The GRAVITY fringe tracker Lacour, S.; Dembet, R.; Abuter, R. ...
Astronomy and astrophysics (Berlin),
04/2019, Volume:
624
Journal Article
Peer reviewed
Open access
Context. The GRAVITY instrument was commissioned on the VLTI in 2016 and is now available to the astronomical community. It is the first optical interferometer capable of observing sources as faint ...as magnitude 19 in K band. This is possible through the fringe tracker, which compensates the differential piston based on measurements of a brighter off-axis astronomical reference source. Aims. The goal of this paper is to describe the main developments made in the context of the GRAVITY fringe tracker. This could serve as basis for future fringe-tracking systems. Methods. The paper therefore covers all aspects of the fringe tracker, from hardware to control software and on-sky observations. Special emphasis is placed on the interaction between the group-delay controller and the phase-delay controller. The group-delay control loop is a simple but robust integrator. The phase-delay controller is a state-space control loop based on an auto-regressive representation of the atmospheric and vibrational perturbations. A Kalman filter provides the best possible determination of the state of the system. Results. The fringe tracker shows good tracking performance on sources with coherent K magnitudes of 11 on the Unit Telescopes (UTs) and 9.5 on the Auxiliary Telescopes (ATs). It can track fringes with a signal-to-noise ratio of 1.5 per detector integration time, limited by photon and background noises. During good seeing conditions, the optical path delay residuals on the ATs can be as low as 75 nm root mean square. The performance is limited to around 250 nm on the UTs because of structural vibrations.
To enable optical long baseline interferometry toward faint objects, long integrations are necessary despite atmospheric turbulence. Fringe trackers are needed to stabilize the fringes and thus ...increase the fringe visibility and phase signal-to-noise ratio (S/N), with efficient controllers robust to instrumental vibrations and to subsequent path fluctuations and flux drop-outs. We report on simulations, analysis, and comparison of the performances of a classical integrator controller and of a Kalman controller, both optimized to track fringes under realistic observing conditions for different source magnitudes, disturbance conditions, and sampling frequencies. The key parameters of our simulations (instrument photometric performance, detection noise, turbulence, and vibrations statistics) are based on typical observing conditions at the Very Large Telescope observatory and on the design of the GRAVITY instrument, a 4-telescope single-mode long-baseline interferometer in the near-infrared, next in line to be installed at VLT Interferometer. We find that both controller performances follow a two-regime law with the star magnitude, a constant disturbance limited regime, and a diverging regime limited by both the detector and photon-noise. Moreover, we find that the Kalman controller is optimal in the high and medium S/N regime owing to its predictive commands based on an accurate disturbance model. In the low S/N regime, the model is not accurate enough to be more robust than an integrator controller. Identifying the disturbances from high S/N measurements improves the Kalman performances in the case of strong optical path difference disturbances.
Context.
Atmospheric refraction modifies the apparent position of objects in the sky. As a complement to the well-known angular offset, we computed the lateral translation that is to be considered ...for short-range applications, such as wavefront sensing and meteor trajectories.
Aims.
We aim to calculate the lateral shift at each altitude and study its variation according to meteorological conditions and the location of the observation site. We also pay special attention to the chromatism of this lateral shift. Moreover, we assess the relevance of the expressions present in the literature, which have been established neglecting Earth’s curvature.
Methods.
We extracted the variation equations of refraction from the geometric tracing of a light ray path. A numerical method and a dry atmosphere model allowed us to numerically integrate the system of coupled equations. In addition to this, based on Taylor expansions, we established three analytic approximations of the lateral shift, one of which is the one already known in the literature. We compared the three approximations to the numerical solution. All these estimators are included in a P
YTHON
3.2 package, which is available online.
Results.
Using the numerical integration estimator, we calculated the lateral shift values for any zenith angle including low elevations. The shift is typically around 3 m at a zenith angle of 45°, 10 m at 65°, and even 300 m at 85°. Next, the study of the variability of the lateral shift as a function of wavelength shows differences of up to 2% between the visible and near infrared. Furthermore, we show that the flat Earth approximation of the lateral shift corresponds to its first-order Taylor expansion. The analysis of the errors of each approximation shows the ranges of validity of the three estimators as a function of the zenith angle. The ‘flat Earth’ estimator achieves a relative error of less than 1% up to 55°, while the new extended second-order estimators improves this result up to 75°.
Conclusions.
The flat Earth estimator is sufficient for applications where the zenith angle is below 55° (most high-resolution applications) but a refined estimator is necessary to estimate meteor trajectories at low elevations.
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