# Near-Infrared Quartz-Enhanced Photoacoustic Sensor for H\({}_{2}\)S Detection in Biogas
## 3 Optimization and Performance of the H\({}_{2}\)S Sensor
When the optical power of the erbium-doped fiber amplifier is 1.6 W, the noise floor is 44 \(\upmu\)V when the 32.7 kHz QTF-based superchphone is used, 12.6 times higher than that measured for custom QTF-based superchphone (3.5 \(\upmu\)V). Hence, the ultimate noise level of the 32.7 kHz QTF-based superchphone is clearly dominated by the photothermal noise contribution. With the custom QTF-based superchphone, the noise floor increases from 2.32 \(\upmu\)V to 3.5 \(\upmu\)V when the laser power passes from 21 mW to 1.6 W, allowing to affirm that the photothermal noise contribution is negligible. The 1\(\sigma\) noise level of the custom QTF-based superchphone increases from 2.1 \(\upmu\)V to 2.6 \(\upmu\)V when the power of the exciting laser varies from milliwatt level (21 mW) to watt level (1.6 W). These values are comparable with the theoretical thermal noise of 2.3 \(\upmu\)V, estimated by using [19]:  
\[\sqrt{V_{m}^{2}}\ =\ R_{g}\sqrt{\frac{4K_{B}T}{R}}\sqrt{\Delta f}, \tag{1}\]  
where \(R_{g}\) is the feedback resistor of the QTF amplifier, \(K_{B}\) is the Boltzmann constant, \(T\) is the temperature, \(\Delta f=0.833\) Hz, and \(R\) is the electrical resistance. By modeling the QTF as an RLC series circuit, the electrical resistance can be related to the quality factor by the following relation:  
\[R\ =\ \frac{1}{Q}\sqrt{\frac{L}{C}}, \tag{2}\]  
where \(L\) is the QTF inductance and \(C\) its capacitance. Thus, variations of the quality factor affect the electrical resistance that in turn causes changes in the thermal noise. Thus, SNR in Figure 2c is affected both by QEPAS signal and quality factor, which have different trends as a function of \(y\). This explains why SNR and QEPAS signal reaches their maximum values at different \(y\) positions. The variation of QEPAS signal with the optical power of the exciting laser in the range 5 mW-1.6 W has been recorded at three different positions of tubes, \(y=250\)\(\upmu\)m, 1.2 mm, and 2.25 mm. The results are plotted in Figure 5.  
Figure 4: Noise level acquired for custom QTF-based superchphone when the laser power is 21 mW (blue line) and 1600 mW (black line). Noise level for standard 32.7-kHz QTF-based superchphone when the laser power is 1600 mW (red line). The data shown in the above figure was obtained while 50 ppm of H\({}_{2}\)S in N\({}_{2}\) was flowing within the acoustic detection module, at atmospheric pressure and room temperature. For each position, the QEPAS signal scales linearly with the laser power, with different slopes. Thus, at high optical power levels, the choice of the optimized tube position is more critical. Hereafter, the tubes will be located at \(y=1.4\) mm, where the maximum SNR was recorded. In the 2_f_-WMS technique, the QEPAS signal intensity is related to the laser modulation depth and the linewidth of the gas absorption line. Hence, the laser modulation depth was optimized at atmospheric pressure. The laser modulation depth optimization was carried out by varying the amplitude modulation of the current dither while a certified concentration of 50 ppm H\({}_{2}\)S:N\({}_{2}\) was flowing in the ADM. The QEPAS peak signals of the 2_f_-WMS scan were acquired at different laser current modulation depths. The results are depicted in Figure 6.  
Figure 5: QEPAS signal plotted as a function of the laser power acquired at three different tube positions, 0.25 mm (**a**), 1.20 mm (**\(\bullet\)**), and 2.25 mm (**\(\blacksquare\)**). Solid lines are best fits to experimental data. The data shown in this figure were obtained while 50 ppm of H\({}_{2}\)S in N\({}_{2}\) was flowing within the acoustic detection module, at atmospheric pressure and room temperature. Figure 2:0 QEPAS signal plotted at different current modulation depth. Solid line is a guide for eyes. The data shown in this 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.