  More than 450 exoplanets are known and this number increases nearly every
day. Only a few constraints on their orbital parameters and physical
characteristics can be determined, as most exoplanets are detected indirectly.
Measuring the astrometric signal of a planet by measuring the wobble of the
host star yields the full set of orbital parameters. With this information the
true masses of the planet candidates can be determined, making it possible to
establish the candidates as real planets, brown dwarfs (BD) or low mass stars.
In the context of this thesis, an M-dwarf with a BD candidate companion,
discovered by radial velocity measurements, was observed within a monitoring
program to detect the astrometric signal. Ground based adaptive optics aided
imaging with ESO/NACO was used to establish its true nature (BD vs. star) and
to investigate the prospects of this technique for exoplanet detection. The
astrometric corrections necessary to perform high precision astrometry are
described and their contribution to the overall precision is investigated. Due
to large uncertainties in the pixel-scale and the orientation of the detector,
no detection of the astrometric orbit signal was possible. The image quality of
ground-based telescopes is limited by the turbulence in Earth's atmosphere. The
induced distortions of the light can be measured and corrected with the
adaptive optics technique. However, the correction is only useful within a
small angle around the guide star. The novel correction technique of multi
conjugated adaptive optics uses several guide stars to correct a larger field
of view. The VLT/MAD instrument was built to demonstrate this technique.
Observations with MAD are analyzed in terms of astrometric precision in this
work. Two sets of data are compared, which were obtained in different
correction modes: pure ground layer correction and full multi conjugated
correction.
