  Using the adaptive optics facilities at the 200-in Hale and 10-m Keck II, we
observed in the near infrared a sample of 12 binary and multiple stars and one
open cluster. We used the near diffraction limited images of these systems to
measure the relative separations and position angles between their components.
In this paper, we investigate and correct for the influence of the differential
chromatic refraction and chip distortions on our relative astrometric
measurements. Over one night, we achieve an astrometric precision typically
well below 1 miliarcsecond and occasionally as small as 40 microarcseconds.
Such a precision is in principle sufficient to astrometrically detect planetary
mass objects around the components of nearby binary and multiple stars. Since
we have not had sufficiently large data sets for the observed sample of stars
to detect planets, we provide the limits to planetary mass objects based on the
obtained astrometric precision.
