Uniqueness of refractive indices and transmission coefficients by an inhomogeneous medium in acoustic scattering

Abstract We are concerned with the inverse scattering problem of recovering the refractive indices and transmission coefficients by the corresponding acoustic far-field measurement encoded into the scattering amplitude. Our first uniqueness result is to determine a constant refractive index by the f...

Full description

Saved in:
Bibliographic Details
Published inIMA journal of applied mathematics Vol. 88; no. 4; pp. 558 - 575
Main Authors Xiang, Jianli, Yan, Guozheng
Format Journal Article
LanguageEnglish
Published Oxford University Press 28.12.2023
Subjects
78A46
uniqueness
35R30
35A02
35P25
inverse scattering
interior transmission eigenvalues
refractive index
boundary integral equation method
Online AccessGet full text

Cover

More Information
Summary:Abstract We are concerned with the inverse scattering problem of recovering the refractive indices and transmission coefficients by the corresponding acoustic far-field measurement encoded into the scattering amplitude. Our first uniqueness result is to determine a constant refractive index by the fixed incident direction scattering amplitude, the proof of which is mainly based on the discreteness of the corresponding interior transmission eigenvalues. Then motivated by the previous work (Xiang & Yan 2021), the second uniqueness result is established to recover a piecewise constant refractive index from the far-field pattern at a fixed frequency.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxad022