**6. Results**

This chapter is dedicated to experimental results and illustrates:


#### **6.1 Complementarity**

Figure 6 shows results obtained on the same optical component tested with the 1/1 and rasterscan procedures, and on the same facility. Results are directly reported in terms of damage density with the presented formalism in §4.1 and 4.2. During rasterscan, about 6000 shots (this corresponds to a scanned area of about 6 cm²) are fired with fluences between 2.5 and 4.5 J/cm². During the 1/1 tests, only 200 shots have been fired with fluences between 4.5 and 6.5 J/cm². These results, which were presented, in the past, in terms of damage probabilities, are translated in terms of damage densities. The good complementarity of the two test results leads to validate the developed formalisms (for clarity, fluence error bars are

Laser-Induced Damage Density Measurements of Optical Materials 75

0 10 20 30 40

**Fluence (J/cm² - 5,5 ns)**

Fig. 7. Repeatability. Damage densities D vs fluence F for three different optical components

treatment must provide the same and accurate results. In Fig. 8 results obtained on the same optic (330\*330 mm²) for 5 different steps are reported (0.15; 0.3; 0.6; 1; 2 mm corresponding to an overlap of 95; 92; 66; 31 and 3%). For a step smaller than 0.15 mm, catastrophic damage growth was observed. No tests were conducted under this value. As can be seen in

> 0 5 10 15 20 **Fluence (J/cm² @ 3ns)**

Fig. 8. Steps. Damage densities vs fluence D(F) for the same optic tested on the same facility

with 5 different steps on 5 different zones. Data have been processed following data

reduction presented in § 4.2, this example is extracted from a Gaussian test.

(from the same vendor) tested on the same facility within a one year period with the

1

0,1

1,0

10,0

**Damage density (/cm²)**

100,0

1000,0

0.15 mm 0.30 mm 0.60 mm 1.00 mm 2.00 mm

10

100

Sample A Sample B Sample C

**Damage density (/cm²)**

rasterscan procedure.

1000

not reported). We remark that due to a large number of tested sites, low damage densities are available with the rasterscan technique. On the opposite, 1/1 test covers damage probabilities between 0 and 1, and due to the small illuminated area, damage densities available are higher. We observe that the intervals of confidence are smaller for rasterscan procedures, due to a large number of damage sites in spite of small damage densities, than for 1/1 where a limited number of sites are tested. Nevertheless, the overlap of damage densities indicates a good measurement complement and that data reduction permits to determine repeatable damage densities; in spite of a non 100% overlap during rasterscan and a small number of tested sites during 1/1. Identical results were also obtained with different pulse durations and spatial beam profiles.

Fig. 6. Comparison of 1/1 and rasterscan procedures. Damage densities vs fluence measured on the same optical component with the 1/1 test procedure (diamonds) and 3 rasterscans at 3 different fluences (squares).

#### **6.2 Repeatability**

It is necessary to check that the procedures applied on similar optics give always similar results on a unique set-up. This should be done regularly. Fig. 7 shows results obtained on 3 samples from the same vendor, tested on the same facility on a one year period. Damage densities lay inside confidence limits. This result and those obtained with other lasers (not presented here) show that it is possible to achieve a good repeatability.

#### **6.3 Beam overlap**

A non-negligible parameter of the procedure is the shot-to-shot step i.e. the beam overlap. In order to scan a large area and to be sure to irradiate all the defects, a good overlap is necessary. That is possible with top-hat beams but not with Gaussian ones. In the latter case, it is preferable not to use too small a step, in order to avoid that the defects experience a long irradiation ramp, that the scan duration is too long and that damage grows due to successive shots on the same site. Moreover, a good correspondence between damage and fluence maps requires the step not to be too small. On the contrary, a large step implies a large area to be scanned or a low statistic. At last, whatever steps and overlaps, data

not reported). We remark that due to a large number of tested sites, low damage densities are available with the rasterscan technique. On the opposite, 1/1 test covers damage probabilities between 0 and 1, and due to the small illuminated area, damage densities available are higher. We observe that the intervals of confidence are smaller for rasterscan procedures, due to a large number of damage sites in spite of small damage densities, than for 1/1 where a limited number of sites are tested. Nevertheless, the overlap of damage densities indicates a good measurement complement and that data reduction permits to determine repeatable damage densities; in spite of a non 100% overlap during rasterscan and a small number of tested sites during 1/1. Identical results were also obtained with

