  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.
