Abstract

We present a comprehensive statistical model which includes both the probability of growth and growth rate to describe the evolution of exit surface damage sites on fused silica optics over multiple laser shots spanning a wide range of fluences. We focus primarily on the parameterization of growth rate distributions versus site size and laser fluence using Weibull statistics and show how this model is consistent with established fracture mechanics concepts describing brittle materials. Key growth behaviors and prediction errors associated with the present model are also discussed.

© 2014 Optical Society of America

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    [CrossRef]
  29. M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
    [CrossRef]
  30. J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  38. Z. M. Liao, G. M. Abdulla, R. A. Negres, D. A. Cross, C. W. Carr, “Predictive modeling techniques for nanosecond-laser damage growth in fused silica optics,” Opt. Express 20, 15569–15579 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  46. S. G. Demos, R. N. Raman, R. A. Negres, “Time-resolved imaging of processes associated with exit-surface damage growth in fused silica following exposure to nanosecond laser pulses,” Opt. Express 21, 4875–4888 (2013).
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    [CrossRef]
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    [CrossRef]
  49. F. Y. Gènin, A. Salleo, T. V. Pistor, L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18, 2607–2616 (2001).
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2013 (2)

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
[CrossRef]

S. G. Demos, R. N. Raman, R. A. Negres, “Time-resolved imaging of processes associated with exit-surface damage growth in fused silica following exposure to nanosecond laser pulses,” Opt. Express 21, 4875–4888 (2013).
[CrossRef] [PubMed]

2012 (5)

Z. M. Liao, G. M. Abdulla, R. A. Negres, D. A. Cross, C. W. Carr, “Predictive modeling techniques for nanosecond-laser damage growth in fused silica optics,” Opt. Express 20, 15569–15579 (2012).
[CrossRef] [PubMed]

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

T. A. Laurence, J. D. Bude, S. Ly, N. Shen, M. D. Feit, “Extracting the distribution of laser damage precursors on fused silica surfaces for 351 nm, 3 ns laser pulses at high fluences (20–150 J/cm2),” Opt. Express 20, 11561–11573 (2012).
[CrossRef] [PubMed]

R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, C. W. Carr, “Probability of growth of small damage sites on the exit surface of fused silica optics,” Opt. Express 20, 13030–13039 (2012).
[CrossRef] [PubMed]

2011 (4)

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
[CrossRef]

L. Lamaignère, G. Dupuy, T. Donval, P. Grua, H. Bercegol, “Comparison of laser-induced surface damage density measurements with small and large beams: toward representativeness,” Appl. Opt. 50, 441–446 (2011).
[CrossRef] [PubMed]

R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, C. W. Carr, “Exploration of the multi-parameter space of nanosecond-laser damage growth in fused silica optics,” Appl. Opt. 50, D12–D20 (2011).
[CrossRef] [PubMed]

2010 (5)

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
[CrossRef]

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

R. A. Negres, M. A. Norton, D. A. Cross, C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010).
[CrossRef] [PubMed]

2009 (2)

R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
[CrossRef]

B. Bertussi, P. Cormont, S. Palmier, P. Legros, J. L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express 17, 11469–11479 (2009).
[CrossRef] [PubMed]

2008 (4)

G. M. Guss, I. L. Bass, R. P. Hackel, C. Mailhiot, S. G. Demos, “In situ monitoring of surface postprocessing in large-aperture fused silica optics with optical coherence tomography,” Appl. Opt. 47, 4569–4573 (2008).
[CrossRef] [PubMed]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

2007 (5)

M. J. Matthews, M. D. Feit, “Effect of random clustering on surface damage density estimates,” Proc. SPIE 6720, 67201J (2007).
[CrossRef]

C. W. Carr, M. J. Matthews, J. D. Bude, M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K (2007).
[CrossRef]

C. W. Carr, J. B. Trenholme, M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett 90, 041110 (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
[CrossRef]

2006 (2)

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

C. W. Carr, M. D. Feit, M. C. Nostrand, J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. 17, 1958–1962 (2006).
[CrossRef]

2005 (1)

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

2004 (3)

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

2003 (1)

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

2002 (1)

2001 (2)

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

F. Y. Gènin, A. Salleo, T. V. Pistor, L. L. Chase, “Role of light intensification by cracks in optical breakdown on surfaces,” J. Opt. Soc. Am. A 18, 2607–2616 (2001).
[CrossRef]

