Avalanche photodiode detection statistics for direct detection laser radar

The detection statistics of avalanche photodiode detectors when used in laser radar systems are examined. In the laser radar systems considered here, a diffuse hard target is illuminated by a transmitted laser beam and the photons subtended by the receiving aperture and focused onto the detector obey negative-binomial statistics. The specific negative-binomial distribution is determined by the coherence length of the laser and the angular subtense of the target. These received photons are converted into photoelectrons and amplified by the avalanche photodiode which is an imperfect device. Dark current, amplifier, and background-produced noise electrons must be exceeded by the avalanche photodiode output electron pulse for a detection to occur. The required mean number of signal photons from a given negative-binomial target as a function of probability of detection and probability of false alarm is calculated. For perfect photon counters, the probability of detection at high discrete false alarm probabilities is also calculated. It is shown that for probabilities of detection of 0.9, three to five times more laser power may be required than for the generally assumed Poisson signal photons case. At probabilities of detection of 0.3, corresponding to multipulse waveforms, the statistics are independent of the target photon distribution.