Sketch of the effect of the turbulence in interferometry. On each telescope pupil P(r) separated by the baseline distance B₁₂, the wavefront is affected by a random phase screen, respectively φ₁(r) and φ₂(r). The strength of the turbulence depends on the parameters D/r₀ where D is the diameter of the telescope and r₀ is the Fried parameter (Fried 1965), describing the typical size of a coherent cell in the wavefront. Furthermore, the optical path difference between the two beams is randomly shifted by the turbulent piston , which is the phase difference between the two telescopes, averaged on the pupils. If an AO system is present on each telescope, then the wavefront is partially corrected in real time, and the quantity of interest are the residual phases and and the associated residual turbulent piston.