## 3 Results
The key principle of the R-on-1 technique is that each separate region of the crystal is exposed to laser radiation with a gradual increase in the laser radiation intensity until the occurrence of an optical damage or a given value of the energy density is reached [20]. The testing of samples for LIDT using the R-on-1 technique included the exposure of the studied plate to pulsed laser radiation with a fixed fluence level during the exposure time of 1 s. Further, the fluence was increased with a step of 0.1/cm\({}^{2}\). The fact of the optical damage was established by the appearance of a glow in the area of exposure and a decrease in radiation transmission, as well as upon appearance of a damage on one of the crystal surfaces. Then, the sample was moved 0.7 mm in height or horizontally using a two-coordinate movement, and the experiment was repeated. The measurements were taken five times in order to obtain statistical data. Figure 5 shows the surfaces of GaSe samples with traces of the optical damage. The obtained experimental data served as a basis for constructing a graph of the cumulative probability of an optical damage depending on the fluence of the laser action. The point with the maximum fluence at which the damage occurred was assigned the probability \(\mathrm{P_{D}}=(5/5)=1\); the point with the lower fluence value was assigned the probability \(\mathrm{P_{D}}=(4/5)=0.8\), etc. ; and the point with the minimum fluence value was assigned the probability--\(\mathrm{P_{D}}=(1/5)=0.2\). Then, the experimental data were linearly approximated to the zero value of the optical damage probability. The fluence value of the incident radiation corresponding to the zero probability of the optical damage \(\mathrm{P_{D}}=0\) was taken as the damage threshold \(W_{\mathrm{0d}}\). The average value of the optical damage fluence was also calculated by using Equations (3)-(6):  
\[W_{av}=\frac{\sum W_{i}n_{i}}{N}, \tag{3}\]  
and mean square error:  
\[\Delta W_{av}^{2}=\ \frac{\sum(W_{av}-W_{i})^{2}n_{i}}{N(N-1)}, \tag{4}\]  
where \(N\)--total number of damaged sections, \(W_{av}\)--average value of the damage threshold, \(W_{i}\)--value of the damage threshold at one of \(N\) points, and \(n_{i}\)--number of points with the damage threshold \(W_{i}\). \begin{table}
\begin{tabular}{c c c c} \hline
**Sample** & **T, \%** & **d, mm** & \(\alpha_{v}\)**cm\({}^{-1}\)** \\ \hline GaSe & 0.6 & 3.1 & 0.17 \\ \hline GaSe:In & 0.47 & 4.49 & 0.39 \\ \hline \end{tabular}
\end{table} 
Table 1: Absorption coefficient of the samples at a wavelength of the Ho3+:YAG laser—2.091 μm. Figure 5: Surface of studied GaSe samples no. 1 (**left**) and no. 2 (**right**) upon laser radiation exposure. The following formula was used to find the confidence interval for LIDT (\(W_{D}\)):  
\[W_{D}=W_{av}\pm k<\Delta W_{av}^{2}>^{1/2}, \tag{5}\]  
where \(k\)--Student's coefficient. Student's \(t\)-distribution was used for the confidence probability Equation (5) [20; 21]:  
\[F(k,N)=\frac{\Gamma(N/2)}{\sqrt{\pi(N-1)\Gamma[(N-1)/2]}}\int_{-k}^{k}\left(1+ \frac{z^{2}}{N-1}\right)^{-N/2}dz, \tag{6}\]  
where \(\Gamma\)--gamma function. After the absorption of the samples was determined, LIDT values were obtained for each sample in terms of the fluence \(W_{0d}^{E}\) and the peak power \(W_{0d}^{p}\) of laser radiation at the probability of laser-influenced damage \(P_{D}=0\), according to the method described above. The average fluence \(W_{av}^{E}\) and the peak power \(W_{av}^{p}\) of the test radiation were found using Equations (1)-(5), at which the laser-induced damage of the sample took place. The confidence interval of LIDT in terms of the fluence \(W_{D}^{E}\) and the peak power \(W_{D}^{p}\) was also obtained. The experimental results are shown in Figures 6 and 7 and Table 2.