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Reconstruction of penetrable grating profiles
1. | Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
2. | LSEC and Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, China |
References:
[1] |
T. Arens and N. Grinberg, A complete factorization method for scattering by periodic surfaces,, Computing, 50 (2005), 111.
doi: 10.1007/s00607-004-0092-0. |
[2] |
T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures,, Inverse Problems, 519 (2003), 1195.
doi: 10.1088/0266-5611/19/5/311. |
[3] |
G. Bruckner and J. Elschner, A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,, Inverse Problems, 19 (2003), 315.
doi: 10.1088/0266-5611/19/2/305. |
[4] |
G. Bruckner and J. Elschner, The numerical solution of an inverse periodic transmission problem,, Math. Meth. Appl. Sci., 28 (2005), 757.
doi: 10.1002/mma.588. |
[5] |
A-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem,, Math. Meth. Appl. Sci., 17 (1994), 305.
doi: 10.1002/mma.1670170502. |
[6] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory,, Wiley, (1983).
|
[7] |
D. Colton, R. Kress and P. Monk, Inverse scattering from an orthotropic medium,, J. Comput. Appl. Math., 81 (2007), 269.
doi: 10.1016/S0377-0427(97)00065-4. |
[8] |
J. Elschner, G. C. Hsiao and A. Rathsfeld, Grating profile reconstruction based on finite elements and optimization techniques,, SIAM J. Appl. Math., 64 (2003), 525.
doi: 10.1137/S0036139902420018. |
[9] |
F. Hettlich, Iterative regularization schemes in inverse scattering by periodic structures,, Inverse Problems, 18 (2002), 701.
doi: 10.1088/0266-5611/18/3/311. |
[10] |
G. Hu, F. Qu and B. Zhang, A linear sampling method for inverse problems of diffraction gratings of mixed type,, Math. Methods Appl. Sci., 35 (2012), 1047.
doi: 10.1002/mma.2511. |
[11] |
G. Hu and B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure,, Math. Methods Appl. Sci., 34 (2011), 509.
doi: 10.1002/mma.1375. |
[12] |
K. Ito and F. Reitich, A high-order perturbation approach to profile reconstruction: I. Perfectly conducting grating,, Inverse Problems, 15 (1999), 1067.
doi: 10.1088/0266-5611/15/4/315. |
[13] |
A. Lechleiter, Imaging of periodic dielectrics,, BIT Numer. Math., 50 (2010), 59.
doi: 10.1007/s10543-010-0255-7. |
[14] |
A. Malcolm and D. P. Nicholls, A boundary perturbation method for recovering interface shape in layered media,, Inverse Problems, 27 (2011).
doi: 10.1088/0266-5611/27/9/095009. |
[15] |
G. Schmidt, Integral equations for conical diffraction by coated gratings,, J. Integral Equat. Appl., 23 (2011), 71.
doi: 10.1216/JIE-2011-23-1-71. |
[16] |
J. Yang and B. Zhang, Uniqueness results in the inverse scattering problem for periodic structures,, Math. Methods Appl. Sci., 35 (2012), 828.
doi: 10.1002/mma.1609. |
[17] |
J. Yang, B. Zhang and R. Zhang, A sampling method for the inverse transmission problem for periodic media,, Inverse Problems, 28 (2012).
doi: 10.1088/0266-5611/28/3/035004. |
show all references
References:
[1] |
T. Arens and N. Grinberg, A complete factorization method for scattering by periodic surfaces,, Computing, 50 (2005), 111.
doi: 10.1007/s00607-004-0092-0. |
[2] |
T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures,, Inverse Problems, 519 (2003), 1195.
doi: 10.1088/0266-5611/19/5/311. |
[3] |
G. Bruckner and J. Elschner, A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,, Inverse Problems, 19 (2003), 315.
doi: 10.1088/0266-5611/19/2/305. |
[4] |
G. Bruckner and J. Elschner, The numerical solution of an inverse periodic transmission problem,, Math. Meth. Appl. Sci., 28 (2005), 757.
doi: 10.1002/mma.588. |
[5] |
A-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem,, Math. Meth. Appl. Sci., 17 (1994), 305.
doi: 10.1002/mma.1670170502. |
[6] |
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory,, Wiley, (1983).
|
[7] |
D. Colton, R. Kress and P. Monk, Inverse scattering from an orthotropic medium,, J. Comput. Appl. Math., 81 (2007), 269.
doi: 10.1016/S0377-0427(97)00065-4. |
[8] |
J. Elschner, G. C. Hsiao and A. Rathsfeld, Grating profile reconstruction based on finite elements and optimization techniques,, SIAM J. Appl. Math., 64 (2003), 525.
doi: 10.1137/S0036139902420018. |
[9] |
F. Hettlich, Iterative regularization schemes in inverse scattering by periodic structures,, Inverse Problems, 18 (2002), 701.
doi: 10.1088/0266-5611/18/3/311. |
[10] |
G. Hu, F. Qu and B. Zhang, A linear sampling method for inverse problems of diffraction gratings of mixed type,, Math. Methods Appl. Sci., 35 (2012), 1047.
doi: 10.1002/mma.2511. |
[11] |
G. Hu and B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure,, Math. Methods Appl. Sci., 34 (2011), 509.
doi: 10.1002/mma.1375. |
[12] |
K. Ito and F. Reitich, A high-order perturbation approach to profile reconstruction: I. Perfectly conducting grating,, Inverse Problems, 15 (1999), 1067.
doi: 10.1088/0266-5611/15/4/315. |
[13] |
A. Lechleiter, Imaging of periodic dielectrics,, BIT Numer. Math., 50 (2010), 59.
doi: 10.1007/s10543-010-0255-7. |
[14] |
A. Malcolm and D. P. Nicholls, A boundary perturbation method for recovering interface shape in layered media,, Inverse Problems, 27 (2011).
doi: 10.1088/0266-5611/27/9/095009. |
[15] |
G. Schmidt, Integral equations for conical diffraction by coated gratings,, J. Integral Equat. Appl., 23 (2011), 71.
doi: 10.1216/JIE-2011-23-1-71. |
[16] |
J. Yang and B. Zhang, Uniqueness results in the inverse scattering problem for periodic structures,, Math. Methods Appl. Sci., 35 (2012), 828.
doi: 10.1002/mma.1609. |
[17] |
J. Yang, B. Zhang and R. Zhang, A sampling method for the inverse transmission problem for periodic media,, Inverse Problems, 28 (2012).
doi: 10.1088/0266-5611/28/3/035004. |
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