| INVERSE MEDIUM SCATTERING PROBLEMS IN NEAR-FIELD OPTICS |
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| 作者姓名： | Gang Bao Peijun Li |
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| 作者单位： | [1]Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA [2]Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA |
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| 基金项目： | The research was supported in part by the 0NR grant N000140210365, the NSF grants DMS-0604790 and CCF-0514078, and the National Science Foundation of China grant 10428105. |
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| 摘 要： |
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| 关 键 词： | 反介质散射问题 近场光学 回归线性化法 Helmholtz方程 |
| 修稿时间： | 2006-11-072007-02-27 |
INVERSE MEDIUM SCATTERING PROBLEMS IN NEAR-FIELD OPTICS |
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| Gang Bao Peijun Li.INVERSE MEDIUM SCATTERING PROBLEMS IN NEAR-FIELD OPTICS[J].Journal of Computational Mathematics,2007,25(3):252-265. |
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| Abstract: | A regularized recursive linearization method is developed for a two-dimensional in-verse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy experiments. In addition to the ill-posedness of the inverse scattering problems, two difficulties arise from the layered back-ground medium and limited aperture data. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to the weak scattering at a low frequency, each update is obtained via recursive linearization with respect to the wavenumber by solving one forward problem and one adjoint problem of the Helmholtz equation. Numerical experiments are included to illustrate the feasibility of the proposed method. |
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| Keywords: | Inverse medium scattering Helmholtz equation Near-field optics Recursivelinearization |
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