Abstract
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering ambiguities that arise in central potentials. We show that scattering is a tomographic projection: The integrated scattering angle is a projection of a scattering function onto the impact parameter. This function depends on the potential but may be multivalued, allowing for ambiguities where several potentials share the same scattering data. In addition, multivalued scattering angles also lead to ambiguities. We apply our theory to show that it is, in principle, possible to construct an invisibility device without infinite phase velocity of light.