Identifying of the refractive index for the acoustic equation at fixed   frequency
  In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acoustic equation from the partial Dirichlet to Neumann map(DN) associated to ${\bf n}$. We apply these results to identify locations and values of small volume perturbations of this refractive index at fixed frequency $\omega$. 
Christian Daveau, Abdessatar Khelifi, Anton Sushchenko