  In this paper we give a general expression for the energy shift of massless
particles travelling through the gravitational field of an arbitrary matter
distribution as calculated in the weak field limit in an asymptotically flat
space-time. It is {\it not} assumed that matter is non-relativistic. We
demonstrate the surprising result that if the matter is illuminated by a
uniform brightness background that the brightness pattern observed at a given
point in space-time (modulo a term dependent on the oberver's velocity) depends
only on the matter distribution on the observer's past light-cone. These
results apply directly to the cosmological MBR anisotropy pattern generated in
the immediate vicinity of of an object like a cosmic string or global texture.
We apply these results to cosmic strings, finding a correction to previously
published results for in the small-angle approximation. We also derive the
full-sky anisotropy pattern of a collapsing texture knot.
