Calculation of error bars for laser damage observations

Jonathan W. Arenberg

doi:10.1117/12.804247

30 December 2008 Calculation of error bars for laser damage observations

Jonathan W. Arenberg

Proceedings Volume 7132, Laser-Induced Damage in Optical Materials: 2008; 71320Z (2008) https://doi.org/10.1117/12.804247
Event: Boulder Damage Symposium XL Annual Symposium on Optical Materials for High Power Lasers, 2008, Boulder, Colorado, United States

Abstract

The use of the error bar is a critical means of communicating the quality of individual data points and a processed result. Understanding the error bar for a processed measurement depends on the measurement technique being used and is the subject of many recent works, as such, the paper will confine its scope to the determination of the error bar on a single data point. Many investigators either ignore the error bar altogether or use a "one size error fits all" method, both of these approaches are poor procedure and misleading. It is the goal of this work to lift the veil of mysticism surrounding error bars for damage observations and make their description, calculation and use, easy and commonplace. This paper will rigorously derive the error bar size as a function of the experimental parameters and observed data and will concentrate on the dependent variable, the cumulative probability of damage. The paper will begin with a discussion of the error bar as a measure of data quality or reliability. The expression for the variance in the parameters is derived via standard methods and converted to a standard deviation. The concept of the coverage factor is introduced to scale the error bar to the desired confidence level, completing the derivation

Citation Download Citation

Jonathan W. Arenberg "Calculation of error bars for laser damage observations", Proc. SPIE 7132, Laser-Induced Damage in Optical Materials: 2008, 71320Z (30 December 2008); https://doi.org/10.1117/12.804247

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