## 6 Multi-Gas Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{3}{*}{\begin{tabular}{c} **Mixture** \\ **No.** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Nominal CH\({}_{4}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Nominal C\({}_{2}\)H\({}_{6}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Calculated CH\({}_{4}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Calculated C\({}_{2}\)H\({}_{4}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Calculated C\({}_{2}\)H\({}_{6}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Calculated C\({}_{2}\)H\({}_{4}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Calculated C\({}_{2}\)H\({}_{6}\)** \\ **Concentration** \\ **[ppm]** \\ \end{tabular} } \\ \cline{6-9}
**No.** & **[ppm]** & & & & **SWLR** & **MWLR** & **SWLR** & **MWLR** & **SWLR** & **MWLR** \\ \hline
1 & 6.11 & 6.37 & 6.37 & 5.25 & 6.27 & 5.32 & 6.09 & 6.99 & 6.62 \\  & & & \(-\)14.1\% & 2.6\% & \(-\)16.5\% & \(-\)4.4\% & 9.7\% & 3.9\% \\ \hline
2 & 13 & 13 & 13 & 11.01 & 12.75 & 10.11 & 11.7 & 12.74 & 13.17 \\  & & & \(-\)15.3\% & \(-\)1.9\% & \(-\)22.2\% & \(-\)10.0\% & \(-\)2.0\% & 1.3\% \\ \hline
3 & 29.9 & 30.0 & 30.1 & 27.66 & 29.79 & 32.37 & 32.75 & 29.64 & 28.98 \\  & & & \(-\)7.5\% & \(-\)0.4\% & 7.9\% & 9.2\% & \(-\)1.5\% & \(-\)3.7\% \\ \hline
4 & 53.3 & 53.5 & 53.7 & 52.02 & 52.33 & 52.28 & 57.55 & 56.36 & 56.21 \\  & & & \(-\)2.4\% & \(-\)1.8\% & \(-\)2.3\% & 7.6\% & 5.0\% & 4.7\% \\ \hline
5 & 49 & 47.6 & 11.4 & 47.60 & 49.35 & 45.08 & 47.44 & 10.52 & 10.84 \\  & & & \(-\)2.9\% & 0.7\% & \(-\)5.3\% & \(-\)0.3\% & \(-\)7.7\% & \(-\)4.9\% \\ \hline
6 & 11.9 & 47.5 & 34.3 & 10.65 & 10.85 & 41.97 & 47.76 & 35.66 & 35.11 \\  & & & \(-\)10.5\% & \(-\)8.8\% & \(-\)11.6\% & 0.5\% & 4.0\% & 2.4\% \\ \hline
7 & 44.9 & 15.7 & 34.9 & 43.69 & 40.66 & 9.37 & 14.87 & 35.13 & 35.67 \\  & & & \(-\)2.7\% & \(-\)9.4\% & \(-\)40.3\% & \(-\)5.3\% & 0.7\% & 2.2\% \\ \hline \end{tabular}
\end{table} 
Table 2: Nominal and calculated concentrations of the gas mixtures (SWLR: single wavelength linear regression, MWLR: multiple wavelength linear regression, Error = (\(C_{\text{Calculated}}-C_{\text{Nominal}}\))/\(C_{\text{Nominal}}\) * 100%). (Table 1). When using single wavelength data for the linear solution, the calculated results of methane and ethylene have large errors in some cases because the cross-interference of ethane to ethylene reaches 20% (\(-0.3626\) / \(-1.778\)), and the interference of methane to ethylene is approximately 7.3%. To reduce the impact of cross-interference on the detection accuracy, we carried out broadband multiwavelength linear regression through which the accidental error can be significantly reduced. Specifically, 20% of the scan data are evenly extracted in the whole dynamic range of the laser current (55-90 mA), and then the selected data with high concentration-signal linearity (R\({}^{2}\) > 0.99) are further chosen for multiwavelength fitting to obtain the gas concentrations through linear regression (Figure S2 and Table 2). The broadband scanning spectra of all mixed gases samples and the spectra fitted by linear regression verify that the multiwavelength correction method notably improves the detection accuracy. Taking the mixture 3 in Table 2 as an example, the contribution curves of each of the three different gases to the fitted spectra are shown in Figure 11a. The superimposed spectra are in good agreement with the measured spectrum of the mixture (residuals plot shown in Figure 11b). The detection error of ethylene and methane is reduced to less than \(\pm 10\)%, and the detection error of ethane is less than \(\pm 5\)%, which can meet practical application requirements (e.g., for DGA).