2000 (1)

M. J. Runkel, R. Sharp, “Modeling KDP bulk damage curves for prediction of large-area damage performance,” Proc. SPIE 3902, 436–448 (2000).
[CrossRef]

1994 (1)

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

1988 (1)

V. Kachitvichyanukul, B. W. Schmeiser, “Binomial random variate generation,” Commun. ACM 31, 216–222 (1988).
[CrossRef]

1984 (1)

1969 (1)

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Cer. Soc. 52, 99–105 (1969).
[CrossRef]

1921 (1)

A. A. Griffith, “The phenomena of rupture and flow in solids,” Philos. Trans. R. Soc. London A 221, 163–198 (1921).
[CrossRef]

Abdulla, G. M.

Adams, J. J.

C. W. Carr, M. D. Feit, M. C. Nostrand, J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. 17, 1958–1962 (2006).
[CrossRef]

Atherton, L. J.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Auerbach, J.

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Balakrishnan, N.

N. L. Johnson, S. Kotz, N. Balakrishnan, “Weibull distributions,” in Continuous Univariate Distributions, 2nd ed. (Wiley, 1994), Vol. 1, pp. 628–722.

Balas, M.

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

Bass, I. L.

I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
[CrossRef]

G. M. Guss, I. L. Bass, R. P. Hackel, C. Mailhiot, S. G. Demos, “In situ monitoring of surface postprocessing in large-aperture fused silica optics with optical coherence tomography,” Appl. Opt. 47, 4569–4573 (2008).
[CrossRef] [PubMed]

Bechtel, H. A.

M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
[CrossRef]

Beeler, R.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Benoist, A.

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

Bercegol, H.

L. Lamaignère, G. Dupuy, T. Donval, P. Grua, H. Bercegol, “Comparison of laser-induced surface damage density measurements with small and large beams: toward representativeness,” Appl. Opt. 50, 441–446 (2011).
[CrossRef] [PubMed]

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
[CrossRef]

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

Bertussi, B.

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

B. Bertussi, P. Cormont, S. Palmier, P. Legros, J. L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express 17, 11469–11479 (2009).
[CrossRef] [PubMed]

Boscheron, A.

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

Bourgeade, A.

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

Bude, J. D.

T. A. Laurence, J. D. Bude, S. Ly, N. Shen, M. D. Feit, “Extracting the distribution of laser damage precursors on fused silica surfaces for 351 nm, 3 ns laser pulses at high fluences (20–150 J/cm2),” Opt. Express 20, 11561–11573 (2012).
[CrossRef] [PubMed]

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
[CrossRef]

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

C. W. Carr, M. J. Matthews, J. D. Bude, M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K (2007).
[CrossRef]

Canty, A.

A. Canty, B. Ripley, boot: Bootstrap R (S-Plus) Functions(2012), R package version 1.3–7.

Carr, A. V.

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

Carr, C. W.

R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, C. W. Carr, “Probability of growth of small damage sites on the exit surface of fused silica optics,” Opt. Express 20, 13030–13039 (2012).
[CrossRef] [PubMed]

Z. M. Liao, G. M. Abdulla, R. A. Negres, D. A. Cross, C. W. Carr, “Predictive modeling techniques for nanosecond-laser damage growth in fused silica optics,” Opt. Express 20, 15569–15579 (2012).
[CrossRef] [PubMed]

M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
[CrossRef]

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, C. W. Carr, “Exploration of the multi-parameter space of nanosecond-laser damage growth in fused silica optics,” Appl. Opt. 50, D12–D20 (2011).
[CrossRef] [PubMed]

R. A. Negres, M. A. Norton, D. A. Cross, C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010).
[CrossRef] [PubMed]

R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
[CrossRef]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

C. W. Carr, M. J. Matthews, J. D. Bude, M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K (2007).
[CrossRef]

C. W. Carr, J. B. Trenholme, M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett 90, 041110 (2007).
[CrossRef]

C. W. Carr, M. D. Feit, M. C. Nostrand, J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. 17, 1958–1962 (2006).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

M. J. Matthews, R. A. Negres, C. W. Carr, A. M. Rubenchik, Lawrence Livermore National Laboratory, are preparing a manuscript to be called “Probability distribution model for multi-shot laser damage on fused silica surfaces.”

