scholarly journals Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation

2015 ◽  
Vol 32 (1) ◽  
pp. 015005 ◽  
Author(s):  
Michael V Klibanov ◽  
Vladimir G Romanov
Keyword(s):  
Helmholtz Equation ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem

AN ALGORITHM FOR THE FULLY NONLINEAR INVERSE SCATTERING PROBLEM AT FIXED FREQUENCY

2001 ◽  
Vol 09 (03) ◽  
pp. 935-940 ◽  
Author(s):  
F. NATTERER
Keyword(s):  
Helmholtz Equation ◽  
Multiple Scattering ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Scattering Process ◽  
Fixed Frequency ◽  
Fully Nonlinear ◽  
Complex Valued

We reconstruct an object which is described by a complex valued function from the scattered waves generated by irradiating plane waves at fixed frequency. The scattering process is modeled by the Helmholtz equation and includes multiple scattering. We present numerical results from computer generated data.

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.

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