TY - JOUR
T1 - Inverse Medium Scattering Problems in Near-Field Optics
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 - <p style="text-align: justify;">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.</p>