Carr, W.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Casella, G.

C. P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd ed. (Springer, 2004).
[CrossRef]

Casey, A.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Chang, J.

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

Chase, L. L.

Clark, R.

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

Conder, A.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

Cormont, P.

Courchinoux, R.

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

Cross, D.

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

Cross, D. A.

Davison, A. C.

A. C. Davison, D. V. Hinkley, Bootstrap Methods and Their Applications (Cambridge University, 1997).
[CrossRef]

De Marco, F. P.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Demos, S. G.

Di-Nicola, J. M.

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

Donohue, E. E.

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

Donval, T.

L. Lamaignère, G. Dupuy, T. Donval, P. Grua, H. Bercegol, “Comparison of laser-induced surface damage density measurements with small and large beams: toward representativeness,” Appl. Opt. 50, 441–446 (2011).
[CrossRef] [PubMed]

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

Dupuy, G.

L. Lamaignère, G. Dupuy, T. Donval, P. Grua, H. Bercegol, “Comparison of laser-induced surface damage density measurements with small and large beams: toward representativeness,” Appl. Opt. 50, 441–446 (2011).
[CrossRef] [PubMed]

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

Fallejo, R.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Fan, Z.

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Feit, M. D.

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
[CrossRef]

T. A. Laurence, J. D. Bude, S. Ly, N. Shen, M. D. Feit, “Extracting the distribution of laser damage precursors on fused silica surfaces for 351 nm, 3 ns laser pulses at high fluences (20–150 J/cm2),” Opt. Express 20, 11561–11573 (2012).
[CrossRef] [PubMed]

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. J. Matthews, M. D. Feit, “Effect of random clustering on surface damage density estimates,” Proc. SPIE 6720, 67201J (2007).
[CrossRef]

C. W. Carr, M. D. Feit, M. C. Nostrand, J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. 17, 1958–1962 (2006).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

Ferriera, J. L.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

Flegel, M.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Gènin, F. Y.

Griffith, A. A.

A. A. Griffith, “The phenomena of rupture and flow in solids,” Philos. Trans. R. Soc. London A 221, 163–198 (1921).
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Grua, P.

Guss, G. M.

I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
[CrossRef]

G. M. Guss, I. L. Bass, R. P. Hackel, C. Mailhiot, S. G. Demos, “In situ monitoring of surface postprocessing in large-aperture fused silica optics with optical coherence tomography,” Appl. Opt. 47, 4569–4573 (2008).
[CrossRef] [PubMed]

Hackel, R. P.

G. M. Guss, I. L. Bass, R. P. Hackel, C. Mailhiot, S. G. Demos, “In situ monitoring of surface postprocessing in large-aperture fused silica optics with optical coherence tomography,” Appl. Opt. 47, 4569–4573 (2008).
[CrossRef] [PubMed]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Haupt, D. L.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

Haynam, C.

J. Heebner, P. Wegner, C. Haynam, “Programmable beam spatial shaping for the National Ignition Facility,” SPIE Newsroom (July 21, 2010). doi:.
[CrossRef]

Heebner, J.

J. Heebner, P. Wegner, C. Haynam, “Programmable beam spatial shaping for the National Ignition Facility,” SPIE Newsroom (July 21, 2010). doi:.
[CrossRef]

Hinkley, D. V.

A. C. Davison, D. V. Hinkley, Bootstrap Methods and Their Applications (Cambridge University, 1997).
[CrossRef]

Hollingsworth, W. G.

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

Honig, J.

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Hrubesh, L. W.

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

Hu, G.

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Hutcheon, I. D.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

Hutton, M.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Jancaitis, K.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
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Johnson, N. L.

N. L. Johnson, S. Kotz, N. Balakrishnan, “Weibull distributions,” in Continuous Univariate Distributions, 2nd ed. (Wiley, 1994), Vol. 1, pp. 628–722.

Josse, M.

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

Journot, E.

