## 2 Experimental
Using the line area of the NO\({}_{2}\) line at 2919.59 cm\({}^{-1}\), derived for the data in Figure 2b, the NO\({}_{2}\) amount fraction (concentration) \(x_{\text{NO}2}\) can be derived using Equation (1) (which is derived from the Beer Lambert law) [7]:  
\[x_{\text{NO}_{2}}=\frac{k_{\text{B}}\cdot T}{S_{T}\cdot L\cdot p_{\text{total }}}\int_{-\infty}^{\infty}A(\widetilde{v})d\widetilde{v}=\frac{k_{\text{B}} \cdot T}{S_{T}\cdot L\cdot p_{\text{total}}}\cdot A_{\text{line}} \tag{1}\]  
where the quantity \(k_{\text{B}}\) is the Boltzmann constant, \(S_{T}\) is the line strength of the probed molecular transition at gas temperature \(T\), \(L\) is the optical path length of the light beam transmitted through the absorbing medium, \(p_{\text{total}}\) the total gas pressure, \(A(\widetilde{v})\) the spectral absorbance and \(A_{\text{line}}\) the line area. The amount fraction (concentration) results \(x_{\text{NO}2}\) is directly traceable to the SI if all the quantities in the right-hand side of Eqn. 1 are traceable to the SI as well [7; 8; 9; 37]. To this end, \(x_{\text{NO}_{2}}\) results are derived without the calibration of the instruments with a reference gas mixture. As introduced, an instrument that can deliver amount fraction results that are directly traceable to the SI shall be referred to as an optical gas standard (OGS). From the data in Figure 2b, a line area value of 0.0010999414 cm\({}^{-1}\) is derived for the NO\({}_{2}\) line 2919.59 cm\({}^{-1}\), and a dTDLAS amount fraction value of (982.0 \(\pm\) 49.1) \(\upmu\)mol/mol calculated according to Eqn. 1 is combined with the TILSAM method [36]. This measured NO\({}_{2}\) amount fraction is in good agreement with the certified value of (979 \(\pm\) 20) \(\upmu\)mol/mol reported for the probed gas mixture, demonstrating the capability of the instrument for an absolute (\"calibration-free\") direct NO\({}_{2}\) amount fraction measurements. Table 1 holds an uncertainty budget for dTDLAS NO\({}_{2}\) results. As shown in Table 1, the combined uncertainty of the NO\({}_{2}\) results is 5.1% (\(k=1\)). The quantity \(k\) is a coverage factor [34]. The uncertainty of the amount fraction results of 5.1% is dominated by the uncertainty of the measured line area (1%) and the literature line strength value (5% [45]) as indicated by the higher index values (% individual contribution) in Table 1. The uncertainties of the other significant input quantities (\(p_{\text{total}}\), \(T\), \(k_{\text{B}}\), \(L\)) are all less than 0.2%. Figure 2: (**a**) Typical waves at 108 hPa signals measured using the spectrometer in Figure 1; (**b**) absorbance data derived from the data in Figure 2a. With the eight NO\({}_{2}\) lines shown (in red) in the line strength plot (right \(y\) axis), eight Voigt profiles are fitted to the data in order to derive the line areas. In order to determine the repeatability of the measurements delivered by the instrument, Figure 3a shows repeated measurements of NO2 amount fractions performed with the 979 umol/mol NO2 in synthetic air gas mixture. The mean value of the results in Figure 3a is 982.6 umol/mol, the reproducibility (1\(\sigma\), standard deviation) is 8.7 umol/mol (0.9%) and the repeatability (standard deviation of the mean) is 0.5 umol/mol (0. 1%). The excellent repeatability of 0.1% demonstrates the capability of a dTDLAS instrument for NO2 OGS applications. The inset in Figure 3a shows a histogram of the measurements, depicting a normal distribution of the results with a full width at half maximum (FWHM) of 9.2 umol/mol (corresponding to an SNR of 107 for the amount fraction results at 979 umol/mol). Figure 3b depicts a plot of the Allan deviation [49] of the NO2 amount fraction results (here, the measurements are done at 2 Hz, i.e., at 0.5 s with 10 averaged scans) as a function of time.