Removal of scratches on fused silica optics by using a CO 2 laser

We investigate the efficiency of local CO2 laser processing of scratches on silica optics in order to enhance the nanosecond UV-laser damage resistance. The surface deformations induced by the process have been measured for different CO2 laser parameters and then the pulse duration and the beam diameter have been chosen accordingly to limit those deformations below 1 μm. From the study of the laser damage resistance as a function of different material modifications we identify a range of optimal radiation parameters allowing a complete elimination of scratches associated with a high threshold of laser damage. Calculation of the temperature of silica using a two-dimensional axi-symmetric code was compared with experiment, supporting an optimization of the laser parameter as a function of the maximal dimensions of scratches that could be removed by this process. ©2013 Optical Society of America OCIS codes: (140.3330) Laser damage; (220.4610) Optical fabrication; (160.6030) Silica. 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Introduction
Fusion class power laser facilities such as National Ignition Facility (NIF) [1] or Laser Mega-Joule (LMJ) [2] need large optical components with high wavefront quality and high resistance to laser-induced damage, especially for Ultra-Violet (UV) wavelength (351 nm).Major efforts have been made in the last decade to improve nanosecond UV-laser damage resistance of fused silica surface by developing new finishing processes [3,4].The manufacture of these optical components includes a double challenge associated with the polishing step.The first challenge is to minimize wavefront distortion.The second challenge is to have no surface defects like scratches or pits on the optical components.High surface quality in terms of flatness can be obtained by polishing for a long time, with frequent controls during it.On the other hand, the safest way to prevent surface defects is to limit polishing time and optics handling.The optics costs can be prohibitive if the proper compromise is not found between optical specification and surface defects.
The work done in making microelectronic components, for example, shows that it is really difficult to polish without scratch formation, and every improvement is cost effective for production.There is intense research under way to reduce defects using chemical and mechanical processes to achieve high planarity in the fabrication of microelectronic devices [5][6][7][8].Possible sources in generating these scratches are agglomerated particles, pad debris, and hard defects coming from the wafer bulk.Among these, the major sources were the presence of large particles or the agglomeration of slurry particles during the process.Most research has been done on studying the methods of scratch reduction by controlling different polishing conditions and analyzing the residues.Although some progress has been made, some problems persist.
Nevertheless, scratches on laser optics must be eliminated, because they initiate UV-laser damage at lower fluences than on the unscratched part of the component [9].Traditional fabrication methods attempt to take off scratches by an additional step of polishing, but with low removal rates that require a long polishing time.Moreover, such further treatment may also spoil the quality of surface waveform and create new scratches.We propose here another approach consisting in removing each scratch by melting locally the silica surface with a CO 2 laser.Polishing optics using a CO 2 laser had been studied in the early 1980's [10] and since then, CO 2 lasers are used in a wide range of application for fused silica optics [11][12][13][14].One of the most interesting applications is the repair treatment for damage sites in laser optics caused by previous use in a high-power laser system [15][16][17][18][19].In the case that concerns us, scratched silica reparation requires different parameters than for mitigating the growth of laser-induced damage (LID).
In this study we investigate the scratches removal by CO 2 laser on fused silica optics.We do this by making reproducible and well-characterized defects, whose properties are established in advance.For this purpose, scratches on a super polished fused silica surface were generated using a diamond indenter, which makes precise identical scratches.For each scratch, its topography was characterized in lateral and depth dimensions, by using a confocal microscope (part 2).The scratched samples are then irradiated by a CO 2 laser, whose power, pulse duration and beam diameter were varied.The impact of these different CO 2 laser parameters for eliminating scratches was analysed by a Nomarski microscope, a confocal microscope and an optical profiler (part 3).The next step is to compare the resistance to high fluence as a function of these parameters.This was done by exposing the samples to a Nd:YAG laser in order to measure the damage threshold (part 4).We interpret our results in terms of silica temperature evolution using a two-dimensional axi-symmetric code [20] (part 5.1).To complete this work, the effect of heating with different beam diameters and pulse durations is analysed experimentally and compared with calculations (part 5.2 and 5.3).

