# Advances in High-Precision NO2 Measurement by Quantum Cascade Laser Absorption Spectroscopy
## 2 Materials and Methods
### Description of the Dual-Laser Spectrometer
#### 2.1.2 Performance Assessment  
The measurement precision of our instrument for NO\({}_{2}\) was estimated by using the Allan-Werle deviation technique [44]. For this, synthetic air was continuously measured over 12 h, and the NO\({}_{2}\) line position was locked by using the passive frequency-locking method described above. The reference water line was obtained by artificially humidifying the air to about 200 ppmv H\({}_{2}\)O using humidified charcoal in the sampling line. Figure 4 summarizes measurements obtained under various operating conditions by showing the associated Allan-Werle deviation plot. Measurements at two different sample pressures (gas pressure in the MPC), namely 80 and 30 mbar, are presented as we found this parameter to have the most significant influence on the results especially in terms of water induced spectral interferences, as described in Section 2.1.3. In addition, two distinct operating modes are considered: (i) NO\({}_{x}\) mode, corresponding to the detection of both NO and NO\({}_{2}\) for which both lasers are emitting alternatively at a repetition rate of 10 kHz; and (ii) NO\({}_{2}\) mode, corresponding to the detection of NO\({}_{2}\) only, which allows a higher repetition rate (up to 15 kHz). Figure 3: Reflection spot patterns of the MPC. (**a**) (stars) Paraxial (transfer-matrix based) and (dots) non-paraxial (ray tracing) spot simulations on the front MPC mirror (with coupling hole) for the N366 and N274 patterns. (**b**) Simulated interference fringes spectrum for the N366 pattern based on the paraxial propagation simulation. The fringe intensities are given in arbitrary units. The number of passes corresponds to the fringe generating length. (**c**) Simulated and measured interference fringe spectra for the N274 pattern. Both simulated spectra are normalized to the simulated fringe intensity at 22 passes. Similarly, the measured spectrum is normalized to the measured fringe intensity at 22 passes. Within the examined measurement conditions, we found that the best short-term (1 s) precision (\(\sigma_{1s}\)) for NO\({}_{2}\) is achieved at 80 mbar sample pressure and operating in NO\({}_{2}\) mode. In this case, the Allan-Werle deviation minimum (\(\sigma_{min}\)) of 0.8 pptv is achieved after 150 s averaging time. At 30 mbar, the precision is about twice lower, which is simply due to the decrease in number density caused by the lower sample pressure. In NO\({}_{x}\) operating mode, the precision decreases further, which is the result of lower repetition rate, i.e., fewer spectra are averaged within 1 s. Repeated measurements between 30 and 80 mbar in NO\({}_{2}\) mode resulted in \(\sigma_{1s}\) values consistently between 5 and 10 pptv and \(\sigma_{min}\) values between 0.8 and 2 pptv with corresponding optimal averaging times between 100 and 300 s. A similar test for NO at 80 mbar in NO\({}_{x}\) mode showed Allan-Werle deviation values of \(\sigma_{1s}\) = 70 pptv and \(\sigma_{min}\) = 20 pptv at 150 s integration time. In summary, our custom-made instrument can reach, depending on the operating conditions, sub-pptv precision for NO\({}_{2}\). This represents a factor 2-3 improvement compared to previous work on high-precision NO\({}_{2}\) measurements by QCLAS, despite the short OPL of 110 m. Table 1 summarizes the results of this work in terms of Allan deviation and those found in the literature. It only includes studies about high-precision measurements with \(\sigma_{min}\) <10 pptv. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **OPL (m) / N / D (cm)** & **Lasers** & **P (mbar)** & \(\sigma_{1s}\) (pptv) & \(\sigma_{min}\) (pptv) / Time (s)** \\ \hline
[34] & 204/434/47 & dual & 50 & 20 & 3/180 \\
[33] & 210/238/88 & dual & 53 & 10 & 1.7/60 \\
[45] & 153/174/88 & dual & 33 & 30 & 7/60 \\ \hline this work & 110/274/40 & single & 80 & 5.5 & 0.8/150 \\ this work & 110/274/40 & single & 30 & 9 & 1.6/150 \\ this work & 110/274/40 & dual & 30 & 15 & 4/150 \\ \hline \hline \end{tabular}
\end{table}