  We study the problem of unique recovery of a non-smooth one-form $\mathcal A$
and a scalar function $q$ from the Dirichlet to Neumann map, $\Lambda_{\mathcal
A,q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We prove
uniqueness of the one-form $\mathcal A$ up to the natural gauge, under weak
regularity conditions on $\mathcal A,q$ and under the assumption that $(M,g)$
is simple. Under an additional regularity assumption, we also derive uniqueness
of the scalar function $q$. The proof is based on the geometric optic
construction and inversion of the light ray transform extended as a Fourier
Integral Operator to non-smooth parameters and functions.
