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.

scholarly journals The factorization and monotonicity method for the defect in an open periodic waveguide

2020 ◽  
Vol 28 (6) ◽  
pp. 783-796
Author(s):  
Takashi Furuya
Keyword(s):  
Field Data ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Infinite Medium ◽  
Periodic Waveguide ◽  
Reconstruction Algorithms ◽  
Transmission Eigenvalues ◽  
Numerical Examples

AbstractWe consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.

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.

scholarly journals Energy- and Regularity-Dependent Stability Estimates for Near-Field Inverse Scattering in Multidimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Isaev
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Uniform Norm ◽  
Stability Estimate ◽  
Stability Estimates ◽  
Logarithmic Stability

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimensiond≥3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimensiond=2is also given.

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.

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