  We investigate an inverse scattering problem for a thin inhomogeneous
scatterer in R^m, m = 2,3, which we model as a m-1 dimensional open surface.
The scatterer is referred to as a screen. The goal is to design target
signatures that are computable from scattering data in order to detect changes
in the material properties of the screen. This target signature is
characterized by a mixed Steklov eigenvalue problem for a domain whose boundary
contains the screen. We show that the corresponding eigenvalues can be
determined from appropriately modified scattering data by using the generalized
linear sampling method. A weaker justification is provided for the classical
linear sampling method. Numerical experiments are presented to support our
theoretical results.
