2. Marker-based watershed algorithm with gray control

When considering multiple damage sites in one damage image, damage site extraction requires a clear edge contour to calculate the damage site area. To obtain the dimensions of damage sites and their distribution, the MWGC is applied to segment the damaged regions and accurately extract the lateral size information. Vincent et al. ^{[Reference Vincent and Soille17]} proposed a immersion simulation-based watershed segmentation algorithm, which used regions growing from local minima in nature. Benefiting from the advantage of fast computation speed, closed contours, and accurate positioning, the watershed algorithm is applied in many fields. Moreover, this algorithm has a sensitive response to weak edges. Because of the non-uniform illumination field in dark-field imaging systems^{[Reference Rainer15]} and the presence of optical aberrations, both noise and dark textures appear in the damage image and give rise to fake local minima. If the watershed algorithm is applied to these fake minima then image over-segmentation will possibly occur. To overcome the problem of over-segmentation of the image, gray control is implemented before the watershed calculation to remove noise and gradient non-uniformity.

The gray control is realized by setting a threshold that directly affects the image processing results. The threshold is determined by the gray level histogram of pixels in the damage image. For a damage image obtained by dark-field imaging technology, the image background has a low pixel gray value and maximum probability in the pixel gray histogram statistic. When the probability drops to the minimum from the peak, the gray value corresponding to the minimum probability is defined as the threshold of gray control. Figure 1 shows the flow chart of the improved algorithm.

Figure 2 shows the damage images extracted by different segmentation techniques. Figure 2(a) is the original damage image obtained by a microscope with CCD. The image binarization (Figure 2(b)) is merely an image denoising process for the gray information and cannot divide the damage sites. Since the selected threshold values in the threshold segmentation algorithm are generally determined by the gray scale for different regions, region segmentation based on this will be over-sensitive, which makes the damage pits inside one site divided into multiple sites unfavorably. This can be seen from damage regions with low gray contrast between the object and background in Figure 2(c). Over-segmentation can be observed in Figure 2(d) using marker-based watershed algorithms without gray control. In contrast, the MWGC clearly marks the different damage sites, which facilitates obtaining the damage growth and damage site size distribution. The different colors in Figures 2(c)–(e) represent different segmented damaged regions.

Figure 2.

Results of image segmentation. (a) Original damage image; (b) by image binarization; (c) by threshold segmentation; (d) by marker-based watershed algorithm without gray control; (e) by MWGC.

Table 1 shows a comparison between the diameters $d_{1}$ of damage site areas extracted using the MWGC and the diameters $d_{2}$ measured using an optical microscope (OM) with $200\times $ magnification. The morphology of damage sites obtained by the OM is shown in Figure 3. The average absolute error $\langle d_{1}-d_{2}\rangle $ is 0.93 $ \mu \mathrm{m}$, which is much less than the pixel size (as shown in Table 2). Also, the average relative error $\bigl \langle \frac {d_{1}}{d_{2}}-1\bigr \rangle $ is 2.8%, indicating that the sizes of damage sites extracted by the MWGC are believable. It is clear that the segmentation algorithm incorporating gray control is effective in processing the damage image produced by a large-aperture laser.

Table 2.

Pixel Size Calibration for Different Damage Images.

Figure 3.

Damage site morphology captured by OM.

3. Experimental set-up

The experimental set-up is shown schematically in Figure 4, and consists of modules for third-harmonic generation, laser parameter measurements, damage initiation, and image capture. A 1053 nm laser with a beam aperture of $1.8 \times 1.8\, \mathrm{cm}^{2}$ exits from a four-pass amplifier, the pulse width of which is 3 ns, as shown in Figure 5. The 351 nm laser is generated through frequency conversion of 1053 nm laser using two KDP crystals. By sampling the laser output from KDP crystals, the laser parameters are measured. Next, fused silica samples are exposed to the laser transmitted through a focusing lens. The beam sizes on the damage samples are 0.56–0.86 cm and are achieved by adjusting the distance between the samples and the lens (1 and 1.5 m in focal lengths for Corning-7980 and Heraeus-Suprasil 312 samples, respectively). The laser energies and near-field energy density distribution are measured by the measurement set of laser parameters. Figure 6 shows the near-field energy density distribution at 351 nm with a beam contrast (peak to average) of 1.75. The damage images after each shot are observed by a microscope with a CCD. The microscope magnification is calibrated using Group 0-4 of a 1951USAF resolution test chart with 1.41 line pairs per millimeter. Subsequently, the pixel size of the damage image is calibrated as shown in Table 2.

