Interferometric data reduction with AMBER/VLTI.: Principle, estimators, and illustration

Aims. In this paper, we present an innovative data reduction method for single-mode interferometry. It has been specifically developed for the AMBER instrument, the three-beam combiner of the Very Large Telescope Interferometer, but it can be derived for any single-mode interferometer. Methods. The algorithm is based on a direct modelling of the fringes in the detector plane. As such, it requires a preliminary calibration of the instrument in order to obtain the calibration matrix that builds the linear relationship between the interferogram and the interferometric observable, which is the complex visibility. Once the calibration procedure has been performed, the signal processing appears to be a classical least-square determination of a linear inverse problem. From the estimated complex visibility, we derive the squared visibility, the closure phase, and the spectral differential phase. Results. The data reduction procedures have been gathered into the so-called amdlib software, now available for the community, and are presented in this paper. Furthermore, each step in this original algorithm is illustrated and discussed from various on-sky observations conducted with the VLTI, with a focus on the control of the data quality and the effective execution of the data reduction procedures. We point out the present limited performances of the instrument due to VLTI instrumental vibrations which are difficult to calibrate.