and an alternative approximation for the total electric field within the support of the investigated scatterer. Analytical (Mie) plane-wave scattering by a layered, circularly symmetric, lossy dielectric cylinder, and finite-difference time-domain simulations involving plane-wave scattering first by a more general, lossless dielectric phantom and then by embryo models involving various mitochondrial distributions are utilized to compare the performance of the proposed method with that of the standard ODT techniques which are based on the Born/Rytov approximations and Fourier diffraction theorem. Quantitative and qualitative superiority of the presented method is demonstrated. The proposed method can be used without being confined to far-zone observations with a proper (cylindrical-spherical) receiver configuration, and can be easily modified to handle multi-frequency data for a wideband reconstruction whenever applicable. The proposed 2D technique can be readily extended to more realistic three dimensional scenarios, and can be used in tomographic microscopy for various purposes, such as the cell-embryo health assessment for in vitro fertilization procedures.

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“…One recent area of application is the determination of the specific absorption rate of mobile phones [9]. A modal expansion of the field can be utilized if the reconstruction surface is cylindrical or spherical [1,10,11]. This method has been used to calculate the insertion phase delay (IPD) and to detect defects on a spherical radome [12].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction and Visualization of Equivalent Currents on a Radome Using an Integral Representation Formulation

Persson¹,

Gustafsson²,

Kristensson³

2010

PIER B

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Abstract-In this paper an inverse source problem is investigated. The measurement set-up is a reflector antenna covered by a radome. Equivalent currents are reconstructed on a surface shaped as the radome in order to diagnose the radome's interaction with the radiated field. To tackle this inverse source problem an analysis of a full-wave integral representation, with the equivalent currents as unknowns, is used. The extinction theorem and its associated integral equation ensure that the reconstructed currents represent sources within the radome. The axially symmetric experimental set-up reduces the computational complexity of the problem. The resulting linear system is inverted by using a singular value decomposition. We visualize how the presence of the radome alters the components of the equivalent currents. The method enables us to determine the phase shift of the field due to the transmission of the radome, i.e., the IPD (insertion phase delay). Also, disturbances due to defects, not observable in the measured near field, are localized in the equivalent currents.

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The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution

Cited by 68 publications

References 6 publications

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Modal-based tomographic imaging from far-zone observations

Reconstruction and Visualization of Equivalent Currents on a Radome Using an Integral Representation Formulation

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