Uniqueness in determining refractive indices by formally determined far-field data

Guanghui Hu, Jingzhi Li, Hongyu Liu
2014 Applicable Analysis  
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a variable index of refraction by the fixed incident-direction scattering amplitude. The inverse problem is formally posed with such measurement data. The second one is a global uniqueness in determining a constant refractive index by a single far-field
more » ... ent. The arguments are based on the study of certain nonlinear and non-selfadjoint interior transmission eigenvalue problems.
doi:10.1080/00036811.2014.924215 fatcat:frgw5zb4vndqjjkm4rxcfwkrnm