## 4 Results and Discussion
### CO\({}_{2}\) Broadening Coefficient  
A NO/CO\({}_{2}\) gas mixture was prepared using the above-mentioned gas mixture preparation procedure to derive the NO-CO\({}_{2}\) broadening coefficient. Figure 2a depicts a subset of the measured NO/CO\({}_{2}\) gas mixture line profiles at two pressures. The measured lines were averaged across 20 scans, and the Voigt model was fitted with a third-order background polynomial and a non-linear Levenberg-Marquart technique. Two absorption peaks were fitted simultaneously as well as a CO\({}_{2}\) line between two NO peaks.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Peak** & **Wavenumber (cm\({}^{-1}\))** &
\begin{tabular}{c} **Line Strength** \\ **(cm\({}^{-2}\) atm\({}^{-1}\))** \\ \end{tabular} & **Line Number** \\ \hline \multirow{8}{*}{Peak 1 \(\Omega\)1/2} & 1914.984827 & 1.474 \(\times\) 10\({}^{-20}\) & R11.5e \\  & 1914.984833 & 1.597 \(\times\) 10\({}^{-20}\) & R11.5e \\  & 1914.984854 & 1.731 \(\times\) 10\({}^{-20}\) & R11.5e \\  & 1914.986297 & 1.029 \(\times\) 10\({}^{-22}\) & R11.5e \\  & 1914.986307 & 1.029 \(\times\) 10\({}^{-22}\) & R11.5e \\  & 1914.992367 & 1.028 \(\times\) 10\({}^{-22}\) & R11.5f \\  & 1914.992494 & 1.028 \(\times\) 10\({}^{-22}\) & R11.5f \\  & 1914.994619 & 1.730 \(\times\) 10\({}^{-20}\) & R11.5f \\  & 1914.994622 & 1.473 \(\times\) 10\({}^{-20}\) & R11.5f \\ \hline \multirow{8}{*}{Peak 2 \(\Omega\)3/2} & 1915.767290 & 9.245 \(\times\) 10\({}^{-21}\) & R11.5e \\  & 1915.767318 & 5.494 \(\times\) 10\({}^{-23}\) & R11.5e \\ \cline{1-1}  & 1915.767321 & 5.494 \(\times\) 10\({}^{-23}\) & R11.5e \\ \cline{1-1}  & 1915.767342 & 8.530 \(\times\) 10\({}^{-21}\) & R11.5e \\ \cline{1-1}  & 1915.767384 & 7.869 \(\times\) 10\({}^{-21}\) & R11.5e \\ \cline{1-1}  & 1915.769033 & 5.494 \(\times\) 10\({}^{-23}\) & R11.5f \\ \cline{1-1}  & 1915.769214 & 9.244 \(\times\) 10\({}^{-21}\) & R11.5f \\ \cline{1-1}  & 1915.769217 & 5.494 \(\times\) 10\({}^{-23}\) & R11.5f \\ \cline{1-1}  & 1915.769246 & 8.529 \(\times\) 10\({}^{-21}\) & R11.5f \\ \hline \end{tabular}
\end{table}
Table 1: The HITRAN database’s line list.  
The spectra fitting residuals were around (1\(\sigma\)) 2 \(\times\) 10\({}^{-3}\) optical density, as shown in Figure 2a. The signal-to-noise-ratio (SNR) was close to 200 when compared to the absorption peak. In our spectra fitting algorithm, the Gaussian width was calculated according to Equation (3) using the gas temperature measured by the temperature sensor. The Lorentzian line width was set as a fitting parameter. A linear regression was used to calculate the pressure broadening coefficient \(\gamma_{\rm f}\) from the fitted Lorentzian line widths at different pressures. According to the calibration certificate from PTB, the uncertainty (k = 1) of the pressure values was in the range of 0.1-0.15 mbar. As shown in Figure 2b, the pressure uncertainty was used as the x-error bar in the linear regression. The 1 standard deviation of the Lorentzian line width results (multiple measurements, typical 50-100 spectra) at each pressure step was used as the y-error bar, along with the uncertainty of the relative laser wavelength. As described in Equation (4), the fitted Lorentzian line widths exhibit very good linearity with pressures (only the second term, as the self-broadening contribution is negligible due to the trace NO level in the gas cell). Thus, we determined NO-CO\({}_{2}\) broadening coefficients of \(\gamma_{\rm co2}\) = 72.92(52) \(\times\) 10\({}^{-3}\) cm\({}^{-1}\)/atm and 79.99(44) \(\times\) 10\({}^{-3}\) cm\({}^{-1}\)/atm for Peak 1 and 2, respectively.