  We consider the inverse problem of the reconstruction of the spatially
distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \
\mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's
equations, from time-dependent backscattering experimental radar data
associated with a single source of electric pulses. The refractive index is
$n\left(\mathbf{x}\right) =\sqrt{\varepsilon_{r}\left(\mathbf{x}\right)}.$ The
coefficient $\varepsilon_{r}\left(\mathbf{x}\right) $ is reconstructed using a
two-stage reconstruction procedure. In the first stage an approximately
globally convergent method proposed is applied to get a good first
approximation of the exact solution. In the second stage a locally convergent
adaptive finite element method is applied, taking the solution of the first
stage as the starting point of the minimization of the Tikhonov functional.
This functional is minimized on a sequence of locally refined meshes. It is
shown here that all three components of interest of targets can be
simultaneously accurately imaged: refractive indices, shapes and locations.
