  For the light ray transform on globally hyperbolic Lorentzian manifolds of
dimension $n+1 \geq 3$ acting on compactly supported distributions, we show
that the Schwartz kernel of the normal operator is a paired Lagrangian
distribution with non-vanishing principal symbols on each Lagrangians. We
obtain Sobolev estimates for the light ray transform, and clarify the
determination of light-like singularities using the normal operator.
