## Predictive modeling techniques for nanosecond-laser damage growth in fused silica optics |

Optics Express, Vol. 20, Issue 14, pp. 15569-15579 (2012)

http://dx.doi.org/10.1364/OE.20.015569

Acrobat PDF (1286 KB)

### Abstract

Empirical numerical descriptions of the growth of laser-induced damage have been previously developed. In this work, Monte-Carlo techniques use these descriptions to model the evolution of a population of damage sites. The accuracy of the model is compared against laser damage growth observations. In addition, a machine learning (classification) technique independently predicts site evolution from patterns extracted directly from the data. The results show that both the Monte-Carlo simulation and machine learning classification algorithm can accurately reproduce the growth of a population of damage sites for at least 10 shots, which is extremely valuable for modeling optics lifetime in operating high-energy laser systems. Furthermore, we have also found that machine learning can be used as an important tool to explore and increase our understanding of the growth process.

© 2012 OSA

## 1. Introduction

1. S. T. Yang, M. J. Matthews, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt. **49**, 2606–2616 (2010). [CrossRef]

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

7. 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, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE **4347**, 468–473 (2001). [CrossRef]

11. R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, and 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]

7. 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, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE **4347**, 468–473 (2001). [CrossRef]

8. 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, and P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE **7132**, 71321H (2008). [CrossRef]

9. R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, and 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]

10. R. A. Negres, M. A. Norton, D. A. Cross, and 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]

11. R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, and 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]

11. R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, and 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]

## 2. Growth model

7. 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, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE **4347**, 468–473 (2001). [CrossRef]

10. R. A. Negres, M. A. Norton, D. A. Cross, and 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]

*α*being the growth coefficient,

*ϕ*is the measured local fluence, and

*n*is the shot index. Although this work is within the range where Eq. (1) is valid, there is evidence suggesting that this model applies more generally to damage growth on the exit surface growth and for pulses longer than a few ns in duration. In contrast, an additional linear growth term is needed to describe growth on the input surface and/or shorter pulse durations [10

10. R. A. Negres, M. A. Norton, D. A. Cross, and 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]

**50**, D12–D20 (2011). [CrossRef] [PubMed]

*f*(

*α*) given by: with

*k*and

*λ*being the shape and scale parameters of the distribution. The mean of the Weibull distribution is given by

*μ*(

*λ*,

*k*) =

*λ*Γ(1 + 1/

*k*), with Γ representing the Gamma function, and it describes the average growth rate observed from a population of damage sites under narrowly constrained conditions (site size, pulse duration, fluence). However, these Weibull parameters are also found to be dependent on the laser fluence (

*ϕ*) and pulse duration (

*τ*) as well as the current size (diameter,

*D*) of the damage site. The Weibull scale and shape parameters can be generally parameterized as follows: where

*b*,

*g*are the rates of increase with respect to fluence (in cm

^{2}/J) while

*ϕ*,

_{th}*k*are the fluence thresholds (in J/cm

_{th}^{2}) for the shape and scale of the Weibull distribution respectively. These parameters are determined by clustering the growth measurements (

*α*) in terms of fluence, size and pulse duration, and for each cluster, the Weibull parameters (

*λ*,

*k*) that best represent the statistics of the growth measurements are extracted [9

9. R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, and 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]

**50**, D12–D20 (2011). [CrossRef] [PubMed]

*ω*, 5-ns flat in time (FIT) pulses, the coefficients are listed in Table 1. The errors associated with the growth rule coefficients for sites up to 300

*μ*m and 300–1000

*μ*m are estimated at 10% and 20%, respectively. In particular, the accuracy of the shape parameter coefficients (

*g*and

*k*) in Table 1 can be further improved with future experimentation due to insufficient data sampling in some regions of the growth parameter space [11

_{th}**50**, D12–D20 (2011). [CrossRef] [PubMed]

**18**, 19966–19976 (2010). [CrossRef] [PubMed]

## 3. Data

9. R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, and 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]

**18**, 19966–19976 (2010). [CrossRef] [PubMed]

*μ*m were initiated in a regular array with spacing of ∼3 mm using a single pulse from a 355-nm, Nd:YAG table top laser with an 8-ns near Gaussian temporal profile focused to a spatial Gaussian spot of ∼450