Realization and characterization of scratches
In this work we used a commercial apparatus built by CSM Instruments (http://www.csminstruments.com) to create scratches on fused silica.It is computer controlled and can make scratches at various forces ranging from 1 mN up to 1 N.The main advantage of such a procedure is that it is easily reproducible.Previous work realized with this instrument has demonstrated that obtaining calibrated scratches is well-suited to test different experimental conditions [21,22].For our study, the apparatus has been equipped with a diamond tip needle, including a spherical head with a diameter of 40 µm.The fused silica samples used were glass 7980 from Corning (NY, USA).All samples are 50 mm in diameter and 5 mm thick superpolished by THALES-SESO (http://www.seso.com).Finally different combinations of force and speed were applied to create scratches, and results obtained with 750 mN in force and 500 µm/mn of speed are presented here.
We characterized scratches by using a confocal laser surface microscope (CLSM), for its ability to estimate subsurface damage depth [23].With our CLSM furnished by Leica TCS SPE (http://www.leica-microsystems.com/products/confocal-microscopes/), measurement is realized in reflective mode, with a laser at 532 nm wavelengths.Resolution of our CLSM was approximately 150 nm in x-y-axis and 300 nm in Z-axis, using a 63 x oil-immersion objective with numerical aperture of 1.3.As example of CLSM recording, images of typical morphologies of a scratch site made with the diamond needle are given in Fig. 1.We see clearly that the scratch is not ductile and deepest cracks are as profound as 16 µm.Its morphology can be considered as brittle scratches with lateral cracks and this is a common morphology for scratches created during polishing [24].Many cracks are present under the scratched surface and they are distributed almost uniformly along the scratch.This is important for the reproducibility of the CO 2 laser operation and the subsequent laser damage test.Although such a scratch is quite deep compared to most of scratches caused by polishing (less than 10 µm), some exceptions can be observed.To illustrate this, CLSM images of a scratch noticed after optical polishing by one of our vendors are shown in Fig. 2. From the Fig. 2(a) we note that the scratch length is ≤ 200 µm giving only a small area for the laser test.The Fig. 2(b) shows different depth between the two sides of the scratch (left ≈13 µm and right ≈7 µm) that will induce different parameter for CO 2 laser operation.On the contrary, the apparatus and the parameters chosen permit us to make long scratches representative of those created during polishing, and with the advantage of making cracks of almost constant depth whatever the location studied along the scratch was.

Setup description
The CO 2 laser used for silica irradiation is a Synrad Firestar V20, operating at 10.6 µm wavelength with a 20 W maximum power.Power control is achieved by pulsed width modulation at a 5 kHz frequency.The irradiation time can also be easily varied.For our study we have used mostly 1 s and 5 s pulse duration.The laser beam was focused with a ZnSe lens with a 508 mm focal length.The latter is mounted on a z translation stage to adjust the beam diameter on the sample.We have irradiated scratches with different beam diameter on the sample plane ranging from 0.7 mm up to 2 mm.The beam shape is Gaussian and the diameter is given at 1/e 2 .More details about the experimental arrangement can be found in reference [25].
Our operational installation allows the localized irradiation of a damaged site, or a fraction of a scratch.To remove a longer portion of a scratch, several CO 2 laser heating were used and the fused silica sample was shifted by 200 µm along the scratch, between each laser shot.

Observations with a nomarski microscope
The impact on scratches of the interaction of a fused silica sample with CO 2 laser heating is initially determined by observations with Nomarski microscopy.An image of a scratch after only one CO 2 laser shot at a power of 10 W during 1 second and with a beam diameter of 1.4 mm is shown in Fig. 3.The white cross on the left indicates the center of the laser beam and dashed rectangles delimit visual differences of silica behavior.At each of the three zones identified in Fig. 3, a change in the scratch may be observed.Surrounding the center of the laser beam, the Zone A looks like the regular surface of the silica sample.No defect is visible and it looks as if this portion of the scratch is totally removed.In contrast, in the Zone C, the scratch seems not affected by the CO 2 laser irradiation.Although the beam radius is 700 µm, at a distance ≥ 400 µm from the center scratches are unmodified.The intermediate Zone B is a transition region between the removed scratch and the original scratch.The defects still apparent are different from the original scratch, and their number increases with the distance from the center of the beam.To confirm the lack (or not) of cracks under the zone A and to obtain more precision relating to their evolution under the Zone B, we did some CLSM measurements.

