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1.ISO 21254:2011 “Test methods for laser-induced damage threshold,” International Organization for Standardization.
2.S. Schrameyer, M. Jupé, L. Jensen, and D. Ristau, “Algorithm for cumulative damage probability calculations in S-on-1 laser damage testing,” Proc. SPIE 8885, 88851J (2013).
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6.H. Krol, L. Gallais, C. Crèzes-Besset, J.-Y. Natoli, and M. Commandré, “Investigation of nanoprecursors threshold distribution in laser damage testing,” Opt. Commun. 256, 184189 (2005).
7.L. Lamaignère, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Ponetta, and H. Bercegol, “An accurate repeatable and well characterized measurement of laser damage density of optical materials,” Rev. Sci. Instrum. 78, 103105 (2007).
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9. These data sets were generated with random numbers between 0 and 1. If the random number was above the previously chosen model curve, the virtual test spot was set to “not damaged” and for random numbers below the model curve to “damaged.” This leads to realistic distributions of virtual test spots, which fit the model curve very well for high numbers of test spots.
10. In particular the diagonal elements of the covariance matrix state the square root of the standard deviation for each fitting coefficient.8 In this case, the damage threshold and the defect density are the coefficients relevant for this fit (in addition to the p-factor).4

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As a consequence of its statistical nature, the measurement of the laser-induced damage threshold holds always risks to over- or underestimate the real threshold value. As one of the established measurement procedures, the results of S-on-1 (and 1-on-1) tests outlined in the corresponding ISO standard 21 254 depend on the amount of data points and their distribution over the fluence scale. With the limited space on a test sample as well as the requirements on test site separation and beam sizes, the amount of data from one test is restricted. This paper reports on a way to treat damage test data in order to reduce the statistical error and therefore measurement uncertainty. Three simple assumptions allow for the assignment of one data point to multiple data bins and therefore virtually increase the available data base.


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