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
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V. Kachitvichyanukul, B. W. Schmeiser, “Binomial random variate generation,” Commun. ACM 31, 216–222 (1988).
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S. G. Demos, M. Staggs, M. R. Kozlowski, “Investigation of processes leading to damage growth in optical materials for large-aperture lasers,” Appl. Opt. 41, 3628–3633 (2002).
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M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
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R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

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H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
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L. Lamaignère, G. Dupuy, T. Donval, P. Grua, H. Bercegol, “Comparison of laser-induced surface damage density measurements with small and large beams: toward representativeness,” Appl. Opt. 50, 441–446 (2011).
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L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
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L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
[CrossRef]

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
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R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
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M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

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Lindsey, E. F.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

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L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
[CrossRef]

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
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M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
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M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
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M. J. Matthews, R. A. Negres, C. W. Carr, A. M. Rubenchik, Lawrence Livermore National Laboratory, are preparing a manuscript to be called “Probability distribution model for multi-shot laser damage on fused silica surfaces.”

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M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
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L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
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M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
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T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
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M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
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T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
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G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

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H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
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M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

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S. G. Demos, R. N. Raman, R. A. Negres, “Time-resolved imaging of processes associated with exit-surface damage growth in fused silica following exposure to nanosecond laser pulses,” Opt. Express 21, 4875–4888 (2013).
[CrossRef] [PubMed]

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
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R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
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M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. J. Matthews, R. A. Negres, C. W. Carr, A. M. Rubenchik, Lawrence Livermore National Laboratory, are preparing a manuscript to be called “Probability distribution model for multi-shot laser damage on fused silica surfaces.”

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R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, C. W. Carr, “Exploration of the multi-parameter space of nanosecond-laser damage growth in fused silica optics,” Appl. Opt. 50, D12–D20 (2011).
[CrossRef] [PubMed]

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

R. A. Negres, M. A. Norton, D. A. Cross, C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010).
[CrossRef] [PubMed]

R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
[CrossRef]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

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L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
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M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
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I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
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L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
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Potter, D.

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
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C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

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F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
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S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
[CrossRef]

S. G. Demos, R. N. Raman, R. A. Negres, “Time-resolved imaging of processes associated with exit-surface damage growth in fused silica following exposure to nanosecond laser pulses,” Opt. Express 21, 4875–4888 (2013).
[CrossRef] [PubMed]

M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
[CrossRef]

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H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

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R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

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L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
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L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

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S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
[CrossRef]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

M. J. Matthews, R. A. Negres, C. W. Carr, A. M. Rubenchik, Lawrence Livermore National Laboratory, are preparing a manuscript to be called “Probability distribution model for multi-shot laser damage on fused silica surfaces.”

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L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
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[CrossRef]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

Senecal, J.

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

Shao, J.

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Sharp, R.

M. J. Runkel, R. Sharp, “Modeling KDP bulk damage curves for prediction of large-area damage performance,” Proc. SPIE 3902, 436–448 (2000).
[CrossRef]

Sheehan, L. M.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Shen, N.

T. A. Laurence, J. D. Bude, S. Ly, N. Shen, M. D. Feit, “Extracting the distribution of laser damage precursors on fused silica surfaces for 351 nm, 3 ns laser pulses at high fluences (20–150 J/cm2),” Opt. Express 20, 11561–11573 (2012).
[CrossRef] [PubMed]

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

Spaeth, M.

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

Spaeth, M. L.

C. W. Carr, M. J. Matthews, J. D. Bude, M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K (2007).
[CrossRef]

C. W. Carr, J. B. Trenholme, M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett 90, 041110 (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

Staggs, M.

Staggs, M. C.

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

Stanley, J. A.

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Steele, W. A.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

Suratwala, T. I.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

Tappero, J.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

Trenholme, J. B.

C. W. Carr, J. B. Trenholme, M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett 90, 041110 (2007).
[CrossRef]

Venables, W. N.

W. N. Venables, B. D. Ripley, Modern Applied Statistics With S, 4th ed. (Springer, 2002).
[CrossRef]

Vickers, J. L.

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Wegner, P.

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

J. Heebner, P. Wegner, C. Haynam, “Programmable beam spatial shaping for the National Ignition Facility,” SPIE Newsroom (July 21, 2010). doi:.
[CrossRef]

Wegner, P. J.

I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
[CrossRef]

Weiland, T. L.

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

Whitman, P.

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

Whitman, P. K.

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

Wiederhorn, S. M.

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Cer. Soc. 52, 99–105 (1969).
[CrossRef]

Wong, J.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

Wong, L. L.

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

Wu, Z.

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

Xiao, Q.

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Zhao, Y.

