For scattering of some time-dependent puls by a sound-soft
obstacle we study the reconstruction of the time-dependent scattered
field from the measured far field pattern, i.e. we go back in time and
follow the scattered field to the scatterer (time reversal). Then, the
total field in time is used to reconstruct the shape of the unknown
scattering obstacle.
For the reconstructions we use frequency-domain methods. First,
the far field pattern is mapped into the frequency domain by Fourier
transform of the time variable. Then, the total field is reconstructed
using the point-source method. By another Fourier transform we obtain
the time-dependent scattered field. This last step is of large importance,
since the contrast for the fields in frequency domain is low and the
reconstruction of time-data for the point of time where the puls hits the
object provides an efficient and good way to enhance the contrast
at the boundary of the unknown object.
Numerical examples for simulations and reconstructions will be
provided.
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