  We present in this paper 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 can be
derived for any single-mode interferometer. 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 which builds the linear relationship between the interferogram and the
interferometric observable, that 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. The data reduction procedures are
gathered into the so-called amdlib software, now available for the community,
and presented in this paper. Furthermore, each step of 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, difficult
to calibrate.
