The author studies the inverse problem to determine the shape of an open arc from the knowledge of the far field patterns of scattered acoustic waves. A Neumann boundary condition is imposed on the arc. The author proves uniqueness of the inverse problem and Fréchet differentiability of the operator
which maps the parametrization
of the arc into the far field pattern
. He applies a Newton-type method to the equation
for solving the inverse scattering problem. Numerical examples illustrate the practicability of the method.