  Gamma-ray bursts are now known to be a cosmological population of objects,
which are often accompanied by X-ray and optical afterglows. The total energy
emitted in the afterglow can be similar to the energy radiated in the gamma-ray
burst itself. If a galaxy containing a large column density of dust is near the
line of sight to a gamma-ray burst, small-angle scattering of the X-rays due to
diffraction by the dust grains will give rise to an X-ray echo of the
afterglow. A measurement of the angular size of the echo at a certain time
after the afterglow is observed yields a combination of the angular diameter
distances to the scattering galaxy and the gamma-ray burst that can be used to
constrain cosmological models in the same way as a time delay in a
gravitational lens. The scattering galaxy will generally cause gravitational
lensing as well, and this should modify the shape of the X-ray echo from a
circular ring.
  The main difficulty in detecting this phenomenon is the very low flux
expected for the echo. The flux can be increased when the gamma-ray burst is
highly magnified by gravitational lensing, or when the deflecting galaxy is at
low redshift. X-ray echos of continuous (but variable) sources, such as
quasars, may also be detectable with high-resolution instruments and would
allow similar measurements.
