0.2
0.6
1.0
www.edmundoptics.co.uk/LO 51
Section 15.9: Uncertainty in
LIDT Specifications – ADVANCED
LIDT specifications are not an absolute guarantee that damage will not
occur below a certain value. Uncertainty in the LIDT value is introduced
due to fluctuations in the test laser, the damage detection method, and
under-sampling the defects on the optic. This uncertainty leads to a
confidence interval around the true damage probability as a function
of fluence.
What is obtained from LIDT testing is a probability function based on a
binomial distribution of experimental data. The confidence interval of
damage occurring in a real setting can be determined using a Wilson
score interval dependent on the probability function, and the number of
observations made. The Wilson score interval (w) is a binomial proportion
confidence interval given by:
n is the number of shots at each fluence level, P is the experimentally
determined probability of damage, and z is the probit, or the quantile
function of the standard normal distribution.17 z corresponds to the desired
confidence level. For example, z = 1.96 for a 95% confidence level.
The ± sign in Equation 15.7 results in two possible values for the Wilson
score interval. The higher value is the upper range of the confi5ence
interval for whether or not damage will occur in a real application, while
the lower value is the lower limit of the confidence interval of damage.
Plotting w as a function of both n and P creates a 3D plot that represents
a useful visual for determining the probability of damage at a given confidence
level (Figure 15.16). In Figure 15.16, at 10 shots per fluence level,
it is only possible to know the probability of damage to approximately
±25%. If zero damage events are viewed over ten test sites, the worstcase
probability of approximately 25% that damage would occur at the
11th site. In order to know the probability of damage of better than ±5%,
more than 100 shots are required at every fluence level. This high number
of shots per fluence level is usually cost prohibitive, making simulation
the ideal option for predicting the true behavior of an optic.
1.0
0.8
0.6
0.4
0.0
100
0.2
0.0
0.4
0.8
Number of Observations (n)
Probability of Observation (P)
Confidence Interval
Figure 15.16: Confidence interval of the probability of damage of an
optic where the red surface is the upper limit of the confidence interval
of whether damage will occur and the blue surface is the lower limit of
the confidence interval
15.7
References
1. International Organization for Standardization. (2011). Lasers and laser-
related equipment -- Test methods for laser-induced damage threshold --
Part 1: Definitions and general principles (ISO 21254-1:2011).
2. R. M. Wood, Optics and Laser Tech. 29, pages 421-527, 1998.
3. Paschotta, Rüdiger. Encyclopedia of Laser Physics and Technology,
RP Photonics, October 2017, www.rp-photonics.com/encyclopedia.html.
4. Jing, X. et al., Calculation of Femtosecond Pulse Laser Induced
Damage Threshold for Broadband Antireflective Microstructure Arrays.
Opt. Exp. 2009, 17, 24137.
5. Mao, S. S. et al., Dynamics of Femtosecond Laser Interactions with
Dielectrics. Appl. Phys. A 2004, 79, 1695.
6. Nature Photonics, vol. 2, pages 219–225 (2008) https://www.nature.
com/articles/nphoton.2008.47
7. Carr, C. W., et al. “Wavelength Dependence of Laser-Induced Damage:
Determining the Damage Initiation Mechanisms.” Physical Review
Letters, 91, 12, 2003.
8. Koechner, W., 1999. Solid-state laser engineering (Vol. 1). Springer.
9. Bloembergen, N., 1974. Laser-induced electric breakdown in solids. IEEE
Journal of Quantum Electronics, 10(3), pp.375-386.
10. Schott AG., February 5 2013. SCHOTT Identifies Alternative Glass
Materials for High-Power Laser Applications Press release.
https://www.us.schott.com/newsfiles/us/20130204193642_schott_
laser-resistant_optics_final.pdf.
11. Jedamzik, R., Dietrich, V. and Rossmeier, T., 2012. Bulk Laser Damage
Threshold of Optical Glasses. In Proceedings of DGaO (Vol. 113, p. B9).
12. Johnson, Lawrence A. Laser Diode Burn-In and Reliability Testing. ILX
Lightwave, 2006.
13. Ristau, Detlev. Laser-Induced Damage in Optical Materials. CRC Press, 2016.
14. Kanaya, K. Penetration and Energy-Loss Theory of Electrons in Solid
Targets. J. Phys. D: Appl. Phys. 5, 43, 1972.
15. L. Gallais, J. Capoulade, J.-Y. Natoli and M. Commandré, "Investigation
of nanodefect properties in optical coatings by coupling measured and
simulated laser damage statistics," J. Appl. Phys, vol. 104, p. 053120, 2008.
16. Jiang, L., and H. l. Tsai. “Energy Transport and Material Removal in
Wide Bandgap Materials by a Femtosecond Laser Pulse.” International
Journal of Heat and Mass Transfer, vol. 48, no. 3-4, 2005, pp. 487–499.,
doi:10.1016/j.ijheatmasstransfer.2004.09.016.
17. Wilson, Edwin B. “Probable Inference, the Law of Succession, and
Statistical Inference.” Journal of the American Statistical Association,
vol. 22, no. 158, 1927, pp. 209–212., doi:10.2307/2276774.
/LO