> 01234567 **Fluence (J/cm² @ 3ns)**

Fig. 6. Comparison of 1/1 and rasterscan procedures. Damage densities vs fluence measured on the same optical component with the 1/1 test procedure (diamonds) and 3 rasterscans at

It is necessary to check that the procedures applied on similar optics give always similar results on a unique set-up. This should be done regularly. Fig. 7 shows results obtained on 3 samples from the same vendor, tested on the same facility on a one year period. Damage densities lay inside confidence limits. This result and those obtained with other lasers (not

A non-negligible parameter of the procedure is the shot-to-shot step i.e. the beam overlap. In order to scan a large area and to be sure to irradiate all the defects, a good overlap is necessary. That is possible with top-hat beams but not with Gaussian ones. In the latter case, it is preferable not to use too small a step, in order to avoid that the defects experience a long irradiation ramp, that the scan duration is too long and that damage grows due to successive shots on the same site. Moreover, a good correspondence between damage and fluence maps requires the step not to be too small. On the contrary, a large step implies a large area to be scanned or a low statistic. At last, whatever steps and overlaps, data

presented here) show that it is possible to achieve a good repeatability.

different pulse durations and spatial beam profiles.

1/1 rasterscan

0,001

3 different fluences (squares).

**6.2 Repeatability** 

**6.3 Beam overlap** 

0,010

0,100

**Damage density (mm3**

**)**

1,000

10,000

100,000

Fig. 7. Repeatability. Damage densities D vs fluence F for three different optical components (from the same vendor) tested on the same facility within a one year period with the rasterscan procedure.

treatment must provide the same and accurate results. In Fig. 8 results obtained on the same optic (330\*330 mm²) for 5 different steps are reported (0.15; 0.3; 0.6; 1; 2 mm corresponding to an overlap of 95; 92; 66; 31 and 3%). For a step smaller than 0.15 mm, catastrophic damage growth was observed. No tests were conducted under this value. As can be seen in

Fig. 8. Steps. Damage densities vs fluence D(F) for the same optic tested on the same facility with 5 different steps on 5 different zones. Data have been processed following data reduction presented in § 4.2, this example is extracted from a Gaussian test.

Laser-Induced Damage Density Measurements of Optical Materials 77

For the question of representatives, an area of 40 cm² has been tested on a large optic with the small beam rasterscan procedure, i.e. illumination, damage detection and data processing. A second optics has been tested with the large beam. For this comparison, the number of parameters, that are different, is reduced selecting shots that are quite similar: the pulses are single mode longitudinally; the temporal profiles are Gaussian with equivalent

this value being previously determined (see §6.4). Nevertheless, the two pulse durations

any scaling law. The absolute fluence values are known with an accuracy of about 10% (Lamaignère et al., 2010); the sources of errors on the two facilities being different, it is compulsory to take into account these errors. Figure 10 shows that measurements are

quite comparable. This confirms the reproducibility that was noted in the previous

5 10 15 20 25 **Fluence (J/cm² @ 3ns)**

Fig. 10. Damage densities versus fluence measured on two optics from the same batch with

With rigorous data analysis and treatment, it is possible to measure damage density on an optical component with high accuracy and repeatability, whatever the beam overlap and the beam shape. Since tests are destructive, the same area cannot be measured on two different instruments. However the consideration of error bars on damage density allows comparing

pulselength scaling is applied with the help of a temporal scaling law (*F~*

being close, the comparison can also be made with the usual scaling

gathered inside the largest interval of confidence (given at 2

Small beam

Large beam

results from several components assumed to be comparable.

