We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics
- Inhomogeneous medium
- Interior transmission problem
- Inverse scattering
- Transmission eigenvalues