**1. Introduction**

60 Advanced Topics in Measurements

Iwasaki, H.; Nakayama, Y.; Ozutsumi, K.; Yamamoto, Y.; Tokunaga, Y.; Saisho, H.;

Kasrai, M.; Lennard, W. N.; Brunner, R. W.; Bancroft, G. M.; Bardwell, J. A. & Tan, K. H.

and K-edge absorption spectroscopy, *Appl. Surf. Sci.,* Vol. 99, pp. 303-312. Kawamura, T.; Okada, S. & Yamaki, J. (2006). Decomposition reaction of LiPF6 based electrolytes for lithium ion cells, *J. Power Sources*, Vol. 156, pp. 547-554. Krause, M. O. (1979). Atomic Radiative and Radiationless Yields for *K* and *L* Shells, *J. Phys.* 

Lai, B. & Cerrina, F. (2002). SHADOW: A synchrotron radiation ray tracing program, *Nucl.* 

Malitson, I. H. (1965). Interspecimen Comparison of the Refractive Index of Fused Silica, *J.* 

Momma, K. & Izumi, F. (2008). VESTA: a three-dimensional visualization system for electronic and structural analysis, *J. Appl. Crystallogr.*, Vol. 41, pp. 653-658. Nakanishi, K. & Ohta, T. (2009). Verication of the FEFF simulations to K-edge XANES spectra of the third row elements, *J. Phys. : Condens. Matter*, Vol. 21, pp. 104214-104219. Nakanishi, K. & Ohta, T. (In press). Improvement of the Detection System in the Soft X-ray

Nakanishi, K.; Yagi, S. & Ohta, T. (2010). Development of a XAFS Measurement System in

Nakanishi, K.; Yagi, S. & Ohta, T. (2010). XAFS Measurements under Atmospheric Pressure

Ohta, T. (Ed.), (2002). *X-ray AbsroptionSpectrooscopy* (in Japanese), Industrial Publishing &

Rehr, J. J. & Albers, R. C. (2000). Theoretical approaches to x-ray absorption fine structure,

Röhr, C. & Kniep, R. (1994). The crystal structures of Li(PF6) and Li(AsF6) : on the crystal

Sako, E. O.; Kondoh, H.; Nakai, I.; Nambu, A.; Nakamura, T. & Ohta, T. (2005). Reactive

Saleh, B. E. A. & Teich, M. C. (1991). *Fundamentals of Photonics, Wiley Series in Pure and* 

Stöhr, J. (1996). *NEXAFS Spectroscopy, Springer Series in Surface Science,* Vol. 25, Springer-

Welnak, C.; Chen, G. J. & Cerrina, F. (1994). SHADOW: A synchrotron radiation and X-ray optics simulation tool, *Nucl. Instrum. Methods A*, Vol. 347, pp. 344-347. Wiza, J. L. (1979). Microchannel plate detectors, *Nucl. Instr. and Meth.*, Vol. 162, p. 587-601. Wyckoff, R. W. G. (1963). *Crystal Structures,* Vol. 1, Interscience Publishers, New York, ISBN:

Yoon, W-S.; Balasubramanian, M.; Yang, X-Q.; Fu, Z.; Fischer, D.A. & McBreen, J. (2004). Soft

X-Ray Absorption Spectroscopic Study of a LiNi0.5Mn0.5O2 Cathode during Charge,

*Applied Optics*, Wiley-Interscience, ISBN 978-0471358329.

chemistry of compounds A(EVF6), *Zeitschrift für Naturforschung. B, A journal of* 

adsorption of thiophene on Au(111) from solution, Chem. Phys. Lett., Vol. 413, pp.

in the Soft X-ray Region, *AIP Conf. Proc.*, Vol. 1234, pp. 931-934.

the Soft X-ray Region for Various Sample Conditions (in Japanese), *IEEJ Trans. EIS*,

University, *J. Synchro. Rad.,* Vol. 5, pp. 1162-1165.

*Chem. Ref. Data*, Vol. 8, pp. 307-327.

*Opt. Soc. Am.*, Vol. 55, pp. 1205-1208.

Vol. 130, pp.1762-1767.

267-271.

978-0471968696.

*Instrum. Methods A*, Vol. 246, pp. 337-341.

