## 2 Experiments and Results
The minimum signal amplitude was obtained when the laser spot was positioned at the center of the QTF prong (Line B). For higher values, the signal amplitude increased to \(\sim\)40% of the maximum value at Line C. The signal variation is related to the electrode layer pattern on the QTF surface. Most of the area of the QTF prong is coated with a silver layer, which has a high reflectivity for the laser beam [31]. There was no coating In the vicinity of Line A and Line C, which means that more photons were absorbed by the QTF, resulting in a higher signal amplitude. The subsequent decrease beyond Line C was due to the decrease of photothermal effects on the QTF surface. Figure 3: **(a)** Diagram of quartz-enhanced photothermal-acoustic spectroscopy. **(b)** Lines A, B, C represent the edges and central line of the QTF prong, respectively. The values of \(x_{0}\) and \(y_{0}\) represent the distance between the laser-spot center and the QTF y-axis and \(x\)-axis, respectively. **(c)** The normalized  
quartz-enhanced photothermal-acoustic spectroscopy (QEPTAS) signal amplitude as a function of laser spot position, \(x_{0}\). The error of amplitude was less than 1%. In order to determine the optimum laser excitation of the QEPTAS system, the laser wavelength modulation depth was varied from 0.2 cm\({}^{-1}\) to 0.65 cm\({}^{-1}\) to obtain a maximum 2\(f\) QEPTAS signal amplitude. The experimental results shown in Figure 4 illustrate the influence of the laser modulation depth on the QEPTAS signal. In the wavelength modulation, the theoretical modulation index m, defined as the ratio between the modulation depth and the half width at half maximum of the absorption profile, was \(\sim\)2.2, violating the hypothesis of the Taylor series expansions [33]. However, the optimal modulation depth to achieve the maximum signal needs to be optimized experimentally. The signal amplitude increased monotonically with the laser modulation depth and, for values higher than 0.47 cm\({}^{-1}\), the signal amplitude increased only by \(<\)1%. The 2\(f\) signal amplitude started to decrease when the modulation depth was larger than 0.55 cm\({}^{-1}\). Therefore, the optimum laser modulation depth was \(\sim\)0.47 cm\({}^{-1}\). The performance of the QEPTAS sensor was evaluated by detecting H\({}_{2}\)O in ambient air. The QEPTAS acoustic detection module (ADM) was positioned at distances of 1 m and 2 m from the laser head. The emission wavelength of the laser was tuned from 7306.31 cm\({}^{-1}\) to 7308.01 cm\({}^{-1}\) to target the H\({}_{2}\)O absorption line at 7306.75 cm\({}^{-1}\), with a line intensity of \(1.8\times 10^{-20}\) cm/molecule. Figure 5 shows the QEPTAS signal amplitude of \(1.25\times 10^{-3}\) V and \(2.4\times 10^{-4}\) V, corresponding to the QEPTAS ADM distances of 1 m and 2 m, respectively. The 1\(\sigma\) noise was obtained by changing the laser injection current to tune the emission wavelength away from the H\({}_{2}\)O absorption line. The calculated 1\(\sigma\) standard deviation for distances of 1 m and 2 m were 1.19 \(\upmu\)V and 1.02 \(\upmu\)V, respectively. The ambient H\({}_{2}\)O concentration of 1.3% was determined by direct absorption spectroscopy [34]. For Figure 5, the measurement took \(\sim\)5 min. Figure 4: Optimization of laser modulation depth. Figure 5: Optimized QEPTAS 2\(f\) signal obtained at distances of 1 m and 2 m.  
The calculation of the normalized noise equivalent absorption (NNEA) coefficient is given by Equation (2):  
\[NNEA=\frac{a_{min}P_{0}}{\sqrt{\Delta f}}, \tag{2}\]  
where \(a_{\text{min}}\), \(p_{0}\), and \(\Delta f\) are the minimum detectable absorption coefficient at an SNR = 1, the laser optical power, and the equivalent noise detection bandwidth, respectively [35].