Characterizations with a confocal microscope
To pursue our characterization of the interaction of scratched silica with a CO 2 laser irradiation, we compare CLSM observations with previous Nomarski microscope information.The Fig. 4 represents CLSM images of the same region as the Fig. 3, again with optical differences in silica modification pointed out by dashed rectangles.The Zone A as seen by CLSM is smaller than the Zone A defined in Fig. 3.But all cracks on and under the surface are entirely erased and a high resistivity to UV laser irradiation can be expected.Observation of the Zone C in Fig. 4 shows a great similarity with the morphology of cracks in Fig. 1, confirming that the laser did not affect scratches.Finally, the transition Zone B is the more enlightening about the silica alteration after laser heating.Cracks are strongly modified in large spots like lumps that are clearly discernible.These new sub-surface defects conserve the same maximal depth of 16 µm as initial cracks before laser irradiation.A noticeable aspect of such transformation is that the density of these lumps decreases inversely with the silica heating, as expected.

Characterizations with an optical profiler
After visual inspections with Nomarski and confocal microcopies, surface deformations were measured using a 3D optical profiler.Our 3D optical profiler (Talysurf CCI 3000 by Taylor Hobson) is a microscope based on coherence correlation interferometry.An objective with a magnification of 20 and a numerical aperture of 0.4 was used, which permits us to attain a measurement area of 0.9 x 0.9 mm 2 with an optical resolution of 0.9 µm in x-y.Step height standards provided by the manufacturer were used to calibrate the instrument.The manufacturer specifies the vertical resolution as better than 0.1 nm.
Here, we consider a scratch irradiated with the same CO 2 laser parameters as above (power = 10 W, duration = 1 s and beam diameter = 1.4 mm), but with several heatings in order to remove a longer portion of the scratch.The fused silica sample was shifted by 200 µm along the scratch, between each of the n laser shots.Measurement of the surface affected by the last four irradiations, indicated by arrows, is represented in Fig. 5.The deeper spot visible as dark blue area in Fig. 5(a) corresponds to the last CO 2 laser shot, and it is noticeable that craters go deeper with the progression of irradiations.We attribute this effect to the modification of the silica by the previous heating.Such an observation asks for a larger step when translating the sample along the scratch, or an adapted decrease of the laser power between each irradiation.These modifications can be easily done for practical applications.The choice of these two parameters has to be derived from their influence on the UV-laser damage response, together with a lowest possible impact on the silica surface.From the Fig. 5(b) we distinguish a central region with significant matter removal [26] and a surrounding area where silica has been distorted by viscous flow [19], densification [27] or tensile surface forces [28].Different authors have already mentioned similar observations for damage growth mitigation [19,25,27].The wavefront distortion of UV laser propagation through the recovered site is a main concern for laser facilities such NIF and LMJ.The propagation of UV lasers is perturbed not only by surface deformation but also by local refractive index change induced by the heating treatment.Some previous results on beam modulation have found a good correlation between measurements [29] and modeling based on surface deformation [30].This indicates that surface profile has a greater impact than low variation of the refractive index.Nonetheless, to deal with this issue, specific experiments and studies are going to be conducted to evaluate precisely the beam modulation through the recovered site.In this study, we focused on the removal of the morphological defects, and our goal was to maintain surface deformation lower than 1 µm which is in good accordance with a final superpolishing that will restore flatness of the optical surface.
In the case of a scratch longer than the strongly transformed region, like our example, such matter displacement seems perturbed by the presence of cracks, as visible in the righthand-side part of the Fig. 5(a).This region corresponds to the transformed Zone B as referenced in Figs. 3 and 4. To investigate more on this transition, we measured scratched surfaces of silica after one irradiation for different laser power.The change between silica relocation and matter ejection is obtain at different power depending on the heating duration and the beam size.Results achieved with duration of 1 second and beam diameter of 2 mm, are shown in Fig. 6.Fig. 6.Interferential microscopy observation of a scratch removed by one CO 2 laser shot with a beam diameter of 2 mm.The two powers are compared for the same irradiation time of one second.Following the dashed lines indicated in the 3D map of the surface (up), transversal profiles of the removed scratch are given by the curves (down), for each power respectively.The Fig. 6 at 14 W presents a surprising evolution of the scratched silica when heated, since the laser was pointed on the scratch and it appears less altered than the surrounding silica.We presume that a mechanism like discontinuities in the material due to cracked silica perturbs both the thermal conductivity and the absorption of energy.These effects then combine to "protect" the material under the scratch.The crater diameter is 1.5 mm for both powers presented in Fig. 6, but the hole is about half as deep for the irradiation with 14 W than 15 W. In the latter case, the central part of the beam corresponding to the Zone A mentioned above has certainly removed all cracks.But the start of matter ejection generates rapidly a silica surface alteration ≥ 1 µm that is undesirable for our objective.Indeed, the necessary compromise to keep the wave front quality of the optics without long time of repolishing necessitates that only weak surface modifications be induced by the scratch removal.Although the measurement using a 3D optical profiler is useful for estimating the upper limit for the power to be used in reparation, the ultimate test must be based on the laser damage response.

