Measurements of the wave-front outer scale at Paranal: influence of this parameter in interferometry

The Generalized Seeing Monitor (GSM) has undertaken a campaign of measurement of the optical turbulent parameters : the Fried's parameter, the outer scale (L(0)) and the isoplanatic patch, at Paranal, the site of the VLT, in December 1998. The principle aim of this mission was to measure L(0) values at Paranal. In a first part, we present the GSM, the results of the mission and particularly the statistics of L(0). In a second part, we emphasize the effect of L(0) on the optical path difference (OPD) values for the co-phasing of an interferometer. We derive the exact formulation of the OPD for the Von Karman model and we give the expected OPD at Paranal with L(0) values measured by the GSM. We give also the expression of the residual OPD at the output of a fringe tracker system as a function of L(0), of the exposure time of the fringe sensor and of the frequency of the closed-loop of the system.