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20 December 2007 Effect of random clustering on surface damage density estimates
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Identification and spatial registration of laser-induced damage relative to incident fluence profiles is often required to characterize the damage properties of laser optics near damage threshold. Of particular interest in inertial confinement laser systems are large aperture beam damage tests (>1cm2) where the number of initiated damage sites for Φ>14J/cm2 can approach 105-106, requiring automatic microscopy counting to locate and register individual damage sites. However, as was shown for the case of bacteria counting in biology decades ago, random overlapping or 'clumping' prevents accurate counting of Poisson-distributed objects at high densities, and must be accounted for if the underlying statistics are to be understood. In this work we analyze the effect of random clumping on damage initiation density estimates at fluences above damage threshold. The parameter ψ=aρ= ρ/ρ0, where a=1/ ρ0 is the mean damage site area and ρ is the mean number density, is used to characterize the onset of clumping, and approximations based on a simple model are used to derive an expression for clumped damage density vs. fluence and damage site size. The influence of the uncorrected ρ vs. Φ curve on damage initiation probability predictions is also discussed.
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Manyalibo J. Matthews and Michael D. Feit "Effect of random clustering on surface damage density estimates", Proc. SPIE 6720, Laser-Induced Damage in Optical Materials: 2007, 67201J (20 December 2007);

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