My PhD was initiated in the framework of the development of GRAVITY, second generation instrument for the VLTI, whose first light is expected for 2014. GRAVITY will combine up to four telescopes in the K infrared spectral band (~2.2 µm). By stabilizing the phase of a reference star of magnitude as faint as K=10, this instrument will enable astrometric measurements with a precision of 10 µas on objects of magnitude up to K=15, and phase referenced imaging on objects as faint as K=16 with about 4mas angular resolution. The goal of my PhD consists in developing the fringe tracker algorithms of GRAVITY, a critical sub-system to reach these sensitivity limits unequaled in infrared long-baseline interferometry. To enable integrations longer than 100 s on the science beam, the fringe tracker will have to stabilize the optical path differences, with residues as low as 350 nm rms on the reference star, despite disturbance due to atmospheric piston, instrumental vibrations, and variations of flux in the recombined beams. In this aim, I performed numerical simulations of the whole control loop, by realistically modeling different disturbance sources inducing path length fluctuations in the beams, and flux variations in the beams. I demonstrated that fringes will be stabilized down to 310 nm rms on a K=10 magnitude star with the expected observing conditions at VLTI in 2014, with a predictive controller based on Kalman filtering that uses a disturbance model to compute the actuator commands. However, I showed that this performance strongly decreases for less optimistic conditions. In addition, I analyzed the efficiency in correcting both atmospheric piston and vibrations of the Kalman controller, compared to the algorithms currently used at VLTI. From on-sky phase measurements with the PRIMA instrument at VLTI, I showed that the disturbances are better corrected with the Kalman controller than with the PRIMA-FSU. Moreover, I performed numerical simulations demonstrating that the Kalman controller is more efficient to compensate vibrations than the VTK algorithm, dedicated to correct vibrations at VLTI. Moreover, I developed a laboratory demonstrator of the GRAVITY fringe tracker, to experimentally validate its algorithms. I thus analyzed instrumental specificities of the fringe tracker with this prototype that are not included in the simulations, such as the calibration process and bias induced by imperfect dispersive optical systems. Finally, I contributed to an astrophysical study, in which I performed and analyzed infrared interferometric observations of the X-ray binary Vela X-1. I measured a stellar wind with different sizes in the H and K spectral bands, revealing either a strong temperature gradient in the stellar wind, or transient events in the accretion process. When GRAVITY is operational, this study will be extended to fainter X-ray binaries, thanks to the unique sensitivity of the instrument in infrared interferometry. To conclude, my PhD demonstrated that the performance of the fringe tracker matches the specifications of the GRAVITY instrument, making it the first four-telescope fringe tracker operational for faint targets, despite strong disturbances. GRAVITY and the fringe tracker thus pave the way to astrophysical observation unprecedented in optical interferometry.
