## 4 Results and Discussion
In Figure 9, the LIBS signal intensity at the wavelength of 544.65 nm was calibrated with the sulfur concentration in the coal samples. The sulfur concentration in coal varied from 0.5 to 1.1%, as shown in Table 1. The overall peak intensity of sulfur was quite similar to that of oxygen, as shown in Figure 7. In spite of the small variation in the sulfur concentrations, the sulfur showed a better peak intensity variation and smaller error bars compared to oxygen, which allowed for a better estimation of the sulfur concentration. The \(R^{2}\) for the CA, PLS, and SNR methods was 0.98, 0.65, and 0.02, respectively. The maximum errors from the mean values were 17.2, 17.9, and 16.3% for the CA, PLS, and SNR methods, respectively. In the CA and PLS analyses, the signal intensity increased with an increase in the sulfur concentration. In the SNR method, the signal intensity showed the opposite trend. Because the SNR method considers both the peak intensity and the baseline noise, the increased baseline noise at higher sulfur concentrations could result in the opposite trend with other methods. The most significant factor in increasing the LIBS measurement error was the noise, which was greater than the signal of the element. The degree of homogenization of the sample, the laser output, and interference of the plasma spectrum with the emissions from the element are associated with noise. For a more accurate analysis, it is possible to minimize the noise by reducing the background of the spectrum. Figure 8: Correlation between the intensity and O concentration with maximum \(R^{2}\) for CA, PLS, and SNR methods. Figure 7: Correlation between the intensity and H concentration with maximum \(R^{2}\) for CA, PLS, and SNR. Figure 10 shows the relationship between the carbon concentration of a coal sample used for an LIBS measurement and the estimated concentration of the carbon that is obtained from the CA, PLS, and SNR methods with the signal intensity of the target elements from the LIBS spectrum. The dotted line in Figure 9 presents the points where the estimated concentration of the element was equal to the measured concentration in the coal sample. When the mark is closer to the dotted line, the estimation of the elemental concentration of the coal sample is better. In Figure 10, the estimated concentration of carbon from the CA shows a better accuracy compared to other analysis methods. A clear distinction among the signal intensities of carbon for different concentrations in the coal samples could increase the accuracy of the estimation of the carbon content. In Figure 11, the relationship between the estimated concentration of hydrogen using the LIBS signal intensity and the known concentration of hydrogen in the coal sample is depicted. As shown in Table 1, the hydrogen concentration in the coal sample was between 4.8 and 5.2%. The LIBS signal peak intensity difference with changes in the concentration of hydrogen in the sample may not be clear, and this affects the estimation  
Figure 10: Estimated carbon concentrations with CA, PLS, and SNR. Figure 9: Correlation between the intensity and S concentration with maximum \(R^{2}\) for CA, PLS, and SNR methods. accuracy. The peak intensity itself was small when the concentration of the target element in the sample was small. This increased the effects of the baseline noise. For that reason, the estimation accuracy for the hydrogen concentration using the PLS and SNR methods was low compared to that of the CA method. Overall, the hydrogen concentration in the coal sample was underestimated. In Figure 12, the relationship between the estimated concentration of oxygen using the LIBS intensity and the known concentration of oxygen in the coal sample is presented. Because the experiment was performed under atmospheric conditions, the oxygen content in the atmosphere affected the LIBS signal intensity for the oxygen measurement.