We first consider the inverse scattering problem of
determining the shape of an infinite cylinder having an open arc
as cross section from a knowledge of the TM polarized scattered
electromagnetic field corresponding to time harmonic incident
plane waves propagating from arbitrary directions. We assume that
the arc is a possibly partially coated perfect conductor. This leads to
the scattering problem for the Helmholtz equation outside the open arc
(the crack) with mixed Dirichlet-impedance boundary conditions on the
crack. We develop the linear sampling method, which was originally
developedfor solving the inverse scattering problem for obstacles with
nonempty interior, to include the above case of obstacles with
empty interior. Then we extend the analysis to the electromagnetic
scattering by perfectly conducting screens in R3.
We will also present some results of numerical experiments in the both
2D and 3D cases.
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