Bayesian approach to analysis and extrapolation of laser-induced damage fatigue data

Abstract

Virtually all optical materials degrade over time when they are used in high average power or intensity optical systems. Extrapolation of optical components’ lifetime is crucial in such applications in order to avoid downtime or project failure. Measurements of the laser-induced damage threshold (LIDT) fatigue are usually done using the so-called S-on-1 test described in the ISO 21254-2 standard. The standard, however, suggests only rudimentary techniques for extrapolating LIDT, which are rarely used in practice, therefore the goal of this work is to provide a framework for analyzing LIDT fatigue data using well established methods of Bayesian statistics. Numerical S-on-1 experiments (assuming constant fatigue) were performed for cases of online detection, interval detection and offline detection. Appropriate lifetime distributions were determined and used to fit simulated data taking into consideration data censoring. Credible intervals of lifetime predictions were determined using Markov chain Monte Carlo (MCMC) technique and compared with results from multiple experiments. Finally, the Bayesian lifetime analysis method was compared with technique described in the ISO standard for cases of low and high defect densities.