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Invisibility devices exploit ambiguities in the inverse scattering problem oflight in media. Scattering also serves as an important general tool to inferinformation about the structure of matter. We elucidate the nature ofscattering ambiguities that arise in central potentials. We show thatscattering is a tomographic projection: the integrated scattering angle is aprojection of a scattering function onto the impact parameter. This functiondepends on the potential, but may be multi-valued, allowing for ambiguitieswhere several potentials share the same scattering data. In addition,multivalued scattering angles also lead to ambiguities. We apply our theory toshow that it is in principle possible to construct an invisibility devicewithout infinite phase velocity of light

Ambiguities in the Scattering Tomography for Central Potentials