Inverse scattering for three-dimensional quasi-linear biharmonic operator

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Markus Harju ◽  
Jaakko Kultima ◽  
Valery Serov
Keyword(s):  
Inverse Scattering ◽  
Space Variable ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Regularity Conditions ◽  
Biharmonic Operator ◽  
Essential Information ◽  
Complex Valued

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Dielectric Metrology VIA Microwave Tomography: Present and Future

1994 ◽  
Vol 347 ◽  
Author(s):  
J.Ch. Bolomey ◽  
N. Joachimowicz
Keyword(s):  
Inverse Scattering ◽  
A Priori ◽  
Scattering Problem ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Dielectric Characterization ◽  
Sample Shape ◽  
Three Dimensional Configuration ◽  
Characterization Of Materials

ABSTRACTUntil now, the measurement techniques used for the dielectric characterization of materials require severe limitations in terms of sample shape, size and homogeneity. This paper considers the dielectric permittivity measurement as a non-linear inverse scattering problem. Such an approach allows to identify the quantities to be measured and suggests possible experimental arrangements. The problem is shown to be significantly simplified if the shape of the material is known and if some a priori knowledge of the averaged value of the permittivity in the material under test is available. Two test cases have been selected to illustrate the state of the art in solving such inverse problems. The first one consists of a two-dimensional configuration which is applicable to cylindrical objects, and the second one to a vector three-dimensional configuration applicable, for instance, to cubic samples. The main limitations of such an inverse scattering approach are discussed and expected improvements in the near future are analysed.

Inverse scattering problem for transparent obstacles

1982 ◽  
Vol 92 (2) ◽  
pp. 361-367 ◽  
Author(s):  
Vesselin Petkov
Keyword(s):  
Inverse Scattering ◽  
Convex Domain ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Normal Derivative ◽  
Index Of Refraction ◽  
Image Position ◽  
Compact Boundary ◽  
Limiting Values

Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. SetWe wish to study the filtered scattering amplitude, related to the transmission problemHere w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.

The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Michael V. Klibanov ◽  
Vladimir G. Romanov
Keyword(s):  
New York ◽  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Potential Applications ◽  
Inverse Radon Transform ◽  
Standing Problem

AbstractA long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures.

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