  Using drift scan data, a new approach to determining surface brightness
profiles, and techniques for detecting low surface brightness signals, we fit
the light profile of the brightest cluster galaxy (BCG) in the rich cluster
Abell 1651 out to 670 h^{-1} kpc. This radius is a significant fraction of the
virial radius of the cluster (2 h^{-1} Mpc; Girardi et al. 1998), indicating
that the sizes of the BCG and the cluster are comparable. We find that the
profile is consistent with a de Vaucouleurs profile over the radial range
probed. We also find that the integrated light profile of the BCG in Abell 1651
contributes 36% of the total cluster light within 500 h^{-1} kpc. Including all
luminous components, we obtain M/L_I~160 h for the cluster, which would be
overestimated by ~20% without the BCG halo. Furthermore, the relatively red
color of the BCG at large radii suggests that recent disruption and tidal
stripping of spirals and dwarf ellipticals do not contribute significantly to
the halo luminosity. The color and the form of the profile are consistent with
a scenario in which the BCG forms from filamentary collapse during the epoch of
cluster formation, with relatively little evolution in the past 5 Gyrs
(Dubinski 1998). We remove the BCG and other detected galaxies from the image
and construct a two dimensional surface brightness map of the cluster core.
Several knots of excess emission are found, but the total diffuse component is
constrained to contribute less than 5% of the cluster light.
