  The direct observation of extrasolar planets and their spectra is coming into
reach with the new generation of ground-based near-IR interferometers, like the
Very Large Telescope Interferometer (VLTI). The high contrast between star and
planet requires an excellent calibration of atmospheric distortions. Proposed
techniques are the observation of color-differential or closure phases. The
differential phase, however, is only in a first order approximation independent
of atmospheric influences because of dispersion effects. This might prevent
differential phase observations of extrasolar planets. The closure phase, on
the other hand, is immune to atmospheric phase errors and is therefore a
promising alternative. We have modeled the response of the closure phase
instrument AMBER at the VLTI to realistic models of known extrasolar planetary
systems taking into account their theoretical spectra as well as the geometry
of the VLTI. We present a strategy to determine the geometry of the planetary
system and the spectrum of the extrasolar planet from closure phase
observations in a deterministic way without any a priori assumptions. We show
that the nulls in the closure phase do only depend on the system geometry but
not on the planetary or stellar spectra. Therefore, the geometry of the system
can be determined by measuring the nulls in the closure phase and braking the
remaining ambiguity due to the unknown system orientation by means of
observations at different hour angles. Based on the known geometry, the planet
spectrum can be directly synthesized from the closure phases.
