Department of Mathematics
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
This is an Accepted Manuscript of an article published by Taylor & Francis in Applicable Analysis in June 2015, available online: http://www.tandfonline.com/10.1080/00036811.2014.924215.
This work was supported by the German Research Foundation (DFG), [grant number HU 2111/1-1]; the NSF of China [grant number 11371115], [grant number 11201453], [grant number 91130022] and the NSF grant, DMS 1207784.
Link to Publisher's Edition
Hu, G., Li, J., & Liu, H. (2015). Uniqueness in determining refractive indices by formally determined far-field data. Applicable Analysis, 94 (6), 1259-1269. https://doi.org/10.1080/00036811.2014.924215