In this paper, we consider the inverse scattering problem which is to determine the shape of a multilayered scatterer. The adjoint of the far-field operator is found. In scattering theory the boundary data are given by the traces of plane waves. The closure of the span of the images of these plane waves under the far-field operator is characterized. Furthermore, taking the affine hull instead of the span of the plane waves on the boundary, some results are obtained.