Introduction

Fringe tracking in an interferometer with large apertures and spatial filters is known to be very challenging. There are three regimes of interest to PRIMA:

1. Observations where the performance is limited by the S/N for active fringe tracking
2. Observations where the performance is limited by the S/N for passive observations of the Ses when the fringes are phase-stabilised using the PS
3. Observations where the performance is limited by the S/N for passive observations of the Ses when the fringes are not phase-stabilised.

Under regime 1 above, the configuration of the VLTI should be optimised to provided maximum S/N ratio on the PS. Under typical Paranal seeing conditions the AT diameter is close to the optimum for fringe tracking S/N with ideal tip-tilt correction - under poorer seeing or poorer tip-tilt correction it may be beneficial to stop down the aperture diameter at the FSU. The results of simple simulations which investigate the performance of the group tracking performance on seeing and aperture diameter are presented in later this section. The added complication for the baseline geometry if the pupil is stopped down may outweigh the benefit in fringe-tracking performance. If the UTs are used there may be a stronger case for stopping down the apertures, particularly if the AO system can be matched to the stopped-down aperture geometry.

Under regime 2 above, the configuration of the VLTI should be optimised to provided maximum S/N ratio on the SeS. As the fringes are phase-stabilised, this simply requires the flux through the spatial filter to be optimised. [5] shows that even for simple tip-tilt correction the optimum aperture size can be as large as $6r_{0}$ for an interferometer with spatial filters, so the AT apertures will never have to be stopped down. It also seems likely that the UT apertures would not need to be stopped down to a smaller diameter if MACAO was used in PRIMA observations.

Regime 3 will require more detailed analysis, although it is expected that the optimum operating conditions will be similar to those for regime 1.

The precise performance of PRIMA will also depend on specific characteristics such as the wavelength separation of the group delay tracking channels, the bandpass of the phase-tracking channel and the performance of the tip-tilt correction. For this reason, numerical simulations which are more PRIMA-specific will be required in order to produce a realistic model of the fringe-tracking performance of PRIMA.