  The direct detection of binary systems in wide-field surveys is limited by
the size of the stars' point-spread-functions (PSFs). A search for elongated
objects can find closer companions, but is limited by the precision to which
the PSF shape can be calibrated for individual stars. We have developed the
BinaryFinder algorithm to search for close binaries by using precision
measurements of PSF ellipticity across wide-field survey images. We show that
the algorithm is capable of reliably detecting binary systems down to
approximately 1/5 of the seeing limit, and can directly measure the systems'
position angles, separations and contrast ratios. To verify the algorithm's
performance we evaluated 100,000 objects in Palomar Transient Factory (PTF)
wide-field-survey data for signs of binarity, and then used the Robo-AO robotic
laser adaptive optics system to verify the parameters of 44 high-confidence
targets. We show that BinaryFinder correctly predicts the presence of close
companions with a <5% false-positive rate, measures the detected binaries'
position angles within 2 degrees and separations within 25%, and weakly
constrains their contrast ratios. When applied to the full PTF dataset, we
estimate that BinaryFinder will discover and characterize ~450,000
physically-associated binary systems with separations <2 arcseconds and
magnitudes brighter than R=18. New wide-field synoptic surveys with high
sensitivity and sub-arcsecond angular resolution, such as LSST, will allow
BinaryFinder to reliably detect millions of very faint binary systems with
separations as small as 0.1 arcseconds.
