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Applicable Analysis
An International Journal
Volume 81, 2002 - Issue 6
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Original Articles

An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles

Johannes Elschner Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, Berlin, D-10117, Germany
&
Masahiro Yamamoto Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153, Japan
Pages 1307-1328 | Published online: 09 Sep 2010

Citations (33)

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Read on this site (3)

Johannes Elschner & Guanghui Hu. (2015) Elastic scattering by unbounded rough surfaces: solvability in weighted Sobolev spaces. Applicable Analysis 94:2, pages 251-278.
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Jiaqing Yang & Bo Zhang. (2012) An inverse scattering problem for a layered periodic structure. Applicable Analysis 91:4, pages 841-856.
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Guanghui Hu. (2012) Inverse wave scattering by unbounded obstacles: uniqueness for the two-dimensional Helmholtz equation. Applicable Analysis 91:4, pages 703-717.
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Articles from other publishers (30)

Linlin Zhu & Guanghui Hu. (2024) Stability of grating diffraction problems for plane wave incidence: Explicit dependence on wavenumbers and incident angles. Journal of Mathematical Analysis and Applications 531:1, pages 127781.
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Xiaoxu XuGuanghui HuBo ZhangHaiwen Zhang. (2023) Uniqueness in Inverse Diffraction Grating Problems With Infinitely Many Plane Waves at a Fixed Frequency. SIAM Journal on Applied Mathematics 83:1, pages 302-326.
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Lucas Fernandez & Ravi Prakash. (2021) Imaging of small penetrable obstacles based on the topological derivative method. Engineering Computations 39:1, pages 201-231.
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Gang Bao & Peijun LiGang Bao & Peijun Li. 2022. Maxwell’s Equations in Periodic Structures. Maxwell’s Equations in Periodic Structures 45 85 .
Guanghui Hu, Wangtao Lu & Andreas Rathsfeld. (2021) Time-Harmonic Acoustic Scattering from Locally Perturbed Periodic Curves. SIAM Journal on Applied Mathematics 81:6, pages 2569-2595.
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Guanghui Hu, Peijun Li & Yue Zhao. (2020) Elastic scattering from rough surfaces in three dimensions. Journal of Differential Equations 269:5, pages 4045-4078.
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Armin Lechleiter & Ruming Zhang. (2017) Non-periodic acoustic and electromagnetic, scattering from periodic structures in 3D. Computers & Mathematics with Applications 74:11, pages 2723-2738.
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Armin Lechleiter & Ruming Zhang. (2017) A Floquet--Bloch Transform Based Numerical Method for Scattering from Locally Perturbed Periodic Surfaces. SIAM Journal on Scientific Computing 39:5, pages B819-B839.
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Armin Lechleiter & Ruming Zhang. (2017) A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet--Bloch Transform. SIAM Journal on Numerical Analysis 55:2, pages 713-736.
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Gunther Schmidt. (2013) Conical diffraction by multilayer gratings: a recursive integral equation approach. Applications of Mathematics 58:3, pages 279-307.
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Johannes Elschner & Guanghui Hu. (2015) An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles. Communications in Computational Physics 12:5, pages 1434-1460.
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Guanghui Hu, Fenglong Qu & Bo Zhang. (2012) A linear sampling method for inverse problems of diffraction gratings of mixed type. Mathematical Methods in the Applied Sciences 35:9, pages 1047-1066.
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Jiaqing Yang & Bo Zhang. (2012) Uniqueness results in the inverse scattering problem for periodic structures. Mathematical Methods in the Applied Sciences 35:7, pages 828-838.
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JOHANNES ELSCHNER & GUANGHUI HU. (2012) SCATTERING OF PLANE ELASTIC WAVES BY THREE-DIMENSIONAL DIFFRACTION GRATINGS. Mathematical Models and Methods in Applied Sciences 22:04.
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Johannes Elschner & Guanghui Hu. (2012) Elastic Scattering by Unbounded Rough Surfaces. SIAM Journal on Mathematical Analysis 44:6, pages 4101-4127.
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G. Schmidt. (2011) Integral equations for conical diffraction by coated grating. Journal of Integral Equations and Applications 23:1.
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Johannes Elschner & Guanghui Hu. (2010) Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves. Inverse Problems 26:11, pages 115002.
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H. Gross, J. Richter, A. Rathsfeld & M. Bar. (2010) Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry. Journal of the European Optical Society: Rapid Publications 5.
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C Burkard & R Potthast. (2010) A multi-section approach for rough surface reconstruction via the Kirsch–Kress scheme. Inverse Problems 26:4, pages 045007.
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Simon N. Chandler-Wilde & Johannes Elschner. (2010) Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces. SIAM Journal on Mathematical Analysis 42:6, pages 2554-2580.
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Johannes Elschner & Guanghui Hu. (2010) Variational approach to scattering of plane elastic waves by diffraction gratings. Mathematical Methods in the Applied Sciences, pages n/a-n/a.
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Simon N Chandler-Wilde, Eric Heinemeyer & Roland Potthast. (2006) A well-posed integral equation formulation for three-dimensional rough surface scattering. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462:2076, pages 3683-3705.
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C. D. Lines & S. N. Chandler-Wilde. (2005) A Time Domain Point Source Method for Inverse Scattering by Rough Surfaces. Computing 75:2-3, pages 157-180.
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T. Arens & N. Grinberg. (2004) A Complete Factorization Method for Scattering by Periodic Surfaces. Computing 75:2-3, pages 111-132.
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Gottfried Bruckner & Johannes Elschner. (2004) The numerical solution of an inverse periodic transmission problem. Mathematical Methods in the Applied Sciences 28:7, pages 757-778.
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Simon N. Chandler-Wilde & Peter Monk. (2005) Existence, Uniqueness, and Variational Methods for Scattering by Unbounded Rough Surfaces. SIAM Journal on Mathematical Analysis 37:2, pages 598-618.
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JIN CHENG & YAMAMOTO MASAHIRO. (2004) GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES. Chinese Annals of Mathematics 25:01, pages 1-6.
Crossref
J. Elschner, G. Schmidt & M. Yamamoto. (2003) Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number. Journal of Inverse and Ill-posed Problems 11:3, pages 235-244.
Crossref
J Elschner, G Schmidt & M Yamamoto. (2003) An inverse problem in periodic diffractive optics: global uniqueness with a single wavenumber. Inverse Problems 19:3, pages 779-787.
Crossref
Gottfried Bruckner & Johannes Elschner. (2003) A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles. Inverse Problems 19:2, pages 315-329.
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