Statistics of the hot spots of smoothed beams produced by random phase plates revisited

This paper revisits and corrects the statistical theory of hot spots of speckle patterns such as those produced by a random phase plate. Analytical expressions are derived which are sensitively different from the previous results of Rose and DuBois [Phys. Fluids B 5, 590 (1993)]. The departure essentially originates from a careful approach which takes into account the fact that the fields are complex-valued, while the standard mathematical theory deals with the maxima of real-valued Gaussian fields. This gives rise to an enhancement of the number of the most intense hot spots. Excellent agreements between the theoretical formulas and numerical simulations are shown.

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