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Volume 25, Issue 3
Inverse Medium Scattering Problems in Near-Field Optics

Gang Bao & Peijun Li

J. Comp. Math., 25 (2007), pp. 252-265.

Published online: 2007-06

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  • Abstract

A regularized recursive linearization method is developed for a two-dimensional inverse 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 background 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.

  • Keywords

Inverse medium scattering, Helmholtz equation, Near-field optics, Recursive linearization.

  • AMS Subject Headings

78A46, 65N21.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-252, author = {Gang Bao and Peijun Li}, title = {Inverse Medium Scattering Problems in Near-Field Optics}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {3}, pages = {252--265}, abstract = {

A regularized recursive linearization method is developed for a two-dimensional inverse 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 background 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8691.html} }
TY - JOUR T1 - Inverse Medium Scattering Problems in Near-Field Optics AU - Gang Bao & Peijun Li JO - Journal of Computational Mathematics VL - 3 SP - 252 EP - 265 PY - 2007 DA - 2007/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8691.html KW - Inverse medium scattering, Helmholtz equation, Near-field optics, Recursive linearization. AB -

A regularized recursive linearization method is developed for a two-dimensional inverse 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 background 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.

Gang Bao and Peijun Li. (2007). Inverse Medium Scattering Problems in Near-Field Optics. Journal of Computational Mathematics. 25 (3). 252-265. doi:
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