Setup description
Some aspects of CO 2 laser treatment on scratch removing can be evaluated using the microscopy techniques described above.But the real test must depend on the resistance of the repaired samples to laser damage.The UV-laser we used for these damage tests is a Qswitched Nd:YAG laser (Infinity laser by Coherent) operating at 355 nm wavelength with a 160 mJ maximum energy.The pulse is single mode longitudinally, with average pulse duration of 2.5 ns.At the focus point, the spatial profile is very nearly Gaussian, and the beam waist 1/e 2 diameter is 900 µm, which is large compared to the scratch width.The spatial profile is recorded for each shot to determine the exact peak fluence and the exact beam position.Accurate determination of the local energy distribution on the scratches is then obtained.The laser beam is linearly polarized and the incidence is normal.The absolute fluence is determined within an error of as much as ± 10% [31].The samples were tested in a vertical position while the scratches were oriented on the exit surface of the incident light.Before and after the UV-laser irradiation, the tested area could be observed with a long working distance microscope.This in situ diagnostic permits us to evaluate the impact of the laser light on the scratch and to stop the UV-laser irradiation as soon as a damage site is initiated.

Evaluation of the repair
After scratch removal, repaired surfaces were illuminated using the usual procedure of damage testing [32].First, we employed the 1-on-1 mode in order to identify the CO 2 laser parameter that produce a correct reparation.Then we validated our choice thanks to the S-on-1 procedure.Finally, a raster-scan mode was also used to realize homogenous irradiation on a larger region than the heated scratch area.
On untreated scratches like those shown in Fig. 1, no significant evolution has been detected for fluences ≤ 3 J/cm 2 , although a cleaning effect is sometimes observed.In contrast, for fluences ≥ 4 J/cm 2 , catastrophic damage growth is systematically observed.This is a quite low fluence value if we compare with scratches caused during polishing [9] but our manufactured scratches using a diamond indenter contain cracks as deep as 16 µm.For scratches heated by the CO 2 laser without modification as in the mentioned Zone C, equivalent behavior is obtained.
To probe the repairs, we removed a portion of scratches with three successive shots shifted by 200 µm at a fixed laser power.Each section corresponding to different CO 2 laser power was then irradiated by Nd:YAG laser using the 1-on-1 procedure with a high fluence of 16 J/cm 2 .Results achieved by CO 2 laser treatment with duration of 1 second and a beam diameter of 2 mm, are shown in Fig. 7, where white ellipses indicate damage formation.The repairs were carried out only in the central region in each case.It results from the Fig. 7 that a CO 2 laser power > 12 W is necessary to prevent damage initiation with a fluence of 16 J/cm 2 , and density of damage sites increases as the power decreases.Moreover, measurement with the 3D optical profiler with same heating parameters, showed that matter ejection is reached with a power of 15 W. Consequently, a correct repair seems to be obtained with a laser power in the narrow range of 13-14 W, as outlined by the dashed rectangle in the Fig. 7.The next step was to confirm these results with fatigue test using the S-on-1 procedure.We fixed S = 20 shots with the same fluence of 16 J/cm 2 .No evolution was detected with the powers of 13 and 14 W even though the scratch still appears weakly visible in the repaired portion.This confirms the result of Fig. 6, where the 14 W treatments did not evacuate the region under the scratch.
Even if a correctly repaired surface is very resistant to UV-laser up to 16 J/cm 2 , it is essential to correlate this result with a test covering a larger region than the heated scratch area.In that way, we ran the UV-laser with the raster-scan mode at 16 J/cm 2 , and the shot-toshot step has been chosen in order to ensure a beam overlap of about 80% of the maximum fluence.A surface area larger than the removed scratch has been tested.An example of such an experiment is shown in Fig. 8 where the CO 2 laser ran over more than 2 mm via ten successive irradiations at a power of 14 W during 1 second and with a beam diameter of 2 mm.This procedure for UV-irradiation confirms the resistance of the eradicated initial scratch as well as it reveals weaknesses near the reparation.The occurrence of laser damage in the surrounding of the CO 2 laser irradiated area has already been reported and related to residual stress [33,34].Here only three damage sites appeared whereas more than 20 shots along the fragile zone have been made at fluences of 16 ± 1.5 J/cm 2 .One method to overcome this difficulty has been proposed [16].Annealing this zone by applying a second CO 2 laser irradiation increases the UV-laser resistance significantly.Additionally, we fixed at 16 J/cm 2 the fluence of our test to validate the quality of our repair, although the maximum UV intensity expected in LMJ is only 14 J/cm 2 .

Morphology of the repaired surface after laser damage test
The scratch removal must obviously produce a surface that has no visible scratches.But this does not assure that the repair is complete, since lumps may be present beneath the surface.The question is then whether the presence of lumps will lead to breakdown under UV irradiation.We may get more precise information by performing CLSM measurement after UV-irradiation.For the case of a CO 2 laser treatment with duration of 1 second and a beam diameter of 2 mm, we compare Nomarski and confocal microscopy in Fig. 9 for the two fluences surrounding this threshold (the lower = 12 W and the upper = 13 W).The defects typical of the transition zone B already viewed in Fig. 4 are again clearly recognizable in Figs.9(c) and 9(d).These lumps, which are not apparent at the CLSM top view image, become visible as bright white spots by Nomarski microscopy, whereas adjacent black spots correspond to small residual surface defects.The latter seem not to be sources for UV-laser induced breakdown.In Fig. 9(c) the damage initiates on one of the lumps nearest to the surface, because it requires less energy to explode.It is not surprising that collective damage appears, when decreasing slightly the CO 2 laser power (Fig. 7), because of the high density of lumps even with parameters of reparation just under the damage threshold.When heating with a power of 13 W, only at a peripheral zone are some lumps visible and they are at 8-10 µm below the surface.Since these residual defects are on the edge of the heated zone, they were tested at fluence lower than 16 J/cm 2 .Finally, we conclude that fixing scratches correctly requires eradicating the entire crack without leaving any residual lump beneath the surface.Therefore, the laser-induced-damage-threshold is directly correlated with the limit between zone A and B. To increase our understanding of this result, we carried out a calculation of the maximum temperature reached at the end of the heating for the range of our experimental parameters.

Calculation of the temperature at the end of the CO 2 laser pulse
Thanks to our 2D axi-symmetric numerical model presented in reference [20] we have calculated the temperature (T) distribution reached below the surface at the end of the CO2 laser pulse.For the fused silica data we referred to the glass manufacturers [35], except for the thermal conductivity which is approximated by a piecewise linear function, whose slope changes discontinuously at both annealing and softening temperature values [36].As an example of this calculation, results obtained with pulse duration of 1 second and a 2 mm beam diameter, similar to the parameters used prior to laser damage resistance presented above, are shown in Fig. 10.From the evolution of temperature with the distance to the beam centre in Fig. 10(a), we note a temperature variation ≤ 50 K up to 100 µm away, which is much larger than the standard scratch half-width of this study (< 20 µm) and the width of scratches caused by polishing in general.The temperature below the surface as presented in Fig. 10(b) varies also relatively slowly with the depth.For example, the on-axis temperature with 14 W is equal to 1810 K at the surface and to 1770 K at 16 µm below the surface, which is the maximum crack depth in our experiment (this is shown as the limit of the coloured zone).Although the annealing temperature of silica is linked with the upper limit of the Zone C (T = 1315 K), from comparison of calculations with experimental data we deduce the temperature limit separating Zone A from Zone B (T A-B ).As mentioned above, the presence of lumps near the surface when running the laser at 12 W and their complete vanishing at 16 µm depth using 13 W, positions the Zone boundary at T A-B = 1640 ± 30 K. As was previously discussed in reference [25], significant craters (depth in the vicinity of 1 µm) are formed at temperature less that 2000 K, and the authors have proposed a thermodynamical approach to describe such a weak evaporation regime.In the present study, our experimental observation (Fig. 6) indicates that such a threshold (T E ) is reached at a power in the range 14 -15 W. By comparing with our simulations, a temperature limit of the non-evaporative regime T E = 1840 ± 30 K is found, confirming a surface temperature below 2000°K.
From these simulations we conclude that the spatial evolution of temperature is well suited to typical dimensions of scratches on polished optics.This analysis gives us the appropriate operating range of temperature for removing scratches, as pointed out in Fig. 10(b) by the interval between dashed red lines.We require temperatures > T A-B at the maximum crack depth, and < T E at the surface.According to this, with a CO 2 laser power of 14 W, duration of 1 s and 2 mm beam diameter, it should be possible to eliminate scratches as deep as 50 µm.