=2.5 and 2.3 ns, respectively. Data treatments are first applied. Next

) and = 0.6,

) and thus the two results are

½ or without the use of

**6.5 Representativeness** 

1

small and large beams.

**7. Conclusion** 

10

100

**Damage density (/cm²)** 

1000

pulse durations

paragraph.

Fig. 8, from 9 to 15 J/cm², results are gathered inside the largest interval of confidence (given at 2). These results indicate that this procedure, with its data treatment, is able to provide comparable measurements for a wide range of beam overlap. Consequently, comparison is possible between several facilities where the shot-to-shot step inevitably varies from one test to another.

#### **6.4 Reproducibility**

The comparison is on 4 optical components from the same batch. Due to the limited available area on each sample, data exploration is realized for fluences between 10 and 20 J/cm². In this range, damage density increases quickly with fluence and values are sufficiently high for the number of damage sites to be high enough. For lower fluences and lower damage densities, the areas to be scanned become too large and the error bars could be too high to make any conclusion. For each sample, an area about 40 cm² was irradiated.

Data treatment presented in §4.2 is first applied (see insert of Fig. 9). Next pulselength scaling is used. The best correspondence is obtained when is equal to 0.6. (Fig. 9), value slightly different from the usual scaling *1/2*. Up to 18 J/cm², measurements are gathered inside the largest interval of confidence (given at 2). Fluence error bars are not reported for clarity (values are provided with an accuracy around 10%) but taking into account both fluence error bars and level of confidence, results are quite comparable. Above a few hundred damage per cm², damage sites can aggregate and the comparison is no more feasible.

Fig. 9. Reproducibility. Damage densities vs fluence for several components (with the same polishing process) tested on 4 different facilities. Fluences are scaled using a temporal scaling law ( ) with an exponent of 0.6. In the insert, the raw data are reported.

#### **6.5 Representativeness**

76 Advanced Topics in Measurements

Fig. 8, from 9 to 15 J/cm², results are gathered inside the largest interval of confidence (given

The comparison is on 4 optical components from the same batch. Due to the limited available area on each sample, data exploration is realized for fluences between 10 and 20 J/cm². In this range, damage density increases quickly with fluence and values are sufficiently high for the number of damage sites to be high enough. For lower fluences and lower damage densities, the areas to be scanned become too large and the error bars could be too high to make any conclusion. For each sample, an area about 40 cm² was irradiated. Data treatment presented in §4.2 is first applied (see insert of Fig. 9). Next pulselength

clarity (values are provided with an accuracy around 10%) but taking into account both fluence error bars and level of confidence, results are quite comparable. Above a few hundred damage per cm², damage sites can aggregate and the comparison is no more

0 5 10 15 20 25 **Fluence (J/cm² @ 3ns)**

exponent of 0.6. In the insert, the raw data are reported.

Fig. 9. Reproducibility. Damage densities vs fluence for several components (with the same polishing process) tested on 4 different facilities. Fluences are scaled using a temporal

*1/2*. Up to 18 J/cm², measurements are gathered

LUTIN - 2.5 ns BLANCO - 5.5 ns ELAN - 7.5 ns SOCRATE - 16 ns

). Fluence error bars are not reported for

is equal to 0.6. (Fig. 9), value

scaling is used. The best correspondence is obtained when

slightly different from the usual scaling

0,1

1,0

1.00.1

10,0

10.0

**Damage density (/cm²)**

scaling law (

) with an

100,0

100.0

1000,0

1000.0

inside the largest interval of confidence (given at 2

0,1 1,0 10,0 100,0 1000,0

0.11.0

1000.0100.010.0

**Damage density (/cm²)**

0 10 20 30 40 **Fluence (J/cm²)**

). These results indicate that this procedure, with its data treatment, is able to provide comparable measurements for a wide range of beam overlap. Consequently, comparison is possible between several facilities where the shot-to-shot step inevitably varies from one test

at 2

to another.

feasible.

