Laser eye safety: the implications of ordinary speckle statistics and of speckled-speckle statistics

The implications of speckle statistics on laser eye-safety considerations are evaluated. The concept of speckled speckle is introduced, and its statistics are shown to correspond to the K0 function. Speckled speckle is defined in terms of the retinal power density when the eye is viewing an optically rough surface that is illuminated by a laser beam diffused through a ground-glass screen-a situation corresponding to subjective speckle modulated by objective speckle. Extensive numerical results are developed relating the ratio of the average power density on the retina over the eye-damage level to the acceptable probability that speckle statistics will cause the damage level to be exceeded. For ordinary speckle and for speckled speckle, for a probability of 10(-6) (10(-9)) of exceeding the damage level, the average power densities must be 0.072 (0.48) and 0.017 (0.0079) of the damage level, respectively.