Monte-Carlo-based calculation of measurement quality for three variants of the damage frequency method

Abstract

Abstract: This paper quantifies the measurement quality, Q, of three test procedures bysimulating a series of correlation experiments and employing a Monte Carlo technique.The three methods compared are the ISO standard damage frequency method (DFM),the DFM yielding the highest Q (optimal DFM) and a modified DFM. For each trial, twovalues of the normalized damage threshold and uncertainty are derived via a PCspreadsheet based Monte Carlo simulation. To simulate various sets of real optics, thenormalized results are multiplied by a set of uniformly distributed random numberswhich are unique to each trial. The slope of the correlation line for each test procedureis determined via a weighted linear regression, and recorded. The output of the modelis a frequency distribution of the slopes of the correlation lines for each procedure.Comparing the distributions of the slopes of the correlations is a direct measure of Q2for each test procedure. It is shown that a revised DFM results in a much higherlikelihood of making an accurate measurement with a given precision.1 Introduction:This paper addresses itself to evaluating measurement quality, Q, of three variants ofthe damage frequency method (DFM)1 of determining laser damage threshold (LDT)determination. Measurement quality, Q(L), has been previously defined to be theprobability of making an accurate measurement with a fractional precision L.2 Thecalculation of 0(L) for a test procedure is based on simulating a large number ofarchetypal round-robin correlation tests and such tests have been the subject ofprevious reports.3'4 The slopes of the correlation lines are recorded after each trial andthe frequency distributions of the slopes analyzed to yield an estimate for the probabilityof making an accurate measurement with a given precision.2 Procedure: