## 2 Materials and Methods
### FTIR Description
Figure 2c provides the example of the N\({}_{2}\)O, for which the absorption bands need to be selected in an area located outside the CO\({}_{2}\) absorption range, and between the CO absorption peaks. More detailed discussion on spectral regions for the analysis and interferences can be found in the literature [28; 47; 104; 118; 119]. Estimations of cross-sensitivities simulating exhaust gas gave an influence of <<1% for most compounds (NO\({}_{2}\), CO, NH\({}_{3}\)) [114], but >1% for acetaldehyde (CH\({}_{3}\)CHO), acetone (CH\({}_{3}\)COCH\({}_{3}\)), C\({}_{6}\)H\({}_{6}\), and C\({}_{7}\)H\({}_{8}\), because their absorption spectrums are not sharp and strong, and/or the region of possible quantification is small due to the co-existing components. The actual interference might be different if there are interfering compounds not included in the software, if some wavelengths are saturated due to high concentrations, and/or the resolution is not enough to resolve the species, e.g., water, NO, NO\({}_{2}\), and NH\({}_{3}\)[120]. Figure 2: _Cont._  
Principally, transmission-FTIR spectroscopy follows the Lambert-Beer law. Consequently, for a given optical path length, a linear relationship between the compound concentration and the absorbance mediated by this compound can be assumed. However, the output voltage of the detector is not a linear function of the incident radiation power [121] and non-linearity can be seen for components such as CO\({}_{2}\), H\({}_{2}\)O, CO, and NO\({}_{x}\) with a wide range of variations [8]. Thus, for some components, the calibration might not be a linear function, but quadratic, cubic, etc. Because the mirror travels only a finite distance, the interferogram is truncated, and the Fourier transform results in a spectrum with broader features and spurious oscillations at the wings of the features. An apodization function is applied to reduce the magnitude of these oscillations but further broadens the spectral features. This broadening causes the instrument to have a nonlinear response to the spectrum. Figure 2: Example of absorbance versus wavenumbers: (**a**) for various species with concentrations of 398 ppm (CO), 97 ppm (NO), 136 ppm (NO\({}_{2}\)), 93 ppm (N\({}_{2}\)O), 93 ppm (NH\({}_{3}\)), 0.8% (CO\({}_{2}\)), 2.03% (H\({}_{2}\)O). For better visualization, the spectra of H\({}_{2}\)O and CO\({}_{2}\) were reduced by a factor of 10 and displayed in an inverted axis. For the same reason, NH\({}_{3}\) and HCN spectra were increased by a factor of 2 and 4, respectively; (**b**) NH\({}_{3}\), area B of panel (**a**); (**c**) N\({}_{2}\)O, area C of panel (**a**). changes in absorption of the various gases being measured [122]. This can be modeled and corrected. FTIR requires no daily calibration per se. This is possible because the daily background/zero scan is compared point per point to the measurement spectrum and compensates for any instrument drift in the final absorbance spectrum. Since the same number of molecules always absorb the same fraction of incident energy (independent of the total amount of energy), the calibration factor remains the same for a given compound and wavenumber and as a result there is no span drift or calibration drift [115]. However, since background and measurement spectrums are acquired successively, the FTIR needs to be very stable, in terms of infrared source, detectors, but also in terms of composition of the gas included in the instrument. Such stability is insured by keeping the instrument always on (heated), and by purging the optical system with dry gaseous N\({}_{2}\). The sampling lines and the sampling cell for exhaust gas application need to be heated above 100 \({}^{\circ}\)C (usually 191 \({}^{\circ}\)C) to avoid water condensation, which would lead to an underestimation of the hygroscopic compounds (e.g., NH\({}_{3}\)).