We prove that a potential $q$ can be reconstructed from the
Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a
fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that
an admissible metric $g$ in a fixed conformal class can be constructed from the
Dirichlet-to-Neumann map for $\Delta_g$. This is a constructive version of
earlier uniqueness results by Dos Santos Ferreira et al. on admissible
manifolds, and extends the reconstruction procedure of Nachman in Euclidean
space.

This paper analyzes the reconstruction of diffusion and absorption parameters
in an elliptic equation from knowledge of internal data. In the application of
photo-acoustics, the internal data are the amount of thermal energy deposited
by high frequency radiation propagating inside a domain of interest. These data
are obtained by solving an inverse wave equation, which is well-studied in the
literature. We show that knowledge of two internal data based on well-chosen
boundary conditions uniquely determines two constitutive parameters in
diffusion and Schroedinger equations.