Characterization of damage precursor density from laser damage probability measurements with non-Gaussian beams

Damage induced by nanosecond laser in optical materials can often be attributed to the presence of laser damage precursor in the material. The presence of these precursors within dielectric optics can be successfully described by so called distributed defect ensembles. The physical parameters of these precursor presence models can be deduced by fitting experimental laser damage probability data. For a degenerate defect ensemble these parameters are the precursor threshold and the precursor density in the sample. To deduce precursor densities correctly it is essential to consider the real shape of laser beam that often deviates from Gaussian or hat-top models. To address these issues we discuss a new fitting procedure that minimizes significant errors in the deduced model parameters using experimental beam profile images. We suggest two methods: Defining a Gaussian replacement beam or using a numerical approximation of the surface over threshold (SOT) of the real beam. Both methods are discussed at the example of a degenerate damage precursor population but apply to any type of damage precursor population.