Influence of CO 2 laser beam diameter
We have studied the surface deformation as a function of the laser power for different laser beam diameters (D).For this work, we measured the maximum crater depth with the 3D optical profiler after each laser shot and we have reported the values in Fig. 11.The variation of depth as a function of the laser power evolves strongly with D. We have observed that in the case of D = 2 mm, lumps as deep as 16 µm disappear completely (limit between Zone B and Zone A) for a crater depth of about 300 nm, in the region where the slope starts to increase significantly.With smaller beam diameters such as 0.7 mm and 1 mm, the crater depth changes from 0.3 µm to 1 µm as the laser power increases by less than one Watt.For our application, a slow variation of depth for a large range of laser power is preferable.Therefore we compare the effect on the temperature when D = 1.4 mm as compared to that when D = 2 mm.The results of this simulation, performed with the pulse duration of 1 second and a 1.4 mm beam diameter, are shown in Fig. 12.As for the larger beam diameter, the temperature as one moves away from the beam centre decreases slowly (≤ 60 K up to 100 µm), but inside the silica along beam centre axis a greater attenuation is observed with D = 1.4 mm than for D = 2 mm.As is visible in Fig. 12(b), a decrease of about 100 K has been calculated with 10 W up to 16 µm.We found from experimental measurement with D = 1.4 mm that the silica ejection is already effective at a power of 10 W (Fig. 5(b)) and for a power as low as 9 W the heated scratch is resistant to UV-laser up to 16 J/cm 2 (not shown here).Therefore, by comparing experiments with simulations, a temperature in the vicinity of the softening point is obtained for the nonevaporative regime (T E = 1880 ± 50 K) and a value slightly greater than before with D = 2 mm is determined for the boundary between Zones A and B (T A-B = 1710 ± 50 K).Locating these temperatures in Fig. 11 (dashed red arrows) we observe that the decrease of D induces a diminution of the crater depth for temperatures comprised between T A-B and T E although these latter augment by 70 K and 40 K respectively.These weak effects can be explained by a smaller gradient of temperature from the central part of the beam in the case of the smaller diameter, thus reducing the efficiency of a mechanism such as viscous flow.
Finally, the use of a smaller beam diameter (D = 1.4 mm) is also well suited to remove typical dimensions of scratches on polished optics.We found that with a CO 2 laser power of 9 W, duration of 1 s and 1.4 mm beam diameter, it should be possible to eliminate scratches as deep as 30 µm.As shown in Fig. 10(b) and Fig. 12(b), the appropriate operating range of temperature for removing scratches is the interval between T A-B and T E .The latter is quite close to the silica softening point.Moreover, the interval between them is approximately the same for both beam diameters.Further treatment to maintain the quality of surface waveform requires a minimisation of the crater depth after the scratch removal.A compromise has to be found between this constraint (lower beam diameter) and the ease of working with a larger range in laser power.

