This paper is concerned with the statistical distribution of the maximal hot spots of speckle patterns such as those generated by optical smoothing methods designed for inertial con®nement fusion. It is proved that the maximal intensity at the ®rst order is proportional to the logarithm of the ratio of the pulse volume over the mean hot spot volume. Nevertheless the complete description of the maximal intensity exhibits a quite important variance. Di erent ways for reducing either the maximal¯uence or the maximal intensity are investigated, which are based upon time incoherence or polarization smoothing.
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