  We report results of a program to image the extended circumstellar envelopes
of asymptotic giant branch (AGB) stars in dust-scattered Galactic light. The
goal is to characterize the shapes of the envelopes to probe the mass-loss
geometry and the presence of hidden binary companions. The observations consist
of deep optical imaging of 22 AGB stars with high mass loss rates: 16 with the
ESO 3.5 m NTT telescope, and the remainder with other telescopes. The
circumstellar envelopes are detected in 15 objects, with mass loss rates > 2E-6
Msun/year. The surface brightness of the envelopes shows a strong decrease with
Galactic radius, which indicates a steep radial gradient in the interstellar
radiation field. The envelopes range from circular to elliptical in shape, and
we characterize them by the ellipticity (E = major/minor axis) of iso-intensity
contours. We find that about 50 percent of the envelopes are close to circular
with E < 1.1, and others are more elliptical with about 20 percent with E >
1.2. We interpret the shapes in terms of populations of single stars and
binaries whose envelopes are flattened by a companion. The distribution of E is
qualitatively consistent with expectations based on population synthesis models
of binary AGB stars. We also find that about 50 percent of the sample exhibit
small-scale, elongated features in the central regions. We interpret these as
the escape of light from the central star through polar holes, which are also
likely produced by companions. Our observations of envelope flattening and
polar holes point to a hidden population of companions within the circumstellar
envelopes of AGB stars. These companions are expected to play an important role
in the transition to post-AGB stars and the formation of planetary nebulae.
