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Simple statistical detection theory is applied to the problem of detecting small images immersed in a background of laser-produced speckle. The detection device is assumed to be a flying-spot type of scanning machine which has continuous scanning in both the x and y directions. Two main points have emerged. Firstly, the size and transmittance distribution of an aperture used to scan the image are best determined by consideration of probabilistic quantities, and not by signal-to-noise ratio criteria. Secondly, in a typical detection problem of opaque discs in a speckle background, the geometrical image diameter should be at least four times the Rayleigh resolution limit of the lens used to form the image, for reliable detection.
J. C. Dainty (1971) studied this question.