Absorption Spectroscopy, *Surf. Interface Anal.*

Consulting, Inc., Japan, ISBN: 978-4901493215.

*Rev. Mod. Phys.* Vol. 72, pp. 621-654.

*chemical sciences*, Vol. 49, pp. 650-654.

Verlag, Berlin, ISBN: 978-3642081132.

J. Electrochem. Soc., Vol. 151, pp. A246-A251.

Matsubara, T. & Ikeda, S. (1998). Compact Superconducting Ring at Ritsumeikan

(1996). Sampling depth of total electron and fluorescence measurements in Si L-

The prediction of the lifetime of optics in high power fusion lasers is a key point for mastering the facilities (Bercegol et al., 2008). The laser damage scenario is seen as occurring in two distinct steps. The first one concerns the damage occurrence due to the first optic irradiation: the initiation step (Feit et al., 1999). Afterwards, damage sites are likely to grow with successive new shots: the growth step (Norton et al., 2006 ; Negres et al., 2010). The damage growth study requires the use of large beams due to the exponential nature of the process, leading to centimetre damage sites. At the same time, damage density measurements on large optics are mainly performed off-line by raster scanning the whole component with small Gaussian beams (~1mm) (Lamaignère et al., 2007), except for a wide range of results using larger beams which permit also a comparison between procedures (DeMange et al., 2004). Tests are currently done at a given control fluence. The goal is to irradiate a known area in order to reveal all the defects which could create damage. This procedure, named *rasterscan procedure*, gives access to the optical damage densities (Lamaignère et al., 2007). This measurement is accurate and reproducible (Lamaignère et al., 2010). In standard tests (ISO standards, 2011), results are given in terms of damage probability. This data treatment is size dependent; on the contrary, it is important to focus the attention rather on the density of sites that damage at a given fluence.

The purpose of the present chapter is to explain how the knowledge of the entire test parameters leads to a comparable and reproducible metrology whatever beam and test characteristics. To this end, a specific mathematical treatment is implemented which takes into account beam shape and overlap. This procedure, which leads to very low damage densities with a good accuracy, is then compared with 1/1 tests using small beams. It is also presented with a peculiar attention on data reduction. Indeed an appropriate treatment of these tests results into damage densities gives at once good complementarity of the several procedures and permits the use of one procedure or the other, depending on the need. This procedure is also compared with tests realized with large beams (centimetre sized as used on high power facilities). That permits to compare results given by specific table-top test facilities with those really obtained on laser lines (Lamaignère et al., 2011).

In section 2, facilities using small and large beams are described. The several procedures used are presented in section 3. Developments of data treatment and analysis are given in section 4. Section 5 is devoted to the determination of error bars on both the fluence

Laser-Induced Damage Density Measurements of Optical Materials 63


The advantage of tests with large beams is that they are representative of real shots on high power lasers. They are carried out on high power facilities where parametric studies are conducted: pulse duration or phase modulation (FM) effects. With energies about 100J at 1053 nm and 50J at 351nm and after size reduction of the beam on the sample, high fluences are delivered with beam diameters about 16 mm. Due to a contrast inside the beam itself (peak to average) of about few units, a shot at a given average fluence covers a large range of local fluences (Fig. 2). The laser front-end capability makes possible parametric studies like the effect of FM, temporal shapes and pulse durations on laser damage phenomenology. The characteristics of this kind of laser are quite similar to high-power lasers for fusion research: the front-end, the amplification stage, the spatial filters, the frequency converters crystals. Then laser damage measurements performed with this system should be

Fig. 2. Damage test with a centimetre-sized beam. On the left, spatial profile of the 16mmdiametre beam at the sample plane as measured on CCD camera. On the right, the

corresponding damage photography is reported. Matching the two maps allows to extract

The 1/1 test is made on a limited number of sites (ISO standards, 2011). Results are generally given in terms of damage probability as a function of fluence. Since the beam sizes

representative of the damage phenomenon on high-power lasers.

**2.2 Large beam facilities** 

the fluence for each damage site.

16 mm

**3. Procedures** 

**3.1 1on1 procedure** 

measurement and the damage density. Few results presented in section 6 illustrate the complementarity of procedures, the repeatability, the reproducibility and the representativeness.