*μ*m (diameter at 1/e

^{2}of intensity) on the exit surface of a 1-cm thick silica substrate. By maintaining the grid spacing, we can expose all sites simultaneously with the 3-cm diameter Optical Science Laboratory (OSL) laser beam [12

12. 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, and P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE **5273**, 325–333 (2004). [CrossRef]

_{2}laser technique and aid in the accurate registration of the local fluence to an individual site on every laser shot to within 100

*μ*m. More details on the fluence calibration methods can be found in [9

**7504**, 750412 (2009). [CrossRef]

13. C. W. Carr, M. D. Feit, M. C. Nostrand, and 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]

*μ*m. This highly parallel technique greatly enhances data collection rate while maintaining precisions not typically available in-situ [4

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

_{2}samples in high-vacuum, at room temperature with 3

*ω*, 5-ns FIT pulses. Specifically, 58 pre-initiated damage sites on a 2-inch silica substrate were subjected to a series of nearly identical 29 laser shots at the nominal fluence of ∼7 J/cm

^{2}and standard deviation of 0.9 J/cm

^{2}from all the sites. A tabulated data set was compiled for this sample where each entry contains at a minimum the site ID, shot number, current site size, pre-shot site size, single-shot growth rate (according to Eq. (1)), local mean fluence, and a number of other attributes (derived or measured parameters) which will be discussed shortly corresponding to one observation of a site on a specific laser shot. Figure 1 summarizes the evolution of the mean site size (left axis) and fluence (right axis) exposures from 58 sites as a function of shot number (1 to 29), respectively. The dashed lines represent the standard deviation of the mean size and fluence for this population of sites, respectively. As the sites grow the mean size increases but also the size distribution gets wider shot-to-shot (as seen from Fig. 1).

## 4. Analytical predictive model

^{1}D

_{0}...

^{S}D

_{0}) as the initial condition and the measured local fluences

*ϕ*

_{1}on the first shot to calculate the Weibull distribution of the growth coefficient

*α*according to Eqs. (2)–(3) for each site. Recall that each site may have a different starting size and be exposed to a different fluence and therefore have a different

*α*distribution. Next, each site has M=2000 random growth coefficients (

*α*) generated using the Weibull distribution and, for each randomly generated

*α*, a calculated growth size D (i.e.,

^{1}D

_{1,1}...

^{1}D

_{1,M}) is obtained using Eq. (1). In other words, 2000 randomly generated outcomes to the first site and its first shot exposure are generated. Each of these 2000 outcomes (new size) is then propagated with a new alpha distribution for each shot based on its exposure fluence and its size

*projected*from the previous shot. This process is repeated for all N=29 laser shots of the data set (see Figure 2) and results in 2000 trajectories for the first site. The process is then repeated for each of the 58 sites. At the end of the simulation (shot N), each site i will have M=2000 possible sizes; from this size distribution we can calculate the expected size of the prediction <

^{i}D

_{N}>.

^{i}D

_{10}> for site i is lower than measurement and <

^{j}D

_{10}> for site j is higher than measurement, the errors cancel one another when both are incorporated into the CDF. The uncertainty in predicting for an individual site is discussed below in section 5.2. At n=20 shots, the simulation results start to deviate from the measured data on the larger size ranges (∼250

*μ*m to 450

*μ*m). At n=29 shots, the simulation results continue to further deviate, at this point it is difficult to evaluate whether the deviation is a result of compounding residual errors that started at shot n∼20 or reflects the accuracy of the growth model for that size range. This is because the coefficients used for our growth model in Table 1 are mostly based on experimental data for sites with diameters in the 50–250

*μ*m range, as noted in Section 2. As a result, our MC simulation can potentially have a larger error bar on the larger sizes. Despite these limitations, the predicted largest size is very close to the largest measured size up to 18 shots (see inset graph in Fig. 3). This observation has critical practical implications for operations as the largest few sites are the main driver for optics repair and replacement strategies. Furthermore, the measured data shows that the smallest size (i.e., CDF∼0.02) changes very little from shot 0 to shot n=29, this is not well captured from the Monte-Carlo simulation.