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett (1)

C. W. Carr, J. B. Trenholme, M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett 90, 041110 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

M. J. Matthews, C. W. Carr, H. A. Bechtel, R. N. Raman, “Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica,” Appl. Phys. Lett. 99, 151109 (2011).
[CrossRef]

Commun. ACM (1)

V. Kachitvichyanukul, B. W. Schmeiser, “Binomial random variate generation,” Commun. ACM 31, 216–222 (1988).
[CrossRef]

Fusion Eng. Des. (2)

R. Beeler, A. Casey, A. Conder, R. Fallejo, M. Flegel, M. Hutton, K. Jancaitis, V. Lakamsani, D. Potter, S. Reisdorf, J. Tappero, P. Whitman, W. Carr, Z. Liao, “Shot planning and analysis tools on the NIF project,” Fusion Eng. Des. 87, 2020–2023 (2012).
[CrossRef]

L. M. Kegelmeyer, R. Clark, R. R. Leach, D. McGuigan, V. M. Kamm, D. Potter, J. T. Salmon, J. Senecal, A. Conder, M. Nostrand, P. K. Whitman, “Automated optics inspection analysis for NIF,” Fusion Eng. Des. 87, 2120–2124 (2012).
[CrossRef]

J. Am. Cer. Soc. (2)

T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Cer. Soc. 94, 416–428 (2011).
[CrossRef]

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Cer. Soc. 52, 99–105 (1969).
[CrossRef]

J. Appl. Phys. (1)

L. Lamaignère, M. Balas, R. Courchinoux, T. Donval, J. C. Poncetta, S. Reyné, B. Bertussi, H. Bercegol, “Parametric study of laser-induced surface damage density measurements: toward reproducibility,” J. Appl. Phys. 107, 023105 (2010).
[CrossRef]

J. Non-cryst. Solids (1)

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω(355 nm) laser pulses,” J. Non-cryst. Solids 352, 255–272 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Conf. Ser. (1)

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignerè, J. Néauport, G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008).
[CrossRef]

Laser Photonics Rev. (1)

S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photonics Rev. 7, 444–452 (2013).
[CrossRef]

Meas. Sci. Technol. (1)

C. W. Carr, M. D. Feit, M. C. Nostrand, J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. 17, 1958–1962 (2006).
[CrossRef]

Opt. Express (6)

Philos. Trans. R. Soc. London A (1)

A. A. Griffith, “The phenomena of rupture and flow in solids,” Philos. Trans. R. Soc. London A 221, 163–198 (1921).
[CrossRef]

Phys. Rev. Lett. (1)

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

Proc. SPIE (16)

R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, C. W. Carr, “The effect of pulse duration on the growth rate of laser-induced damage sites at 351 nm on fused silica surfaces,” Proc. SPIE 7504, 750412 (2009).
[CrossRef]

M. C. Nostrand, T. L. Weiland, R. L. Luthi, J. L. Vickers, W. D. Sell, J. A. Stanley, J. Honig, J. Auerbach, R. P. Hackel, P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE 5273, 325–333 (2004).
[CrossRef]

M. J. Matthews, M. D. Feit, “Effect of random clustering on surface damage density estimates,” Proc. SPIE 6720, 67201J (2007).
[CrossRef]

C. W. Carr, M. J. Matthews, J. D. Bude, M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K (2007).
[CrossRef]

A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE 7797, 77970P (2010).
[CrossRef]

I. L. Bass, G. M. Guss, M. J. Nostrand, P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE 7842, 784220 (2010).
[CrossRef]

F. Rainer, F. P. De Marco, M. C. Staggs, M. R. Kozlowski, L. J. Atherton, L. M. Sheehan, “Historical perspective on fifteen years of laser damage thresholds at LLNL,” Proc. SPIE 2114, 9–24 (1994).
[CrossRef]

M. J. Runkel, R. Sharp, “Modeling KDP bulk damage curves for prediction of large-area damage performance,” Proc. SPIE 3902, 436–448 (2000).
[CrossRef]

C. W. Carr, D. Cross, M. D. Feit, J. D. Bude, “Using shaped pulses to probe energy deposition during laser-induced damage of SiO2 surfaces,” Proc. SPIE 7132, 71321C (2008).
[CrossRef]

