1 Introduction

The success of Hipparcos (Mignard 1995; van Leeuwen 1997; Kovalevsky 1998) demonstrated the feasibility of obtaining astrometric measurements in space with milliarcsecond accuracy. The result is the construction of a catalogue with 120 000 stars as faint as the visual 12th magnitude (Perryman 1997).

The mission initially called Global Astrometric Interferometer for Astrophysics (GAIA, Lindegren & Perryman 1996), submitted to ESA for its Horizon 2000+ programme as a candidate cornerstone mission, is a successor of Hipparcos. Its goal was to bring a breakthrough in global astrometric observations with extremely high accuracy, down to 10 $\mu$as, with a limiting visual magnitude of 15-16. Later studies (Gilmore et al. 1998) have lead to an improved design which allows observation (at a reduced accuracy) to significantly fainter magnitudes. In the following, we considered as work hypothesis an achievable 10 $\mu$as astrometric accuracy for a 15th magnitude star.

GAIA will provide multi-band, multi-epoch photometry. The mission life-time is expected to be 5 years at least, necessary to attain the desired astrometric accuracy with a considerable amount of by-product results such as a significant survey of extra-solar planets and test of the general relativity theory (Lindegren & Perryman 1996; Perryman et al. 1997; Lattanzi et al. 1997). With 10 $\mu$as astrometry and a 15th magnitude limit, GAIA's parallax horizon will envelope the Milky-way Galaxy, its halo, many globular clusters, reaching very probably the Magellanic Clouds. Among other targets, GAIA will also determine the distance of all galactic Cepheid variables, RR Lyrae and long period pulsators like Miras and will refine at an unrivalled level, the Period - Luminosity - Metallicity relation. The impact of such observations on cosmology is immense but GAIA will certainly bring news that we are far from suspecting at this time.

In order to perform global astrometry, a large number of objects, uniformly distributed on the celestial sphere, should be observed. To achieve the construction of a distortionless reference system over the whole sky from large angle measurements, a sky scanning law similar to that of Hipparcos will be used. As it spins about an axis, the satellite sees, over one revolution, all the stars present over a great circle. Measuring angular deviations yields these stars' positions in mutual relations. Each circle is itself linked to all other in a final data processing step, thereby graduating from one-dimensional to two-dimensional information on position. Thus, a network is built during the mission, that binds together all of the observed objects, yielding both a reference frame and the positions, proper motions and parallaxes of the objects in that reference frame at the end of the mission.

As far as simultaneous observations are needed in several directions, the instrumental concept proposed by Lindegren & Perryman (1996) is composed of three interferometers whose lines of sight are separated by constant angles $54\hbox{$^\circ$}$, $78.5\hbox{$^\circ$}$, and $132.5\hbox{$^\circ$}$. Although only two instruments are sufficient to fulfil the mission, the third one insures a redundancy in the measurements.

The associated optical configuration was analysed by (Loiseau & Shaklen 1996). The choice of a Fizeau interferometer (versus a Michelson configuration) was imposed by the necessity to observe with a large co-phased field of view (the word "co-phased'' being used to describe a field of view in which interference fringes are not degraded by aberrations). The entrance pupil diameter was 0.55 m, the baseline 2.45 m, and the equivalent focal length 11.55 m. The latter, combined with a 1 deg² field of view yields a 20 $\times$ 20 cm² focal plane. In such a configuration, the fringe period is 2.6 $\mu$m (at $\lambda$ = 550 nm) and the Airy disk diameter 28 $\mu$m, requiring a pixel size of 1.3 $\times$ 28 $\mu$m² (maximum size imposed by Shannon criterion), technologically unfeasible as yet. To overcome the pixel size problem, a solution was proposed for the fringe detection consisting in dividing the whole field of view in subfields and linking them with a modulating grid. The observation is recorded in the pupil plane. The spatial modulation of the intensity due to interference fringes in the image plane is transformed into a temporal modulation detected on a mono-pixel detector in the pupil plane. The main drawback of this solution is the confusion effect: the infalling fluxes of different stars within the same subfield cannot be distinguished. One of us (Thomas 1996) evaluated quantitatively the importance of this effect, showing the degradation induced on the signal phase measurement by observing in crowded fields.

To overcome the confusion effect, we propose a new optical configuration (Gai et al. 1997; Thomas et al. 1997) suitable to an astrometric mission such as GAIA, which would enable direct observations in the image focal plane (direct fringe detection), taking into account the expected state-of-the-art CCD technologies. This work was the target of a study conducted under ALENIA's prime contractorship in 1997 (in the framework of the APLT-AMTS ESA contract). Other concepts for GAIA presently exist and are under study. In particular, a Concept and Technology Study performed under a different ESA contract has lead to a rather different (non-interferometric) design, which is currently the baseline version of GAIA considered by ESA. Our study presents an alternative solution, which combines the original concept of a Fizeau interferometer with a technologically reasonable solution for direct fringe detection.

In the following, we derive the requirements of the direct fringe detection configuration (field of view, focal plane, telescope accommodation, calibration and geometrical stability). We present in detail our optical configuration in Sect. 2, as well as the foreseeable CCD technology. We also present the optical quality in terms of rms spot diagram diameter. In Sect. 3, we give the optical configuration performance in terms of aberrations and mechanical tolerances. A way to assess the performance in terms of estimated fringe contrast was implemented using Fourier optics on a Software for Interferometric Visibility Analysis (SIVA), an algorithm developed at Alcatel Space Industries, Cannes.