  An analytical model is derived for the probability of failure (P-fail) to
spatially acquire an optical link with a jittering search beam. The analytical
model accounts for an arbitrary jitter spectrum and considers the associated
correlations between jitter excursions on adjacent tracks of the search spiral.
An expression of P-fail in terms of basic transcendental functions is found by
linearizing the exact analytical model with respect to the correlation
strength. Predictions from the models indicate a strong decrease of P-fail with
increasing correlation-strength, which is found to be in excellent agreement to
results from Monte Carlo simulations. The dependency of P-fail on track-width
and scan speed is investigated, confirming previous assumptions on the impact
of correlations. Expressions and applicable constraints are derived for the
limits of full and no correlations, and the optimal track width to minimize the
acquisition time is computed for a range of scan speeds. The model is
applicable to optical terminals equipped with a fast beam steering mirror, as
often found for optical communication missions in space.