M. A. Norton, L. W. Hrubesh, Z. Wu, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001).
[CrossRef]

G. Razé, J. M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003).
[CrossRef]

M. A. Norton, E. E. Donohue, W. G. Hollingsworth, J. N. McElroy, R. P. Hackel, “Growth of laser initiated damage in fused silica at 527 nm,” Proc. SPIE 5273, 236–243 (2004).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage in sio2 under multiple wavelength irradiation,” Proc. SPIE 5991, 599108 (2005).
[CrossRef]

M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007).
[CrossRef]

L. Lamaignère, S. Reyné, M. Loiseau, J. C. Poncetta, H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007).
[CrossRef]

M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008).
[CrossRef]

Surf. Interface Anal. (1)

G. Hu, Y. Zhao, D. Li, Q. Xiao, J. Shao, Z. Fan, “Studies of laser damage morphology reveal subsurface feature in fused silica,” Surf. Interface Anal. 42, 1465–1468 (2010).
[CrossRef]

Other (10)

B. R. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge University, 1993).
[CrossRef]

L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B, 1–10 (2013).
[CrossRef]

J. Heebner, P. Wegner, C. Haynam, “Programmable beam spatial shaping for the National Ignition Facility,” SPIE Newsroom (July 21, 2010). doi:.
[CrossRef]

R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2013).

A. C. Davison, D. V. Hinkley, Bootstrap Methods and Their Applications (Cambridge University, 1997).
[CrossRef]

A. Canty, B. Ripley, boot: Bootstrap R (S-Plus) Functions(2012), R package version 1.3–7.

W. N. Venables, B. D. Ripley, Modern Applied Statistics With S, 4th ed. (Springer, 2002).
[CrossRef]

C. P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd ed. (Springer, 2004).
[CrossRef]

M. J. Matthews, R. A. Negres, C. W. Carr, A. M. Rubenchik, Lawrence Livermore National Laboratory, are preparing a manuscript to be called “Probability distribution model for multi-shot laser damage on fused silica surfaces.”

N. L. Johnson, S. Kotz, N. Balakrishnan, “Weibull distributions,” in Continuous Univariate Distributions, 2nd ed. (Wiley, 1994), Vol. 1, pp. 628–722.

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Figures (10)

Fig. 1
Fig. 1

Typical exit surface damage site morphologies revealed by SEM imaging. (Left) Type I – approximately 1 μm smooth pits, indicated by white arrows. Type II – single or multiple smooth fracture surfaces lacking damage cores, with overall diameters up to about 30 μm. (Right) Type III – multiple fracture surfaces surrounding damage cores, with overall diameters larger than about 30 μm. Here we examine the growth behavior of type III sites (as-initiated and grown). For all individual images, the scale bars (black horizontal lines) represent 20 μm.

Fig. 2
Fig. 2

Measured single-shot growth rate as a function of laser fluence for type III exit surface damage sites following exposure to 355-nm, 5-ns FIT laser pulses. Sites are grouped by their pre-exposure diameter in four size bins with d=30–50, 50–100, 100–500, and 500–5000 μm corresponding to panels (a) through (d), respectively.

Fig. 3
Fig. 3

Mean growth rate based on the estimated sample means (solid data points) and standard errors (vertical error bars, less than 15% of mean values except for data points indicated by arrows) as a function of laser fluence and site size. Logistic fits to the data using Eq. (6) and parameters from Table 2 are shown by the corresponding solid lines for each size bin.

Fig. 4
Fig. 4

Experimental growth rate distributions vs. laser fluence for damage sites with d= 50–100 μm. Data from each fluence bin (a categorical x-variable as bin center±1/2 width, e.g., 11±0.5 J/cm2) are represented as one-dimensional dot plots along the y-axis (green, closed circles with systematic jittering). For comparison, the Weibull PDF curves with parameter estimates from the data are also shown (blue, solid lines re-scaled to 120% height of the experimental distributions).

Fig. 5
Fig. 5

Weibull shape parameter estimates vs. laser fluence for exit surface damage sites with diameters up to 500 μm (three size bins shown in the legend) using MLE fitting of experimental growth distributions with 1 and 2 J/cm2 fluence bins (solid and open data points, respectively). The estimated standard errors (vertical error bars) are within 10% for all fluences. Dotted lines (green and blue, for d=30–50 and 50–500 μm, respectively) represent the analytical approximation for k(ϕ) given by Eq. (7).

