  The exact profile of a gamma-ray burst (GRB) afterglow image on the plane of
the sky can provide important constraints on the underlying physics. In
particular, it can test whether the magnetic field in the emitting shocked
external medium decreases significantly with the distance behind the shock
front, or remains roughly constant. Moreover, it enables more accurate
measurements of the afterglow image size and the expected scintillation
properties. In this work analytic expressions are derived for the afterglow
image in power law segments (PLSs) of the afterglow synchrotron spectrum in
which the emission originates from a very thin layer just behind the shock,
while simple semi-analytic expressions are derived for the remaining PLSs in
which the emission arises from the bulk of the shocked fluid. In all cases the
expressions are for a general power law external density profile, and are
convenient to use in afterglow studies.
