We present a new reduction pipeline for the VIRCAM@VISTA detector and
describe the method developed to obtain high-precision astrometry with the
VISTA Variables in the V\'ia L\'actea (VVV) data set. We derive an accurate
geometric-distortion correction using as calibration field the globular cluster
NGC 5139, and showed that we are able to reach a relative astrometric precision
of about 8 mas per coordinate per exposure for well-measured stars over a field
of view of more than 1 square degree. This geometric-distortion correction is
made available to the community. As a test bed, we chose a field centered
around the globular cluster NGC 6656 from the VVV archive and computed proper
motions for the stars within. With 45 epochs spread over four years, we show
that we are able to achieve a precision of 1.4 mas/yr and to isolate each
population observed in the field (cluster, Bulge and Disk) using proper
motions. We used proper-motion-selected field stars to measure the motion
difference between Galactic disk and bulge stars. Our proper-motion
measurements are consistent with UCAC4 and PPMXL, though our errors are much
smaller. Models have still difficulties in reproducing the observations in this
highly-reddened Galactic regions.Comment: 11 pages, 10 figures (some in low res), 1 table. Accepted for
publication in MNRAS on March 25, 2015. The FORTRAN routine will be soon made
available at http://groups.dfa.unipd.it/ESPG/ , and via email request to the
first autho