Fig. 6
Fig. 6

Weibull scale parameter estimates vs. laser fluence for exit surface damage sites with diameters up to 500 μm (three size bins shown in the legend) using experimental growth distributions with 1 J/cm2 fluence bins (solid data points, via MLE fitting) and 2 J/cm2 fluence bins (open data points, via Eq. (4)), respectively. Vertical error bars represent the estimated standard errors. Logistic fits to the data using Eq. (6) and parameters from Table 3 are shown by the corresponding dotted lines for each size bin and represent the analytical approximation for λ(ϕ).

Fig. 7
Fig. 7

Measured vs. predicted (mean ± SD) cumulative final size distributions (CDF) using Monte-Carlo simulations of growth behavior over a wide range of local fluences and different number of shots for 150 sites with starting size range of ∼30–100 μm (initial CDF) (see Table 4).

Fig. 8
Fig. 8

(a) Growth rate fracture-derived PDF, fα, assuming a normal local fluence distribution with different mean, ϕ0, and standard deviation, σϕ, parameters (see Eq. (12)) with fixed coupling efficiency, χ =3.4·10−5). (b) The effect of the shape parameter, k, on the Weibull PDF with fixed scale parameter, λ =0.2.

Fig. 9
Fig. 9

Estimated sample statistic [1 + (SD/x̄)2] vs. laser fluence for size bin with d=50–100 μm (solid data points with vertical error bars representing the mean values and standard errors, respectively). (Inset) The corresponding Weibull distribution estimand vs. k, see Eq. (15).

Fig. 10
Fig. 10

Weibull Q-Q plots for three experimental distributions with size and fluence bins (d, ϕ) shown at the top of each graph. The MLE estimates for the Weibull shape and scale parameters (k and λ in Eq. (3)), sample size (N) and p-values from goodness-of-fit tests are also noted.

Tables (4)

Tables Icon

Table 1 Number of observations from growth rate experiments distributed over size and fluence bins (1 J/cm2 fluence bin width up to 11 J/cm2 and wider at higher fluences).

Tables Icon

Table 2 Logistic best fit parameters (estimated values and standard errors) to mean growth rate vs. size range vs. laser fluence in Fig. 3 using Eq. (6) and A1 = 0.

Tables Icon

Table 3 Logistic best fit parameters (estimated values and standard errors) to Weibull scale parameter vs. fluence as a function of size range in Fig. 6 using Eq. (6) and A1 = 0.

Tables Icon

Table 4 Sample sets used for the Monte-Carlo simulation. The size and fluence ranges are summarized as (mean values ± standard deviation).

Equations (15)

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d n = d n 1 e η α ,
B ( X ; m , p ) = C ( m , X ) p X ( 1 p ) m X ,
f ( X ; λ , k ) = { k λ ( X λ ) k 1 e ( X / λ ) k X 0 , 0 X < 0 ,
E [ X ] = λ Γ ( 1 + 1 / k ) ,
var [ X ] = λ 2 [ Γ ( 1 + 2 / k ) ( Γ ( 1 + 1 / k ) ) 2 ] ,
y ( x ) = A 1 A 2 1 + ( x / x 0 ) S + A 2 .
k ( ϕ ) = { ( 0.70 ± 0.03 ) + 0.28 ( ϕ 6.5 ) Θ ( ϕ 6.5 ) , d = 30 50 μ m , ( 1.00 ± 0.06 ) + 0.30 ( ϕ 6.0 ) Θ ( ϕ 6.0 ) , d = 50 500 μ m ,
σ > σ c = K I c ,
Δ A A = χ γ ( ϕ ϕ c ) ,
α = 1 2 ln [ χ γ ( ϕ ϕ c ) + 1 ] .
α = B ( ϕ ϕ th ) ,
f α ( α ) = 2 γ χ σ ϕ 2 π exp { 2 α ( 1 2 ( σ ϕ ) 2 ) [ γ χ ( e 2 α 1 ) + ϕ c ϕ 0 ] 2 } .
x ¯ = 1 N i = 1 N x i , S D = 1 N 1 i = 1 N ( x i x ¯ ) 2 ,
SE x ¯ = SD N .
[ 1 + var ( X ) / E ( X ) 2 ] = Γ ( 1 + 2 / k ) [ Γ ( 1 + 1 / k ) ] 2 .

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