Statistics of the hottest spot of speckle patterns generated by smoothing techniques

This paper is concerned with the statistical distribution of the maximal ho t spots of speckle patterns such as those generated by optical smoothing me thods designed for inertial confinement fusion. It is proved that the maxim al intensity at the first order is proportional to the logarithm of the rat io of the pulse volume over the mean hot spot volume. Nevertheless the comp lete description of the maximal intensity exhibits a quite important varian ce. Different ways for reducing either the maximal fluence or the maximal i ntensity are investigated, which are based upon time incoherence or polariz ation smoothing.