Figure 4.

Experimental set-up for laser-induced damage testing.

Figure 5.

Temporal profile of a 3 ns pulse at 1053 nm.

Figure 6.

(a) Near-field energy density distribution at 351 nm. (b) Profile along the line in (a).

In our experiments, Corning-7980 and Heraeus-Suprasil 312 (secondary cleanliness) samples with a size of $50 \times 50 \times 8\, \mathrm{mm}^{3}$ were prepared to test the damage behavior and the average damage growth and damage site distribution were calculated to illustrate the damage properties of the optical surface.

4. Results and discussion

4.1. Damage growth coefficients

Damage tests at 351 nm are carried out to analyze the damage growth and damage site distributions on Corning-7980 and Heraeus-Suprasil 312 (secondary cleanliness) samples. For successive laser shots, five damage sites are selected to calculate the damage growth coefficients for the two samples. The damage growths for different damage sites are exponential, as shown in Figure 7, which is in good agreement with the reported results^{[Reference Norton, Hrubesh, Wu, Donohue, Feit, Kozlowski, Milan, Neeb, Molander, Rubenchik, Sell and Wegner8, Reference Rubenchik and Feit12]}. Table 3 shows the damage growths for the two samples. The damage growth coefficients $\alpha $ are $1.10 \pm 0.31$ with an average fitting goodness $R^{2}$ of 98.8% and $0.60\pm 0.09$ with an average fitting goodness $R^{2}$ of 97.3%, respectively.

Table 3.

Damage growth for Corning-7980 and Heraeus-Suprasil 312 samples.

Figure 7.

Damage growth of (a) Corning-7980 and (b) Heraeus-Suprasil 312 samples at 351 nm.

Figure 8.

Damage site size distribution for the Corning-7980 sample at 351 nm.

As seen from Figure 7, the damage growth coefficients are distinctly different for the five tested sites in the same sample. The difference possibly results from the site morphologies tested and the local fluence. Numerous researchers^{[Reference Liao, Abdulla, Negres, Cross and Carr9, Reference Norton, Donohue, Hollingsworth, Feit, Rubenchik and Hackel13, Reference Demos, Staggs and Kozlowski18, Reference Negres, Cross and Carr19]} have demonstrated that the complex damage growth process is affected not only by the various laser parameters but also the intrinsic structural features of the optical components. In general, there are various precursors on the optical surface that induce damage sites with different morphologies. Damage sites with different morphologies grow differently. Therefore, damage sites grow with different coefficients after subsequent laser shots.

Note that the standard deviation of the growth coefficient for the Heraeus-Suprasil 312 sample is smaller than that for the Corning-7980 sample. This can be explained by the cleanliness of the optical surface. Most fragile precursors are removed from the Heraeus-Suprasil 312 sample surface with secondary cleanliness treatment. The damage sites induced by residual precursors are possibly similar. It can be inferred that the error bar of the growth coefficient ($\pm 0.09$) of Heraeus-Suprasil 312 is less than that of Corning-7980 ($\pm 0.31$).

4.2. Damage site distribution

Next, the damage site distributions are obtained after one laser shot, as shown in Figures 8 and 9. The number of damage sites decreased sharply with lateral damage site size. The average fluence of the 351 nm laser on Heraeus-Suprasil 312 sample is 22.60 J cm$^{-2}$, larger than that for the Corning-7980 sample (${\sim } 11$ J cm$^{-2})$. Therefore, the number of large-size damage sites (area $ > 0.1\, \mathrm{mm}^{2})$ for Corning-7980 sample is less than that for the Heraeus-Suprasil 312 sample.

Figure 9.

Damage site size distribution for the Heraeus-Suprasil 312 sample at 351 nm.