The inverse problem of wave scattering on inhomogeneities of a medium within the framework of a scalar wave equation is considered. The scattered field in such a model can be described in two ways: either with the help of the surface distribution of secondary sources, or by using volume distribution. These two ways of description completely coincide in the outer domain and at the boundary. They are, however, different inside the inhomogeneity: the volume sources reconstruct the "refracted" field existing inside the inhomogeneity, whereas the Kirchhof description yields zero values there.

From the point of view of the inverse problem, in which the observation data can be gathered only in the outer domain, this leads to the following: it is insufficient to have the full knowledge of the scattered field everywhere in the outer domain to distinguish between volume scattering and surface scattering. It is important to note that this non-uniqueness of the solution is fundamental and is not due to the monochrome character of the wave process under consideration; it is also not eliminated by observation systems with multiple overlapping.