Influence of CO 2 laser heating time
We have repeated our experiment with a CO 2 laser pulse duration of 5 s to measure the influence of increasing by five the heating time of silica.Again we studied the surface deformation as a function of the laser power and tested the laser damage threshold of each repaired zone by irradiation with a Nd:YAG laser using the 1-on-1 procedure with a fluence of 16 J/cm 2 .Sections of scratches were removed with three successive shots shifted by 200 µm at a fixed laser power with a beam diameter of 2 mm; they are shown in Fig. 13.In each case the repairs were carried out to test resistance only in the central region, and white ellipses indicate damage formation.When no damage occurs, results were confirmed with fatigue test using the S-on-1 procedure (S = 20 shots) with the same fluence of 16 J/cm 2 .The above-mentioned (Fig. 6) evolution of the scratched silica that appear less altered than the surrounding silica when heated is again present in Fig. 13 but its effect is reduced by increasing the CO 2 laser duration.With this 5 s duration, it is again possible to prevent damage initiation with a fluence of 16 J/cm 2 , together with avoiding silica matter evaporation.This well-suited repair is obtained in the narrow range of 11-12 W, as outlined by the dashed rectangle in the Fig. 13.The maximum depth measured with the 3D optical profiler after each laser shot are reported in Fig. 14.The variation of crater depth as a function of the laser power evolves significantly with the pulse duration.In contrast to what happens for the diameter, it seems preferable to use the shorter duration, since the variation of crater depth with power is smaller.We observe that T E is just above 12 W for a duration of 5 s that is linked with a crater depth of 800 nm comparable to the value found for 1s.In contrast, T A-B is between 10 W and 11 W for a duration of 5 s and thus is associated with a crater depth of 200 nm that is smaller than the 300 nm for 1 s.We then calculate the temperature in order to see if this difference in depth is caused by a difference in temperature.The results of a simulation performed with the pulse duration of 5 seconds and a 2 mm beam diameter, are shown in Fig. 15.They should be compared with the same calculations with a 1 second duration as already shown in Fig. 10.For the 5 s duration, the plateau of temperature in the radial direction extends further that for the 1 s pulse.The temperature decreases by only 30° K for radial distance < 100 µm.This suggests that an equilibrium between laser heating and radiative losses is emerging.However, concerning the temperature distribution as a function of depth, they are almost identical for the two different durations.In particular, the longer heating period does not produce higher temperatures beyond 16 µm.The values obtained for the temperatures T E and T A-B are: T A-B (5 s) = 1590 ± 20 K. and T E (5 s) = 1810 ± 20 K. Thus the greater duration, while more effective on the surface, has no advantage in the deeper parts of the sample.
To illustrate the time dependence of the laser heating we show in Fig. 16 the surface temperature at the center of the heating spot as a function of duration for laser powers in the interval 10-15 W. The short time behavior indicates a rapid rise in temperature, which slows down around 1 s.At 5 s the curves are approaching but have not yet reached their asymptotic limits.The interesting temperature range, between T A-B and T E are indicated by small rectangles at times 1 and 5 s, respectively.One sees that the longer duration attains the same temperature range with 2 W less laser power.
Notably, we found that the minimum and maximum limits of this appropriate range of temperature vary slightly with the laser duration.

Conclusion
In this study we have demonstrated that CO 2 laser is an appropriate tool to remove scratches on fused silica optics because it is rapid, localized to the scratch and it creates no debris.Indeed we succeeded to remove a 16 µm deep scratch and to increase the laser damage threshold from 4 J/cm 2 to 16 J/cm 2 .
Optics repair is then possible through CO 2 laser machining but great care must be taken on the choice of the operating parameters.As there is a large temperature range between the annealing point and the softening point, it could be expected that it would be easy to melt the silica and to repair the surface.In reality, silica properties change continuously between annealing and softening points.We took great attention to characterize theses changes in terms of microscopic visual inspection, sub-surface defects, surface deformation and UVlaser damage resistance.
The observed physical changes were correlated with the temperature calculated by a 2D axi-symmetric numerical model.Notably, we found that the appropriate range of temperature for scratch removing using the techniques described here is between 1650 K and 1810 K.The numerical model can then be used to find the laser parameters that permit us to attain this range of temperature in order to remove different scratches.Such scratches may have widths as large as 100 µm and depths of up to 40 µm.
One suggestion for improvement of this process is to combine it with a final polishing such as MRF polishing for example.Our reparations have been operated in a research facility but different improvements still need to be studied in order to implement it in the manufacturing of laser optical components.

Fig. 1 .
Fig. 1.Scratch realized by scratch apparatus and observed with a confocal microscope.The image (a) is a top view; the two other are sides view along the scratch (b) and across it (c).

Fig. 2 .
Fig. 2. Scratch created during polishing and observed with a confocal microscope.The image (a) is a top view; the image (b) is a side view along the scratch.

