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Effects Of Illumination Beam Jitter On Photodetection Statistics

An expression for the probability density function for a doubly stochastic Poisson process driven by illumination beam jitter was derived. The formula was used to calculate the effect of jitter on the probability of detecting a point target in presence of both illumination beam jitter and additive background noise. The illumination beam is assumed to have a Gaussian profile with standard deviation σB. The jitter distribution is also Gaussian with standard deviation σj. It was found that for the quantity σj/σB, called the jitter ratio, exceeding 0.5 that the effect of jitter becomes significant.