Ambiguities in the scattering tomography for central potentials

TL;DR

This paper investigates the ambiguities in inverse scattering problems for central potentials, revealing how multiple potentials can produce identical scattering data and discussing implications for invisibility device design.

Contribution

It provides a theoretical framework showing that scattering ambiguities can arise from multi-valued scattering functions and angles, impacting the development of invisibility technologies.

Findings

Scattering is a tomographic projection of a scattering function.

Multiple potentials can share the same scattering data.

Invisibility devices may be constructed without infinite phase velocities.

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 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.