14. R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, and 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]

_{29}/D

_{0}), in an attempt to capture the total growth behavior. Similarly, each site has been exposed to a cumulative (total) fluence over the 29 shots. We then compared how well different attributes are able to capture, to a first order, the growth trends of individual sites. Scatter plots in Figs. 4(a)–(b) illustrate two of these relationships, namely final vs. starting sizes and total growth factor vs. cumulative fluence for all 58 sites, respectively. It is evident from Fig. 4(b) that a fairly good correlation exists between G and total fluence while the correlation is very weak between starting and final sizes as plotted in Fig. 4(a). It is possible that the co-dependency of these attributes is not linear and as such it is beyond the simple 2D scatter plots. In section 5 we will discuss how additional measured attributes could be employed to further improve the model accuracy by using machine learning.

## 5. Machine learning model

### 5.1. Data preparation

*ϕ*) and total growth factor (G) to the measured data set described in Section 3 (which includes shot number n, previous size D

_{n}_{−1}, current size D

*, local fluence*

_{n}*ϕ*). Cumulative fluence is the total fluence that the site has seen and captures the amount of energy deposited at each site up to that instance in time (i.e., shot number). Figure 4b showed that total growth factor G appears to trend reasonably well with ∑

*ϕ*after 29 shots, which is not unexpected. We have now supplemented our data set with these derived attributes after each shot number. We then divided the data into two sets, training and test data. The data was treated as a time series data and the first 20 shots (2/3) of the aggregate data were used for training purposes while the last 10 shots (1/3) were used for testing. The last third of the data includes the more aggressive growth behavior and we will start by predicting that specific region of the data. The training data set contained a total of 1161 instances and covers shots 1 through 20. The test data contained 523 instances and covers shots 21 through 29; these were the shots we needed to predict the sizes for. We developed an algorithm to simulate an online prediction algorithm where the actual size can be measured for an arbitrary number of shots (n). We used the first (n=20) number of shots for training since they represent two thirds of the data which is the percentage recommended by the data characteristics for building the predictive model. To deploy such a model in a practical situation, the model should be built with as many historical instances as possible to increase the accuracy of the prediction.

### 5.2. Model results

### 5.3. Model discovery

16. J. R. Quinlan, “Learning with continuous classes,” in Proceedings AI’92, Adams and Sterling, eds. (World Scientific, 1992). [PubMed]

16. J. R. Quinlan, “Learning with continuous classes,” in Proceedings AI’92, Adams and Sterling, eds. (World Scientific, 1992). [PubMed]

*) is predicted using a linear combination of the attributes given (i.e., shot number n, previous size D*

_{n}

_{n}_{−1}, fluence

*ϕ*, cumulative fluence ∑

*ϕ*, etc.) with the coefficient of each attribute generated by the model to accurately predict the size. Furthermore, we can normalize each coefficient to the maximum value of the attribute; hence the value of each attribute will have the same range of 0 to 1. It is then possible to rank the attributes based on their weighting factors. Below we will show how this can be used to measure the importance of each attribute and track if the attribute contribution changes as the sites grow. The steps of deriving a generalized weighted rule for predicting damage size are exemplified below: where

*x*is the

_{i}*i*-th attribute value (i.e., fluence, shot number, etc.),

*x*̂

*is the maximum value of*

_{i}*i*-th attribute value, and

*x*̄

*is the normalized value of*

_{i}*i*-th attribute (ranges from 0 to 1). The terms

*c*and

_{i}*w*are the un-normalized and normalized weighting coefficients of each attribute, respectively. Lastly, we can rank the attributes by the magnitude of the normalized weighting coefficients such that

_{i}*w*

_{1}has the highest contribution and

*w*has the lowest

_{k}*k*-th contribution to predicting the size. In addition to providing predictions without initially knowing which attributes are important, this type of classification approach can provide insight into which parameters are relevant to a prediction. For example, Table 2 shows the rank order (

*i*) and the weighting coefficient (

*w*) for the shot number attribute for each of the size-dependent rules. The table shows a relatively strong dependence on shot number that was not captured in the previously derived rules (Eqs. (2)–(3)). Specifically, the shot number (n) becomes more important as size increases, as suggested by the increasing rank order in Table 2. Furthermore, for large sizes, the weighting coefficient is actually negative, which seems to imply retardation of growth with shot number.

