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 Via Lactea (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.
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