  Interferometric observations with three telescopes or more provide two
observables: closure phase information together with visibilities measurements.
When using single-mode interferometers, both observables have to be redefined
in the light of the coupling phenomenon betwe en the incoming wavefront and the
fiber. We introduce in this paper the estimator of both so-called modal
visibility and modal closure phase. Then, we compute the statistics of the two
observables in presence of partial correction by Adaptive Optics. From this
theoretical analysis, data reduction process using classical least square
minimization is investigated. In the framework of the AMBER instrument, the
three beams recombiner of the VLTI, we simulate the observation of a single
Gaussian source and we study the performances of the interferometer in terms of
diameter measurements. We show that the observation is optimized, i.e. that the
Signal to Noise Ratio (SNR) of the diameter is maximal, when the full width
half maximum (FWHM) of the source is roughly 1/2 of the mean resolution of the
interferometer. We finally point out that in the case of an observation with 3
telescopes, neglecting the correlation between the measurements leads to
overestimate the SNR by a factor of $\sqrt{2}$. We infer that in any cases,
this value is an upper limit.
