Generic Local Uniqueness and Stability in Polarization Tomography

The problem of polarization tomography is considered on a Riemannian manifold. This problem comes from the physical problem of recovering the anisotropic part of the dielectric permittivity tensor of a quasi-isotropic medium from polarization measurements made around the boundary, but is more general. In greater than three dimensions local uniqueness and stability are established for generic background metrics, and near generic tensor fields through the study of a related linear inverse problem. The same results are established on a natural subspace of tensor fields in dimension three.