Department of Mathematics
Uniqueness in determining refractive indices by formally determined far-field data
© 2014 Taylor & Francis. 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 measurement. The arguments are based on the study of certain non-self-adjoint interior transmission eigenvalue problems.
formally-determined, interior transmission eigenvalues, inverse scattering, refractive index, uniqueness
Source Publication Title
Taylor & Francis
Link to Publisher's Edition
Hu, Guanghui, Jingzhi Li, and Hongyu Liu. "Uniqueness in determining refractive indices by formally determined far-field data." Applicable Analysis 94.6 (2015): 1259-1269.