Inverse acoustic problem of N homogeneous scatterers

The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered field at a plane below all scatterers onto the field and the complex wavenumbers is explicitly constructed. Uniqueness theorems for the inverse problem are proven.