Fig. 3 .
Fig. 3. Nomarski microscope image of a scratch irradiated by one CO 2 laser shot, with the parameters; 10 W of power, 1 s duration and 1.4 mm diameter.Zone A is described as a repaired area, Zone B looks like a transition section and Zone C is not affected by CO 2 laser.

Fig. 4 .
Fig. 4. CLSM image of a scratch irradiated by one CO 2 laser shot, with the parameter; 10 W of power, 1 s duration and 1.4 mm diameter.Both, top view (up) and side view along the scratch (down) are represented.The three Zones A, B and C are respectively described as repaired, transition and not affected areas.

Fig. 5 .
Fig. 5. Interferential microscopy observation of a scratch removed by n CO 2 laser shots, with parameters; 10 W of power, 1 s duration and 1.4 mm diameter.The position of each shot is indicated with white arrows on the 3D map of the surface (a).Following the dashed lines, transversal shape of the shot n-3 and profile along the removed scratch are given by the curves (b) and (c) respectively.

Fig. 7 .
Fig. 7. Nomarski microscope images of scratches removed, in their middle, by CO 2 laser and then irradiated with a Nd:YAG laser for damage test.Each site received three CO 2 laser shots spaced by 200 µm, with 1 s duration, 2 mm diameter and the power ranging from 10 W to 15 W. The damage test procedure is 1-on-1.Drastic evolutions are indicated by white ellipse.

Fig. 8 .
Fig. 8. Nomarski microscope image of a scratch removed by CO 2 laser and then irradiated with Nd:YAG laser in raster-scan mode at 16 J/cm 2 .Each site received ten CO 2 laser shots spaced by 200 µm, with 1 s duration, 2 mm diameter and the power of 14 W. Three damage sites, indicated by white circles, are visible in the zone of residual stress.

Fig. 9 .
Fig. 9. Nomarski microscope and CLSM images of scratches removed by CO 2 laser and then irradiated with Nd:YAG laser in 1-on-1 mode at 16 J/cm 2 .Each site received three CO 2 laser shots spaced by 200 µm, with 1 s duration and 2 mm diameter.For Nomarski images in (a) and (b), close-ups of the effective CLSM measurement are indicated by dashed rectangles.For CLSM images in (c) and (d), both top view (up) and side view along the scratch (down) are shown.In image (c) the laser damage depth is delimited by a dotted line.

Fig. 10 .
Fig. 10.Temperature calculation after one CO 2 laser shot with 1 s duration, 2 mm diameter and the power ranging from 11 W to 16 W.(a) surface temperature as a function of the distance from the beam centre, (b) on-axis temperature as a function of the distance below the surface.

Fig. 11 .
Fig. 11.Maximum surface depth as function of the power, measured with 3D optical profiler after 1 s of heating by CO 2 laser running at different beam diameters varying from 0.7 mm to 2.0 mm.

Fig. 12 .
Fig. 12. Temperature calculation after one CO 2 laser shot with 1 s duration, 1.4 mm diameter and the power ranging from 7 W to 10 W. (a) surface temperature as a function of the distance from the beam centre, (b) on-axis temperature as a function of the distance from the surface.

Fig. 13 .
Fig. 13.Nomarski microscope images of scratches removed, in their middle, by CO 2 laser and then irradiated with a Nd:YAG laser for damage test.Each site received three CO 2 laser shots spaced by 200 µm, with 5 s duration, 2 mm diameter and the power ranging from 9 W to 12 W.The damage test procedure is 1-on-1.Drastic evolutions are indicated by white ellipse.

Fig. 14 .
Fig. 14.Maximum surface depth as function of the power, measured with 3D optical profiler after heating by a CO 2 laser beam of 2.0 mm diameter.Comparison between two heating times: 1 s and 5 s.

Fig. 15 .
Fig. 15.Temperature calculation after one CO2 laser shot with 5 s duration, 2 mm diameter and the power ranging from 9 W to 14 W. (a) surface temperature as a function of the distance from the beam centre, (b) on-axis temperature as a function of the distance from the surface.

Fig. 16 .
Fig. 16.Evolution in time of the temperature at the surface calculated at the beam centre with a beam diameter of 2 mm and for different laser power.Comparison between 1 s and 5 s of the working zone is indicated by pink rectangles.