  The polarization tomography problem consists of recovering a matrix function
f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$
known for every geodesic $\gamma$ of a given Riemannian metric. Here
$\pi_{\dot\gamma}$ is the orthogonal projection onto the hyperplan
$\dot\gamma^{\perp}$. The problem arises in optical tomography of slightly
anisotropic media. The local uniqueness theorem is proved: a $C^1$- small
function f can be recovered from the data uniquely up to a natural obstruction.
A partial global result is obtained in the case of the Euclidean metric on
$R^3$.
