# 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
Further validation by using 3D ray-tracing simulation (FRED, Photon Engineering, Tucson, AZ, USA) showed that a small adjustment of the mirror distance (in the order of 0.1 mm, i.e., 0.025% of the paraxial value) is necessary in order to perfectly fulfill the re-entrant condition under non-paraxial conditions. The patterns obtained with the ray-tracing simulation shown in Figure 3 correspond to the adjusted mirror distance. A mirror diameter of 80 mm was then chosen as a good compromise between spots spreading and MPC footprint and volume (\(\approx\) 3 L). Considering the pattern's high number of passes, it has high demands on the mirror surface quality and reflectivity. Therefore, the astigmatic mirrors were custom-made by diamond-turning (LT Ultra-Precision Technology, Herdwangen-Schonach, Germany) of a NiP coated (100 um) aluminum substrate (RSA 6061). This assures the highest surface quality, which is then further homogenized by a post-polishing process, resulting in a surface roughness better than 2 nm \(R_{a}\). Finally, a custom-made coating (LohnStar Optics, Escondido, CA, USA) was applied to enhance the reflectivity (R > 99.3%) for both the 1600 and 1900 cm\({}^{-1}\) spectral ranges. First tests with this pattern showed that the power on the detector was too low, thus limiting the detection limit. Therefore, an alternative pattern with 274 reflections, using the same mirrors, was chosen, which proved to be a better compromise between optical SNR and final sensitivity (in terms of concentration). This pattern is shown in Figure 3 and corresponds to \(D\) = 39.7 cm and \(\tau\) = 4\({}^{\circ}\). The calculated OPL with the N274 pattern is 109.02 m. This value was confirmed experimentally by measuring the time delay between the optical signal received by the detector when the laser beam is either passing or bypassing the MPC. This resulted in \(109.1\pm 1.7\) m (1 \(\sigma\)) which agrees well with the value obtained from the simulation. The simulated interference fringes spectra for the N366 and N274 patterns are shown in Figure 3. Both spectra are normalized to the intensity of the 22 passes fringe of the N274 pattern to allow for comparison. A measured fringe spectrum for the N274 pattern is also shown in Figure 3. These data are obtained by applying a fast Fourier transform (FFT) to the normalized residual from a polynomial fit of the measured transmission spectrum of NO\({}_{x}\)-free synthetic air (Messer Schweiz AG, Lenzburg, Switzerland; abbreviated in the following text and figures as synthetic air). The measured spectra are normalized to the measured intensity of the strongest fringe, corresponding to 22 passes. The overall agreement between measurement and simulation for N274 is good in terms of both fringe position and relative intensity. The only exceptions are the fringes at four and six passes equivalent FSR in the measured spectrum, which may result from imperfect alignment. This comparison between measured and simulated spectra supports the simulation approach for estimating interference fringes intensity. The comparison between the N274 and N366 simulated spectra shows that, despite the higher number of passes of the latter one, its predicted fringe intensity is similar to or lower than for the N274 pattern. This indicates that a further improvement of the sensitivity would be possible by using a more powerful QCL and the N366 pattern.