  Interferometric measurements of optical path length differences of stars over
large baselines can deliver extremely accurate astrometric data. The
interferometer GRAVITY will simultaneously measure two objects in the field of
view of the Very Large Telescope Interferometer (VLTI) of the European Southern
Observatory (ESO) and determine their angular separation to a precision of 10
micro arcseconds in only 5 minutes. To perform the astrometric measurement with
such a high accuracy, the differential path length through the VLTI and the
instrument has to be measured (and tracked since Earth's rotation will
permanently change it) by a laser metrology to an even higher level of accuracy
(corresponding to 1 nm in 3 minutes). Usually, heterodyne differential path
techniques are used for nanometer precision measurements, but with these
methods it is difficult to track the full beam size and to follow the light
path up to the primary mirror of the telescope. Here, we present the
preliminary design of a differential path metrology system, developed within
the GRAVITY project. It measures the instrumental differential path over the
full pupil size and up to the entrance pupil location. The differential phase
is measured by detecting the laser fringe pattern both on the telescopes'
secondary mirrors as well as after reflection at the primary mirror. Based on
our proposed design we evaluate the phase measurement accuracy based on a full
budget of possible statistical and systematic errors. We show that this
metrology design fulfills the high precision requirement of GRAVITY.
