Scattering by Media

Publisher Summary This chapter starts with the construction of modified fundamental solutions to the Helmholtz equation, which is employed during the analysis of the inverse scattering problem. They are used to establish a unique continuation principle that is needed to prove unique solvability for the direct scattering problem. In the next section, the far field pattern and the far field operator for the direct scattering problem is introduced. The larger part of the chapter is devoted to the inverse scattering problem to recover the refractive index from its far field pattern. It first examines whether the far field pattern contains sufficient information to determine the refractive index uniquely. After the stability estimate, Nachman's method is estimated to reconstruct the refractive index from its far field pattern. Finally, the chapter ends by giving a brief discussion of sampling methods, which only recover the support of the inhomogeneity, and indicating other methods used for the numerical computation of the refractive index.

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