A Newton method is presented for the approximate solution of the inver
se problem to determine the shape of a sound-soft or perfectly conduct
ing are from a knowledge of the far-held pattern for the scattering of
time-harmonic plane waves. Frechet differentiability with respect to
the boundary is shown for the far-field operator, which for a fixed in
cident wave maps the boundary are onto the far-field pattern of the sc
attered wave. For the sake of completeness, the first part of the pape
r gives a short outline on the corresponding direct problem via an int
egral equation method including the numerical solution.