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 3.6 m NTT telescope , and the remainder with other telescopes . The circumstellar envelopes are detected in 15 objects , with mass loss rates \ga 2 \times 10 ^ { -6 } M _ { \odot } yr ^ { -1 } . 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 \sim 50 % of the envelopes are close to circular with E \la 1.1 , and others are more elliptical with \sim 20 % with E \ga 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 \sim 50 % 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 binary 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 .