  Pointing and acquisition are an important aspect of free-space optical
communications because of the narrow beamwidth associated with the optical
signal. In this paper, we have analyzed the pointing and acquisition problem in
free-space optical communications for photon-counting detector arrays and
Gaussian beams. In this regard, we have considered the maximum likelihood
detection for detecting the location of the array, and analyzed the one-shot
probabilities of missed detection and false alarm using the scaled Poisson
approximation. Moreover, the upper/lower bounds on the probabilities of missed
detection and false alarm for one complete scan are also derived, and these
probabilities are compared with Monte Carlo approximations for a few cases.
Additionally, the upper bounds on the acquisition time and the mean acquisition
time are also derived. The upper bound on mean acquisition time is minimized
numerically with respect to the beam radius for a constant signal-to-noise
ratio scenario. Finally, the complementary distribution function of an upper
bound on acquisition time is also calculated in a closed form. Our study
concludes that an array of smaller detectors gives a better acquisition
performance (in terms of acquisition time) as compared to one large detector of
similar dimensions as the array.
