# Near-Infrared Quartz-Enhanced Photoacoustic Sensor for H\({}_{2}\)S Detection in Biogas
## 3 Optimization and Performance of the H\({}_{2}\)S Sensor  
The QTF was coupled with a pair of resonator tubes to realize a QEPAS supertrophone, as shown in Figure 2c. As discussed, in on-beam configuration, the QTF is located between the tubes to probe the acoustic wave excited in the absorbing gas within the tubes. The internal diameter and the length of the two tubes influence the ultimate supertrophone performance [24; 25]. For the custom QTF, [PERSON] et al. [34] optimized the geometrical parameters. The study pointed out that both tubes must be 23 mm long and the optimal diameter must be 2.6 mm. In this way, the signal-to-noise ratio (SNR) increases by a factor of 40, compared to the case of a bare custom QTF. The results mentioned above are extremely useful in the design and assembling of the H\({}_{2}\)S QEPAS supertrophone. Hence, the geometrical parameters mentioned above were adopted in this work. The position of both tubes along the QTF axis, namely the axis parallel to the prong and passing between them, has to be optimized in terms of the QEPAS  
Figure 1: Schematic of the quartz-enhanced photoacoustic spectroscopy (QEPAS) sensor architecture. EDFA: Erbium-doped fiber amplifier. TA: Transimpedance amplifier. Figure 2: **(a)** Sketch of the custom QTF. **(b)** The photograph of the custom QTF. **(c)** The photograph of the acoustic detection module which includes a custom QTF and a pair of resonance tubes. peak signal and noise. Hereafter, the QEPAS peak signal reported in all graphs corresponds to the maximum absorption in a spectral scan of the selected H\({}_{2}\)S absorption line. The position of tubes has to be moved from the top to the bottom, along the QTF axis between the two prongs. The distance between the center position of the tube and the top of the tuning fork is defined as \(y\). The investigation was performed while a certified concentration of 50 ppm of H\({}_{2}\)S in nitrogen was flowing within the ADM, at atmospheric pressure. The experimental QEPAS peak signals, normalized to the highest value, at different tubes positions along the QTF axis are shown in Figure 3a. The QTF signal reaches its maximum value at \(y=1.0\) mm, then the signal decreases slowly with the increase of \(y\), retracing the lateral displacement of a vibrating cantilever. For each position, the QTF quality factor has been measured as a function of \(y\), as shown in Figure 3b. When tubes are located close to the top of prongs (\(y=0\)), the quality factor is the same as the bare QTF. The quality factor drops down to \(\sim\)6300 at \(y=2.0\) mm, 1.0 mm far from where the maximum QEPAS signal has been recorded. Figure 3c reports the signal-to-noise ratio (SNR) as a function of tube position. When \(0<y<1.4\), the SNR increases until it reaches the maximum at \(y=1.4\) mm. When \(1.4\) mm \(<y<2.1\) mm, SNR changes less than 1% with respect to the maximum value. At \(y\) > 2.1, SNR gradually reduces. Hence, the QEPAS signal and the SNR reaches maximum values at different \(y\) values. This behavior can be explained by analyzing the noise level of the spectrophone. It has been acquired while pure nitrogen was flowing within the ADM, at atmospheric pressure. The noise measured when both the laser power was boosted at 1.6 W and when the amplifier was off is reported in Figure 4. As a comparison, the noise acquired with the superophone composed of the standard QTF and tubes 4.0 mm-long with an internal diameter of 800 \(\upmu\)m is also reported, with the same experimental conditions [25]. Figure 3: (**a**) QEPAS peak signal, (**b**) quality factor and (**c**) signal-to-noise ratio as a function of the position of tubes \(y\), measured starting from the top of the QTF. The data shown in the above figure were obtained while 50 ppm of H\({}_{2}\)S in N\({}_{2}\) was flowing within the acoustic detection module, at high optical power (1.6 W), atmospheric pressure and room temperature.