Laser damage testing of optics and optical materials is an integral part of the laser system development/improvement cycle. A typical damage test system consists of precision X, Y, and Z stages with rotation capability to hold the test part and a nanosecond laser operating at pulse repetition frequencies up to 100 Hz. The beam must be fully controllable, focused to provide destructive fluences at the test piece, and sampled to monitor energy and temporal and spatial characterization.

*Smoothly rising curve of damage probability as a function of fluence indicates sufficient and generally reliable data; Weibull analysis provides additional insight into large-area damage behavior.*

The International Standards Organization (ISO) has established ISO11254, a statistical method for damage testing that allows the user to develop a damage probability curve from a series of damage probability measurements at various test fluences for both single shot per site (1-on-1) and multiple shot-per-site, single-fluence (*S*-on-1) exposures.^{1} To generate the damage probability curve, users expose at least 10 sites to a fluence and count the number that sustain damage. They adjust the fluence and repeat the process until damage probability values range from zero to 100%. If the damage probability versus fluence plot does not go as a smoothly rising curve, it is possible that not enough data has been taken, or the fluence bins are statistically indistinguishable (because of the fluence measurement imprecision).

Correct interpretation of the damage curve is fundamentally important in understanding optic performance. ISO11254 calls for the determination of damage threshold (fluence at 0% damage probability) by linear regression of the damage probability data. This method is reasonably adequate for small optics but breaks down when the optic is exposed to beams substantially larger than the area tested. This is because the probability for defect-driven damage is intrinsically exponential and can be written as *P* = 1e^{C(F)A}, where *C*(*F*) is the defect concentration and *A* is the area exposed to the fluence *F*. By knowing the area of the damage beam it is possible to determine a defect concentration and then calculate the shift in damage probability for the actual beam used in the system.

The damage data can also be analyzed using Weibull^{2} statistics by assuming that *C*(*F*)~*F*^{m}. A plot of ln{1/*A*[ln(1-*P*)^{-1}]} versus ln(*F*) will usually be linear with slope equal to m, the Weibull exponent (see figure). Such an analysis will also reveal multiple slopes to the curve and indicate multiple damage mechanisms or classes of defects. In general, the damage test methods defined in ISO11254 and the Weibull analysis should be adequate to predict the large area damage behavior of an optic typically found in a tabletop laser system.

The test method requires further refinement when the defect density is low and the optic is very large, as is the case for 40-cm optics found in fusion-class laser systems. For these optics, laser raster scanning is the only feasible means of obtaining the defect concentration data to fill in the lower portion of the damage curve. For such optics, it is this part of the curve where differences between finishing processes will be revealed. In principle, the defect concentration can be obtained by counting the number of damage sites in a given area at a given fluence, but the curve obtained must be corrected for the actual spatial profile and pointing stability of the laser as well as the degree of beam overlap. **oe**

*References*

*1. ISO11254-1:2000 Determination of laser-induced damage threshold for optical surfaces, International Organization for Standardization; Geneva, Switzerland.*

*2. M. D. Feit, F. Y. Genin, Proc. SPIE 3492, p. 188-195 (1988).*

**Mike Runkel**

*Mike Runkel is an electronics engineer at Lawrence Livermore National Laboratory, Livermore, CA.*