## 3 Results and Discussion
### THz Absorption Spectroscopy Measurements
According to the Lambert-Beer law, the area under the absorption profile is directly proportional to the density of NH\({}_{3}\) and given by  
\[\int_{\text{line}}\text{Absorbance}(\
u)\text{ d}\
u=n_{\text{NH}_{3}}\,L\,S(T), \tag{2}\]  
Figure 6: Spectral absorption profile of the R(7,5)-transition of \({}^{15}\)NH\({}_{3}\) at 158.257314 cm\({}^{-1}\), measured in an RGC with NH\({}_{3}\) (pressure of 1.6 mbar, length of 15 cm) using a laser tuning frequency of 201 Hz and a tuning range of 564 mA to 590 mA. The measured data are averaged over 2000 single measurements. A Voigt fit was fitted to the profile; the corresponding residual is given in the bottom part of the figure. where \(L\) is the absorption length, \(S(T)\) the line strength of the investigated absorption transition [26; 27], and \(n_{\text{NH}_{3}}\) the density of NH\({}_{3}\), which is related to the pressure \(p\) by the ideal gas law (\(p=n_{\text{NH}_{3}}\,k_{\text{B}}\,T\), with \(T=296\) K). Following this, the pressure inside the gas cell was determined from the absorption spectrum shown in Figure 6, resulting in \((1.65\pm 0.10)\) mbar. A similar value was obtained after analysing the measurements with the broader tuning range of 480 mA to 600 mA, i.e., the red curve in Figure 5a. The indicated possible error of approximately 6% accounts for uncertainties in the estimation of the baseline and \(I_{0}\) as well as uncertainties in the fitting. The obtained result is in excellent agreement with the known pressure of (1.61 \(\pm\) 0.01) mbar, determined using frequency-comb-based Fourier-transform spectroscopy. This demonstrates that the pyroelectric receiver allows for accurate measurements and can be reliably used as detector for absorption spectroscopy measurements in the THz range. In a previous work by [PERSON] et al. [18], a comparable pyroelectric detector in a THz-QCL-based cryogen-free spectrometer was used but with a 3 dB bandwidth of only 30 Hz. The THz QCL was tuned in a similar fashion as was done in this study but with a tuning frequency that was too high for the detector's bandwidth, resulting in the same type of deformations as we observed when using a bolometer as detector [15; 16]. The PR No1 detector enables fast data acquisition and high sensitivity, and, in particular, its extraordinary bandwidth avoids any deformations of the absorption features. Lastly, similar measurements were carried out with the pyroelectric receiver and the bolometer to investigate how the noise level of the pyroelectric receiver compared to that of the bolometer. To this end, absorption spectra similar to the one shown in Figure 6 were recorded for a variation of the total measurement time using laser tuning frequencies of 11 Hz and 201 Hz when measuring with the bolometer and the pyroelectric receiver, respectively. The total measurement time was given by the number of averages multiplied by the chopper frequency, i.e., half the laser tuning frequency, as the oscilloscope was triggered on the chopper signal. The measurements were performed in a comparable configuration, as illustrated in Figure 2a; however, no purging with nitrogen was performed, as the increase in the signal intensity would cause a saturation of the bolometer. Figure 7 shows the standard deviation of the noise of the absorption spectra as a function of the total measurement time on a double logarithmic scale. For both the bolometer and the pyroelectric receiver, the results lie on a line with a slope of \(-0.5\), as would be expected for shot-noise limited detection, implying that white noise is the dominating noise contribution for measurement times below 10 s. On these timescales, the SNR can be effectively improved by increasing the measurement time. The faster measurement rate possible with the pyroelectric receiver allows for a higher number of averages within the same measurement time, which compensates to some extent for its lower SNR.