Atmospheric coherence times in interferometry: definition and measurement

Current and future ground-based interferometers require knowledge of the atmospheric time constant t_0, but this parameter has diverse definitions. Moreover, adequate techniques for monitoring t_0 still have to be implemented. We derive a new formula for the structure function of the fringe phase (piston) in a long-baseline interferometer, and review available techniques for measuring the atmospheric time constant and the shortcomings. It is shown that the standard adaptive-optics atmospheric time constant is sufficient for quantifying the piston coherence time, with only minor modifications. The residual error of a fast fringe tracker and the loss of fringe visibility in a finite exposure time are calculated in terms of the same parameter. A new method based on the fast variations of defocus is proposed. The formula for relating the defocus speed to the time constant is derived. Simulations of a 35-cm telescope demonstrate the feasibility of this new technique for site testing.