  We study the dynamical Casimir effect in the presence of a finite coherence
time, which is associated with a finite quality factor of the optical cavity.
We use the time refraction model, where a fixed cavity with a modulated optical
medium, replaces the empty cavity with a vibrating mirror. Temporal coherence
is described with the help of cavity quasi-mode operators. Asymptotic
expressions for the number of photon pairs generated from vacuum are derived.
