  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 multi-valued, 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.