**6.4 Reproducibility** 

For the question of representatives, an area of 40 cm² has been tested on a large optic with the small beam rasterscan procedure, i.e. illumination, damage detection and data processing. A second optics has been tested with the large beam. For this comparison, the number of parameters, that are different, is reduced selecting shots that are quite similar: the pulses are single mode longitudinally; the temporal profiles are Gaussian with equivalent pulse durations =2.5 and 2.3 ns, respectively. Data treatments are first applied. Next pulselength scaling is applied with the help of a temporal scaling law (*F~* ) and = 0.6, this value being previously determined (see §6.4). Nevertheless, the two pulse durations being close, the comparison can also be made with the usual scaling ½ or without the use of any scaling law. The absolute fluence values are known with an accuracy of about 10% (Lamaignère et al., 2010); the sources of errors on the two facilities being different, it is compulsory to take into account these errors. Figure 10 shows that measurements are gathered inside the largest interval of confidence (given at 2) and thus the two results are quite comparable. This confirms the reproducibility that was noted in the previous paragraph.

Fig. 10. Damage densities versus fluence measured on two optics from the same batch with small and large beams.

#### **7. Conclusion**

With rigorous data analysis and treatment, it is possible to measure damage density on an optical component with high accuracy and repeatability, whatever the beam overlap and the beam shape. Since tests are destructive, the same area cannot be measured on two different instruments. However the consideration of error bars on damage density allows comparing results from several components assumed to be comparable.

**5** 

*Mexico* 

**Fringe Pattern Demodulation** 

*1Centro de Investigaciones en Optica A.C.,* 

*Artificial Inteligence Laboratory,* 

(1)

(,) *x y* is the phase

 **Using Evolutionary Algorithms** 

*2Center for Computing Research, National Polytehnical Institute,* 

L. E. Toledo1, F. J. Cuevas1, J.F. Jimenez Vielma2 and J. H. Sossa2

 *Dept. of Computer Vision and Artificial Intelligence, Optical Division, Leon,* 

Interferometers are used in metrology to measure temperature, displacement, stress and other physical variables. A typical interferometer split a laser beam using a beam divisor. Beam A is called reference, and is projected directly over a film or a CCD camera using mirrors or fiber optic. Beam B interact with the physical phenomenon to be measured. The interaction modifies the optic path of beam B; then it is projected over the same film or CCD

*Ixy axy bxy xy* , , , cos ,

The information about the measure is embodied on an interferogram, that is, a fringe pattern image. In optical metrology, a fringe pattern carries information embedded in its phase, that represents the difference in optical path between beam A and beam B. *x y*, are integer values representing coordinates of the pixel location in the fringe image, *a x*(,) *y* is

term related to the physical quantity being measured. Figure 1 shows an interferogram and

(a) (b)

camera that beam A. The total irradiance is modelled on eq. 1.

the background illumination, *b x*(,) *y* is the amplitude modulation, and

**1. Introduction** 

its associated phase

(,) *x y* .

Fig. 1. Fringe pattern(a) and its phase map (b).

A particular attention has to be devoted to the error budget on fluence determination, more precisely on the measurement of beam equivalent area. CCD cameras have to be carefully qualified. Thus the error on calculation could be estimated. It is vital to ensure that this equivalent area determined on the reference path is equal to that on the sample controlling the CCD position and by verifying that the optics in front of the camera do not alter the beam profile. This measurement has to be recorded at the frequency laser to monitor shotto-shot laser fluctuations. The calculations on error bars not only allow comparing results from several samples tested on several facilities but also give an upper limit of damage density, particularly useful when a small area is scanned or in a low damage density range.

Depending on the available area on the sample to be tested and the level of damage density, it appears that the 1/1 and rasterscan procedures are comparable and complementary with the use of an appropriate data reduction. More, these procedures give access to representative measurements when compared to results and behaviours observed on high laser facilities irradiated with very large beams.

#### **8. References**

