Shape identification in inverse medium scattering problems with a single far-field pattern
- Hu, Guanghui
- Salo, Mikko
- Vesalainen, Esa V.
2010 Mathematics Subject Classification
- 35R30 74B05 78A46
- uniqueness, inverse medium scattering, shape identification, Helmholtz equation
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle embedded in a homogeneous background medium. The index of refraction characterizing the material inside the obstacle is supposed to be Holder continuous near the corners. We prove that the shape and location of a convex polygon can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In three dimensions, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of non-scattering wavenumbers in domains with corners. As a byproduct, we show that the smoothness conditions in previous corner scattering results are only required near the corners.
- SIAM J. Math. Anal., 48 (2016) pp. 152--165.