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On the Far Field in Obstacle Scattering

We will establish far field identities for the scattering of time-harmonic acoustic waves from sound-soft and sound-hard obstacles and will illustrate two applications of these identities for the inverse obstacle scattering problem. First, we will provide an alternate proof for the Frechet differentiability of the far field pattern with respect to the boundary. Second, we will connect the identities with a new method for the approximate solution of the inverse obstacle scattering problem recently suggested by Potthast.