_{i}## 6. Discussion

^{2}) shots among the last 9 shots discussed above (using the same sample and laser parameters). These additional laser shots most probably do not lead to damage growth [11

**50**, D12–D20 (2011). [CrossRef] [PubMed]

14. R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, and 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]

## 7. Conclusion

## Acknowledgments

## References and links

1. | S. T. Yang, M. J. Matthews, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt. |

2. | S. T. Yang, M. J. Matthews, S. Elhadj, V. G. Draggoo, and S. E. Bisson, “Thermal transport in CO |

3. | S. Elhadj, M. J. Matthews, S. T. Yang, and D. J. Cooke, “Evaporation kinetics of laser heated silica in reactive and inert gases based on near-equilibrium dynamics,” Opt. Express |

4. | A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, and P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE |

5. | I. L. Bass, G. M. Guss, M. J. Nostrand, and P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO |

6. | B. Bertussi, P. Cormont, S. Palmier, P. Legros, and J. L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express |

7. | 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, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE |

8. | 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, and P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE |

9. | R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, and 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 |

10. | R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express |

11. | R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, and C. W. Carr, “Exploration of the multi-parameter space of nanosecond-laser damage growth in fused silica optics,” Appl. Opt. |

12. | 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, and P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE |

13. | C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. |

14. | R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, and C. W. Carr, “Probability of growth of small damage sites on the exit surface of fused silica optics,” Opt. Express |

15. | I. H. Witten and E. Frank, |

16. | J. R. Quinlan, “Learning with continuous classes,” in Proceedings AI’92, Adams and Sterling, eds. (World Scientific, 1992). [PubMed] |

**OCIS Codes**

(140.3330) Lasers and laser optics : Laser damage

(160.4670) Materials : Optical materials

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: April 18, 2012

Revised Manuscript: June 7, 2012

Manuscript Accepted: June 8, 2012

Published: June 26, 2012

**Citation**

Zhi M. Liao, Ghaleb M. Abdulla, Raluca A. Negres, David A. Cross, and Christopher W. Carr, "Predictive modeling techniques for nanosecond-laser damage growth in fused silica optics," Opt. Express **20**, 15569-15579 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15569

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### References

- S. T. Yang, M. J. Matthews, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt.49, 2606–2616 (2010). [CrossRef]
- S. T. Yang, M. J. Matthews, S. Elhadj, V. G. Draggoo, and S. E. Bisson, “Thermal transport in CO2 laser irradiated fused silica: In situ measurements and analysis,” J. Appl. Phys.106, 103106 (2009).
- S. Elhadj, M. J. Matthews, S. T. Yang, and D. J. Cooke, “Evaporation kinetics of laser heated silica in reactive and inert gases based on near-equilibrium dynamics,” Opt. Express20, 1575–1587 (2012). [CrossRef] [PubMed]
- A. Conder, J. Chang, L. Kegelmeyer, M. Spaeth, and P. Whitman, “Final optics damage inspection (FODI) for the National Ignition Facility,” Proc. SPIE7797, 77970P (2010). [CrossRef]
- I. L. Bass, G. M. Guss, M. J. Nostrand, and P. J. Wegner, “An improved method of mitigating laser-induced surface damage growth in fused silica using a rastered pulsed CO2 laser,” Proc. SPIE7842, 784220 (2010). [CrossRef]
- B. Bertussi, P. Cormont, S. Palmier, P. Legros, and J. L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express17, 11469–11479 (2009). [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, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE4347, 468–473 (2001). [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, and P. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE7132, 71321H (2008). [CrossRef]
- R. A. Negres, M. A. Norton, Z. M. Liao, D. A. Cross, J. D. Bude, and 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. SPIE7504, 750412 (2009). [CrossRef]
- R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express18, 19966–19976 (2010). [CrossRef] [PubMed]
- R. A. Negres, Z. M. Liao, G. M. Abdulla, D. A. Cross, M. A. Norton, and 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]
- 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, and P. Wegner, “A large aperture, high energy laser system for optics and optical components testing,” Proc. SPIE5273, 325–333 (2004). [CrossRef]
- C. W. Carr, M. D. Feit, M. C. Nostrand, and 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]
- R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, and C. W. Carr, “Probability of growth of small damage sites on the exit surface of fused silica optics,” Opt. Express20, 13030–13039 (2012). [CrossRef]
- I. H. Witten and E. Frank, Data Mining: Practical Machine Learning Tools and Techniques, 2nd ed. (Morgan Kaufmann, 2005).
- J. R. Quinlan, “Learning with continuous classes,” in Proceedings AI’92, Adams and Sterling, eds. (World Scientific, 1992). [PubMed]

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