This paper is concerned with the classical inverse scattering problem to
recover the refractive index of a medium given near or far field measurements
of scattered time-harmonic acoustic waves. It contains the first rigorous proof
of (logarithmic) rates of convergence for Tikhonov regularization under Sobolev
smoothness assumptions for the refractive index. This is achieved by combining
two lines of research, conditional stability estimates via geometrical optics
solutions and variational regularization theory
