  We calculate the radial surface brightness profile of the image of a
Gamma-Ray-Burst (GRB) afterglow. The afterglow spectrum consists of several
power-law segments separated by breaks. The image profile changes considerably
across each of the spectral breaks. It also depends on the density profile of
the ambient medium into which the GRB fireball propagates. Gravitational
microlensing by an intervening star can resolve the afterglow image. We
calculate the predicted magnification history of GRB afterglows as a function
of observed frequency and ambient medium properties. We find that intensive
monitoring of a microlensed afterglow lightcurve can be used to reconstruct the
parameters of the fireball and its environment, and provide constraints on
particle acceleration and magnetic field amplification in relativistic blast
waves.
