Threshold detection in the presence of atmospheric turbulence

Recently there has been increased interest in threats to spacecraft from ground-based lasers. It has been suggested that some spacecraft should use laser-threat-warning receivers. We consider the effects of atmospheric turbulence on threshold detection of optical signals by an exoatmospheric receiver. The results are applicable to both cw and pulsed optical illumination that results from ground-based lasers. In particular we obtain accurate analytical expressions, over a wide range of conditions of practical interest, that yield the required signal-to-noise ratio for a given (single-event) probability of detection, false-alarm rate, and turbulence-induced log-intensity variance. The degrading effects of atmospheric turbulence on threshold detection are most important for large zenith angles in the blue-green region of the visible. As an illustrative example, a false-alarm rate of 1 in 3 years is assumed, and specific numerical results are presented for the required signal-to-noise ratio necessary to obtain a detection probability of at least 95% over a range of optical wavelengths and propagation conditions of interest.