# Towards a Fast, Open-Path Laser Hygrometer for Airborne Eddy Covariance Measurements
## 3 Static Validation with a Dew Point Mirror and Spectroscopic Performance  
The spectroscopic performance and accuracy of the new optics design are validated with constant gas flow, but under stable H\({}_{2}\)O amount fraction conditions with a spectrometer prototype with the angled coupling optics in an open-path configuration. For this, the prototype, shown in Figure 4, is placed inside a climate chamber that is continuously purged with dry air. In this configuration, we reduced the H\({}_{2}\)O concentration from above 12,000 ppm to below 1000 ppm over the course of four hours. The climate chamber was heated to 30 \({}^{\circ}\)C to reduce H\({}_{2}\)O adsorption effects on the chamber walls. The slow concentration change makes it possible to use a dew point mirror (DPM) hygrometer as an SI-traceable reference. The inlet of the DPM, as well as temperature and pressure sensors, was placed near the optical plane of the multipass cell.  
Figure 3: (**a**) CAD rendering of the multipass cell with the infrared laser beam visualized in red. (**b**) Top view of the optics. The dashed blue line shows the position of the optical plane of the multipass cell visible in (**a**). Mirrors 1 and 2 are concave mirrors, with a focal length of 85 and 25 mm. Mirror 3 is a plane mirror.  
Figure 5 shows a linear regression of the dTDLAS and DPM H\({}_{2}\)O measurements between 1300 ppm and 11,500 ppm. The systematic deviation between both instruments is 2.61% with a good linearity, as indicated by the R\({}^{2}\)-value being close to one. The maximum relative deviation between dTDLAS and DPM is 2.2%. All observed deviations are well within the predicted uncertainty of 4.5% for the dTDLAS hygrometer and 2.5% for the DPM. It should be noted that an automatic mirror check of the DPM and the subsequent slow stabilization of the dew point temperature made it necessary to exclude the data between 2600 ppm and 6000 ppm from the regression due to non-equilibrated conditions.  
To investigate the spectroscopic performance of the instrument, two water amount fractions, one for the lower and one for the upper end of the regression shown in Figure 5, are analyzed. The laser was modulated at a frequency of 139.8 Hz. The data acquisition hardware used in this static test can evaluate approximately 10% of the scanned absorption profiles. Ten of these recorded profiles are then averaged before the first-principles evaluation method described in Section 2.1 is applied. The data for each absorption profile shown in Figure 6 were acquired over a period of 0.72 s, with an effective total measuring time of 0.036 s. A good estimate of the precision of the instrument can be obtained by dividing  
Figure 4: CAD rendering of the prototype to validate the optical setup. (**a**) shows the front view and (**b**) the back view. The infrared laser beam is visualized in red.  
Figure 5: Correlation plot of the dTDLAS vs. the DPM measurements between 1300 ppm and 11,500 ppm with linear regression. Data where the DPM performed an automatic mirror cleaning are excluded from this plot. The systematic error is around 2.61%.  
the concentration by the signal-to-noise ratio (also called noise equivalent concentration, NEC). As the focus of this evaluation is the performance of the newly designed optics, the influence of the discrepancies between the line shape and the Voigt profile is excluded using the local standard deviation 10\({}_{\text{local}}\). In Figure 6a, the NEC at 1321 ppm is 1.01 ppm, and in Figure 6b, the NEC at 11,542 ppm is 0.86 ppm. To compare these results with other hygrometers, the precision is normalized with the length of the optical path and the square root of the temporal bandwidth (1.4 Hz). This results in 3.6 ppm mHz\({}^{-1/2}\) at 1321 ppm and 3.0 ppm mHz\({}^{-1/2}\) at 11,542 ppm.