  This paper concerns diffraction-tomographic reconstruction of an object
characterized by its scattering potential. We establish a rigorous
generalization of the Fourier diffraction theorem in arbitrary dimension,
giving a precise relation in the Fourier domain between measurements of the
scattered wave and reconstructions of the scattering potential. With this
theorem at hand, Fourier coverages for different experimental setups are
investigated taking into account parameters such as object orientation,
direction of incidence and frequency of illumination. Allowing for simultaneous
and discontinuous variation of these parameters, a general filtered
backpropagation formula is derived resulting in an explicit approximation of
the scattering potential for a large class of experimental setups.
