Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

¹ LESIA, Observatoire de Paris, CNRS, UPMC, Université Paris-Diderot, Paris Sciences et Lettres Research University, 5 place Jules Janssen, 92 195 Meudon, France
e-mail: choquet@stsci.edu
² Groupement d’Intérêt Scientifique PHASE (Partenariat Haute résolution Angulaire Sol Espace) between ONERA, Observatoire de Paris, CNRS and Université Paris Diderot  
³ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD 21218, USA
⁴ Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁵ Onera – The French Aerospace Lab, BP 72, 92 322 Châtillon, France
⁶ Max Planck Institute for extraterrestrial Physics, PO Box 1312, Giessenbachstr., 85 741 Garching, Germany

Received: 14 August 2012
Accepted: 17 June 2014

Abstract

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.