Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors

For a direct-detection laser radar that uses a Geiger-mode detector, theory shows that the single-pulse detection probability is reduced by a factor exp(-K), where K is the mean number of primary electrons created by noise in the interval t between detector turn-on and arrival of laser photons reflected from the target. The corresponding false-alarm probability is at least 1 - exp(-K). For fixed-rate noise, one can improve the detection and false-alarm probabilities by reducing t. Moreover, when background-light noise is significant and dominates dark-current noise and when the laser signal is of the order of ten photoelectrons or more, the probabilities can be improved by reducing the amount of light falling on the detector, even if the laser signal is reduced by the same factor as the background light is. Additional analytical calculations show that identifying coincidences in data from as few as three pulses canreduce the false-alarm probability by orders of magnitude and, for some conditions, can also improve the detection probability.