Journal ArticleDOI
Numerical solution of an inverse diffraction grating problem from phaseless data
Gang Bao,Peijun Li,Junliang Lv +2 more
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TLDR
An efficient continuation method is developed to recover the Fourier coefficients of the periodic grating profile from measurements of the phaseless diffracted field at a constant height above the grating structure.Abstract:
This paper is concerned with the numerical solution of an inverse diffraction grating problem, which is to reconstruct a periodic grating profile from measurements of the phaseless diffracted field at a constant height above the grating structure. An efficient continuation method is developed to recover the Fourier coefficients of the periodic grating profile. The continuation proceeds along the wavenumber and updates are obtained from the Landweber iteration at each step. Numerical results are presented to show that the method can effectively reconstruct the shape of the grating profile.read more
Citations
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Journal ArticleDOI
Inverse scattering problems with multi- frequencies
TL;DR: In this paper, the main idea is that if the reconstruction is restricted to only the observable part, then the inversion will become stable, and the challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit.
Journal ArticleDOI
Reconstruction procedures for two inverse scattering problems without the phase information
TL;DR: This is a continuation of two recent publications of the authors about reconstruction of the Inverse Ill-Posed Probl.
Journal ArticleDOI
Near-Field Imaging of Infinite Rough Surfaces
TL;DR: A spectral cut-off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components, which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near-field regime.
Journal ArticleDOI
Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation
TL;DR: In this paper, the 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered, where only the modulus of the scattering wave field is measured.
References
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Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Book
Integral equation methods in scattering theory
David Colton,Rainer Kress +1 more
TL;DR: In this article, the Riesz-Fredholm theory for compact operators is applied to boundary-value problems for the scalar Helmholtz equation and the time-harmonic Maxwell equations.
Journal ArticleDOI
An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
Zhiming Chen,Haijun Wu +1 more
TL;DR: A finite element adaptive strategy with error control for the wave scattering by periodic structures using the perfectly matched layer technique, which attenuates both the outgoing and evanescent waves in the PML region.
Journal ArticleDOI
Numerical solution of diffraction problems: a method of variation of boundaries
Oscar P. Bruno,Fernando Reitich +1 more
TL;DR: In this article, a simple recursive formula for the derivatives of the efficiencies with respect to the height of the grating is proposed, and a conformal mapping mechanism is introduced to enhance the convergence of the series.