  We present analytic threshold formulae applicable to both dispersive
(time-domain) and diffractive (pattern-forming) instabilities in Fabry-Perot
Kerr cavities of arbitrary finesse. We do so by extending the gain-circle
technique, recently developed for counter-propagating fields in
single-mirror-feedback systems, to allow for an input mirror. In time-domain
counter-propagating systems walk-off effects are known to suppress cross-phase
modulation contributions to dispersive instabilities. Applying the gain-circle
approach with appropriately-adjusted cross-phase couplings extends previous
results to arbitrary finesse, beyond mean-field approximations, and describes
Ikeda instabilities.
