The relationship between laser fluence profile and the cumulative probability of damage curve

The Gaussian profile beam has been de rigeur for damage threshold measurements for decades. This paper formulates the cumulative probability of damage (CPD) curve for the Gaussian and an arbitrary distribution of defects in fluence (intensity) space. It is seen that the CPD for the Gaussian is relatively insensitive to the underlying distribution of defects. The CPD is reformulated for a flat top distribution and shown to be far more influenced by the underlying defect distribution. The paper concludes with a discussion of the relationship between the defect distribution, sample size, threshold and measured threshold, for both the Gaussian and flat top profiles. It will be shown than the CPD for Gaussian beams increases with increasing fluence regardless of the distributions of the defects in fluence. The Flat Top CPD will only increase with increasing defect density.