# Advances in High-Precision NO2 Measurement by Quantum Cascade Laser Absorption Spectroscopy
## 2 Materials and Methods
### Description of the Dual-Laser Spectrometer
#### 2.1.1 Instrument Inlet and Custom-Made Multipass Cell  
The MPC has been developed with special focus on the specific properties of NO\({}_{2}\), known for its reactivity toward surfaces, but also aiming for an optical path length (OPL) of at least 100 m and a high mechanical stability to achieve the targeted precision of a few pptv NO\({}_{2}\). The MPC body is machined out of a single piece of electro-polished aluminum and closed by two high-vacuum KF-flanges and a top lid. All these parts are coated (SilcoNert@2000, SilcoTek, Bellefonte, PA, USA) to minimize surface losses of NO\({}_{2}\). For the same reason, all the gas handling elements up to the MPC are either made out of polytetrafluoroethylen (PTFE) or SilcoNert-coated, while the entire sampling line uses perfluoralkoxy (PFA) tubing. Right after the intake point, the air flows through a solenoid three-way valve (International Polymer Solutions, Irvine, CA, USA), used to switch between ambient and NO\({}_{x}\)-free air, followed by a PTFE membrane filter (TE38, Cytiva Europe GmbH, Freiburg, Germany; pore \(\varnothing\) = 5.0 \(\mu\)m). A coated stainless steel needle valve is placed immediately before the MPC to adjust the sample pressure in the range of 30-100 mbar. This low pressure regime improves the selectivity of the instrument by leading to narrower spectral line widths due to the reduced pressure broadening effect on the absorption lines. A diaphragm pump (KNF Neuberger GmbH, Freiburg, Germany) is used to maintain a constant flow of 0.8 L/min (at ambient pressure) through the system. To optimize the optical performance of the MPC, an extensive investigation on the beam reflection pattern on the mirrors was performed. Previous work have shown that overlapping of neighboring reflection spots on the mirrors creates interference fringes on the measured transmission spectrum that may impact the precision and long-term stability of the measurements [37, 43]. Therefore, two key aspects were considered, searching for patterns with: (i) the highest possible mutual distance between neighboring spots in general; and (ii) a special focus on the lowest possible overlap between spots separated by a low number of passes through the MPC. This latter case corresponds to fringes with a low FSR that more likely interfere with the measurements. Following the approach described by [PERSON] et al. [37], a custom-made software was developed to survey all possible patterns and to identify those fulfilling the above mentioned requirements. A reflection pattern is defined by four independent parameters: the mirrors distance (\(D\)), the radii of the astigmatic mirrors (\(R_{x}\) and \(R_{y}\)) and the relative rotation angle between the two mirrors (\(\tau\)) around the optical axis. Within the full range of each of these parameters, a large number of patterns exist that fulfill the re-entrant condition, i.e., the beam exits  
Figure 2: Measured transmission spectrum (red dots, averaged over 10\({}^{4}\) spectral scans, corresponding to 1 s acquisition time) of an ambient air sample containing 10 ppbv of NO\({}_{2}\) and 0.1% (absolute) of H\({}_{2}\)O, along with the associated Voigt profile (blue line) and baseline fit (green line). The fit residual is shown on the top panel. the cell after a certain number of reflections (\(N\)). Limiting the range for \(\tau\) (\(\pm\) 15\({}^{\circ}\)) and the astigmatism (ratio \(R_{x}/R_{y}\), 10%) for a given mirror distance (\(400\pm 5\) mm) reduces the number of possible re-entrant patterns to a few hundred. The final choice among all these possibilities requires estimating the intensity and spectral positioning of interference fringes resulting from spots overlapping on the mirrors reflective surfaces. Based on this survey, a pattern of 366 passes (abbreviated as N366) corresponding to an OPL of 146 m was selected (Figure 3). This pattern is obtained with a mirror spacing of 40 cm and twist of 5\({}^{\circ}\) for mirror radii of 610.0 and 676.6 mm. These parameters were calculated based on the paraxial approximation.