  The detection of an afterglow, following a gamma-ray burst (GRB), can be
described reasonably well by synchrotron emission from a relativistic spherical
expanding blast wave, driven by an expanding fireball. We perform detailed
calculations considering the emission from the whole region behind the shock
front. We use the Blandford McKee self similar adiabatic solution to describe
the fluid behind the shock. Using this detailed model, we derive expressions
for the peak flux, and the peak frequency at a given observed time. These
expressions provide important numerical corrections to previous, more
simplified models. We calculate the observed light curve and spectra for
several magnetic field models. We show that both the light curve and the
spectra are flat near the peak. This rules out the interpretation of the
optical peak of GRB970508 as the peak of the light curve, predicted by the
existing fireball models. We calculate the observed image of a GRB afterglow.
The observed image is bright near the edge and dimmer at the center, thus
creating a ring. The contrast between the edge and the center is larger at high
frequencies and the width of the ring is smaller.
