## 4 Results and Discussion  
The H\({}_{2}\)O concentration detection was based on a 2_f_-WMS approach by modulating and scanning the laser current. In order to obtain the maximum QEPAS signal amplitude, the modulation current of the laser must be optimized. The signal amplitude as a function of modulation current from 2 mA to 21 mA was shown in Figure 6. The QEPAS signal appeared and increased from 2-mA modulation current at atmospheric pressure and room temperature. When the modulation depth reached 15 mA, an optimum value of the modulation depth, the QEPAS signal amplitude tended to be stable with no significant changes.  
Figure 5: The laser wavelengths as a function of laser driving current at different temperatures.  
In the sensing system, the output power of the elliptical beam converged by the convex lens (M\({}_{2}\)) was 2.1 mW and the final QEPAS signal amplitude was 253 \(\upmu\)V. The optimum signal was obtained by optimizing the vertical position of the elliptical laser beam along the symmetry axis of the QTF prong spacing. We fixed the distance from the center of the elliptical laser to the QTF tips at 1.3 mm. As the distance continues to increase, the beam will illuminate on the bottom of the QTF which can generate a non-negligible photothermal noise. However, when the distance is too small or even negative, the acoustic energy will leak from the top of QTF, resulting in a decreasing QEPAS signal.  
The output power of the circular laser beam before passing through the Powell lens was 14.26 mW and the maximum signal value was 1.183 mV. Compared with the original circular laser beam, the optimum QEPAS signal of the elliptical beam increased by 1.4 times in the case of normalized power, which verified that strip laser beam can better promote the vibration of QTF prongs as shown in Figure 7.  
Figure 6: The QEPAS signal amplitude as a function of laser modulation current.  
Figure 7: The comparison of normalized signal between the circular beam and the elliptical beam at atmospheric pressure.  
In this case, although the number of excited gas molecules increases, the vibration amplitude of the different part of the QTF prongs are different, such as the top and bottom of QTF prongs. In fact, when the same external force is applied to every part of the inner surface of the QTF prongs, the displacement of the top part is much greater than that of the bottom part, resulting in a smaller contribution to the signal, so that the QEPAS signal did not increase as expected. In addition, due to the fact that the intensity of elliptical laser beam is Gaussian distribution, the energy is mainly centralized on the center of the laser spot, which is also an important factor in this phenomenon.  
In the laboratory environment with 1.324% H\({}_{2}\)O, the optimum SNR was calculated as 31.6 with the 1\(\sigma\) noise level of 8 uV, resulting in a minimum detection limit (MDL) of 418.6 ppmv. Accordingly, the normalized noise equivalent absorption (NNEA) of \(1.51\times 10^{-6}\) cm\({}^{-1}\) W/\(\surd\)Hz with a laser power of 2.1 mW was obtained. The NNEA of the QEPAS sensor using the exciting light with an elliptical beam is higher than the traditional QEPAS sensor in which the circular laser beam is used. This is quite understandable as only a bare QTF was used as the photoacoustic detector. Furthermore, the NNEA value can be further reduced by applying micro-resonators to the QEPAS system for an improved sensor performance.  
An Allan-Werle deviation analysis for the investigation of the long-term stability of the QEPAS sensor was performed as a function of the lock-in averaging time at atmospheric pressure. From the Allan deviation plot shown in Figure 8, the sensitivity of the QEPAS based system can be improved by increasing the averaging time, and an optimal detection limit of 16.3 ppm was obtained at the averaging time of 202 s.