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

Guanghui Hu, Jingzhi Li*, Hongyu Liu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)
31 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1259-1269
Number of pages11
JournalApplicable Analysis
Issue number6
Publication statusPublished - 3 Jun 2015

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • formally-determined
  • interior transmission eigenvalues
  • inverse scattering
  • refractive index
  • uniqueness


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