Reconstruction of an obstacle from the scattering amplitude at a fixed frequency

We present a reconstruction formula (procedure) for the three-dimensional sound-soft/sound-hard obstacle by means of the scattering amplitude at a fixed frequency. The procedure requires a sequence of solutions of the Helmholtz equation in an open ball B, which locally converges to the fundamental solution of the Helmholtz equation in the domain obtained by excising from B a part of a curve connecting two points on partial derivative B.