30,108 research outputs found
Shape identification in inverse medium scattering problems with a single far-field pattern
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle
embedded in a homogeneous background medium. The index
of refraction characterizing the material inside is supposed to be H\"older
continuous near the corners. If is a convex polygon, we
prove that its shape and location can be uniquely determined by the far-field
pattern incited by a single incident wave at a fixed frequency. In dimensions
, the uniqueness applies to penetrable scatterers of rectangular type
with additional assumptions on the smoothness of the contrast. Our arguments
are motivated by recent studies on the absence of non-scattering wavenumbers in
domains with corners. As a byproduct, we show that the smoothness conditions in
previous corner scattering results are only required near the corners
Locating Multiple Multi-scale Electromagnetic Scatterers by A Single Far-field Measurement
Two inverse scattering schemes were recently developed in
\cite{LiLiuShangSun} for locating multiple electromagnetic (EM) scatterers,
respectively, of small size and regular size compared to the detecting EM
wavelength. Both schemes make use of a single far-field measurement. The scheme
of locating regular-size scatterers requires the {\it a priori} knowledge of
the possible shapes, orientations and sizes of the underlying scatterer
components. In this paper, we extend that imaging scheme to a much more
practical setting by relaxing the requirement on the orientations and sizes. We
also develop an imaging scheme of locating multiple multi-scale EM scatterers,
which may include at the same time, both components of regular size and small
size. For the second scheme, a novel local re-sampling technique is developed.
Furthermore, more robust and accurate reconstruction can be achieved for the
second scheme if an additional far-field measurement is used. Rigorous
mathematical justifications are provided and numerical results are presented to
demonstrate the effectiveness and the promising features of the proposed
imaging schemes.Comment: Any comments are welcom
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