The PRIMA (Phase-Referenced Imaging and Microarcsecond Astrometry) instrument at ESO/VLTI is scheduled
for commissioning in late 2008. It is designed for phased-referenced imaging and narrow-angle astrometry. The
latter, which is the focus of this paper, may be used for exoplanet detection.
A key PRIMA subsystem consists of two fringe sensing units. They employ polarized and dispersive optics
to measure cross fluxes and differential phases in five narrow K band channels without the need of delay-line
dithering. The differential phases are used to correct the differential delays, which are the primary observables
used to determine relative proper motions, relative parallaxes, and planetary orbits. Real optical components
are imperfect, which means that systematics will appear in the differential phases.
In this paper, we 1) present a closed mathematical form for the differential phase, including small systematic
offsets and random errors; 2) perform Monte Carlo simulations to understand how the small systematic offsets
and random errors affect the differential phases; and 3) show that delay-line stepping can be used to eliminate
the effects of small systematic offsets and random errors.
PRIMA/PACMAN is scheduled for commissioning on Paranal in late 2008 as part of the VLTI. In this paper, we
discuss the important aspects of its astrometric data-reduction software. For example, the top-level requirements,
interfaces to existing ESO software, data types, data levels, and data flow among the recipes dictate the overall
design of any software package. In addition, the complexity of the PACMAN instrument, the long-term nature
of astrometric observations, and the need to improve algorithms as the understanding of the hardware improves,
impose additional requirements on the astrometric data-reduction software.