Nondestructive Testing of the Delaminated Interface between Two Materials

Cakoni, Fioralba; Teresa, Irene de; Haddar, Houssem; Monk, Peter

doi:10.1137/16m1064167

Cited by 14 publications

(27 citation statements)

References 27 publications

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“…where j n is the derivative of the spherical Bessel function j n . Let us denote now by S ε κ , D ε κ , D ε κ and N ε κ the boundary integral operators related to the boundary ∂ B ε (x), namely, the counterpart operators to those defined in (9). They are mean values of the interior and exterior Dirichlet and Neumann traces on ∂ B ε (x) of the layer potentials S ε κ and D ε κ .…”

Section: =1mentioning

confidence: 99%

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Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Louër

Rapún

2022

J Math Imaging Vis

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In this paper, we investigate shape inversion algorithms based on the computation of iterated topological derivatives for the detection of multiple particles coated by a complex surface impedance in two- and three-dimensional acoustic media. New closed-form formulae for the topological derivative of the misfit functional are derived when an approximate set of unknown particles has already been recovered. Proofs rely on the computation of shape derivatives followed by the topological asymptotic analysis of a boundary integral equation formulation of the forward and adjoint problems. The relevance of the theoretical results is illustrated by various 2D and 3D experiments using monochromatic imaging algorithms either fully or partially based on topological derivatives.

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Section: =1mentioning

confidence: 99%

“…Full imaging algorithms of thin coated objects using very reduced data are of high importance in many fields of applied physics such as nondestructive testing, biomedical and radar imaging [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Louër

Rapún

2022

J Math Imaging Vis

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“…Hence it is reasonable to use an asymptotic method for small δ and derive an approximate model where the inhomogeneity S is reduced to the open surface Γ. There is a vast literature in asymptotic methods for thin layers [17], [18], [28] [29], [30], [31], [37], where the different ways of performing the asymptotic analysis lead to particular types of jump conditions across Γ. For example following the asymptotic approach developed in [27] and used in [17] for a different inverse problems, ( 2) is replaced by the following approximate transmission conditions…”

Section: Introductionmentioning

confidence: 99%

A Spectral Target Signature for Thin Surfaces with Higher Order Jump Conditions

Cakoni¹,

Lee²,

Monk³

et al. 2022

Preprint

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In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in R m , m = 2, 3 from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open m − 1 dimensional manifold (here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second order surface differential operator. We show that all the surface coefficients (possibly matrix valued and complex) are uniquely determined from far field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data, adapting the approach in [19]. Changes in the measured eigenvalues are used to identified changes in the coefficients without making use of the governing equations that model the healthy screen. In our investigation the shape of the screen is known, since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach.

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“…However if the scatterer is thin compared to the wavelength of the probing radiation, it is often desirable to treat it as a screen with zero thickness but having special transmission conditions across the surface that model, approximately, the thin body. In this paper we will use a special case of the transmission condition developed in [11] (see also [17]) for delaminating media.…”

Section: Introductionmentioning

confidence: 99%

Target signatures for thin surfaces

Cakoni,

Monk,

Zhang

2021

Preprint

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We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R m , m = 2, 3, which we model as a m − 1 dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are computable from scattering data in order to detect changes in the material properties of the screen. This target signature is characterized by a mixed Steklov eigenvalue problem for a domain whose boundary contains the screen. We show that the corresponding eigenvalues can be determined from appropriately modified scattering data by using the generalized linear sampling method. A weaker justification is provided for the classical linear sampling method. Numerical experiments are presented to support our theoretical results.

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Nondestructive Testing of the Delaminated Interface between Two Materials

Cited by 14 publications

References 27 publications

Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

A Spectral Target Signature for Thin Surfaces with Higher Order Jump Conditions

Target signatures for thin surfaces

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