44 research outputs found
Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures
This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method
Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures
This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method
Direct and inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves
Consider a time-harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with homogeneous compressible inviscid fluid with a constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by the Lam'e constants. This paper is concerned with direct (or forward) and inverse fluid-solid interaction (FSI) problems with unbounded bi-periodic interfaces between acoustic and elastic waves. We present a variational approach to the forward interaction problem with Lipschitz interfaces. Existence of quasi-periodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Concerning the inverse problem, we show that the factorization method by Kirsch (1998) is applicable to the FSI problem in periodic structures. A computational criterion and a uniqueness result are justified for precisely characterizing the elastic body by utilizing the scattered acoustic near field measured in the fluid
Direct and inverse elastic scattering problems for diffraction gratings
This paper is concerned with the direct and inverse scattering of time-harmonic plane elastic
waves by unbounded periodic structures (diffraction gratings). We present a variational approach
to the forward scattering problems with Lipschitz grating profiles and give a survey of recent
uniqueness and existence results. We also report on recent global uniqueness results within the
class of piecewise linear grating profiles for the corresponding inverse elastic scattering problems. Moreover, a discrete Galerkin method is presented to efficiently approximate solutions of direct
scattering problems via an integral equation approach. Finally, an optimization method for solving
the inverse problem of recovering a 2D periodic structure from scattered elastic waves measured
above the structure is discussed
A stable imaging functional for anisotropic periodic media in electromagnetic inverse scattering
The paper is concerned with the inverse scattering problem for Maxwell's
equations in three dimensional anisotropic periodic media. We study a new
imaging functional for fast and stable reconstruction of the shape of
anisotropic periodic scatterers from boundary measurements of the scattered
field for a number of incident fields. This imaging functional is simple to
implement and very robust against noise in the data. Its implementation is
non-iterative, computationally cheap, and does not involve solving any
ill-posed problems. The resolution and stability analysis of the imaging
functional is investigated. Our numerical study shows that this imaging
functional is more stable than that of the factorization method and more
efficient than that of the orthogonality sampling method in reconstructing
periodic scatterers.Comment: 23 page