## 3 Experimental Phenomenon and Theoretical Analysis
### Experimental Results and Discussion  
To further verify the theoretical results, the minimum detectable light intensity of the system (sensitivity) needs to be calculated. The residual between the measured data and the spectra fitted in the absence of the etalon effect represents the system's sensitivity.  
Firstly, it is necessary to eliminate this special effect. The most effective way is to eliminate the etalon effect caused by the feedback light from the end mirror. Depending  
Figure 4: (a) Simulated transmitted light intensity of M1 and M2 with different transmission loss; (b) Ripple amplitude variation curve with transmission loss of M2.  
on the application requirements of the optical cavity, \"optically glued prisms or spherical mirrors with different radius of curvature\" can be selected to attenuate or eliminate this phenomenon. Among all the current methods, \"optically glued prism\" is the most practical method in our experimental setup. Therefore, a prism is optically glued onto the back of M1, which can fully destroy the two surfaces parallel to the mirror to eliminate this asymmetric etalon effect. The results of the OF-CEAS signal measurement are shown in Figure 5. The periodic spectral fluctuation of M1 disappears, and four absorption peaks can be observed in this experimental result.  
Then, after eliminating this symmetric etalon effect, the residual water vapor concentration in the cavity was set to 1.5% (corrections were made based on experimental results), the transmission signal of M2 in the presence of absorption was simulated according to Equation (3) and the HITRAN 2020 database. The fitting residual results of M2 are shown in Figure 6, the standard deviation of the fitted residuals of the measured signal is \(8.18\times 10^{-3}\), larger than the theoretical ripple amplitude of M2 of \(6.5\times 10^{-3}\). The experimental results agree well with the theoretical simulations, and it is clear that the ripple effect of the folded mirror M2 is too weak to be detected by the system.  
In summary, since the loss of the mirror is inversely proportional to the ripple amplitude, the ripple amplitude of the folded mirror is much smaller than that of the end mirror. The ripple with less than the minimum detectable light intensity cannot be measured by the system. Finally, the CEAS spectrum is calculated according to Equation (3), and the results are shown in Figure 7.  
As is shown in Figure 7, four water vapor absorption peaks can be accurately measured by the improved system. The absorption coefficient can be obtained by Equation (3). The \"empty cavity\" ring down time \(\tau_{0}\) is 8.2 \(\upmu\)s at 1510 nm, the cavity corresponding loss is 191.8 ppm in a single pass, and the equivalent reflectivity \(R_{loss}\) is 0.9998082. A minimum detectable absorption coefficient of \(\alpha_{\rm min}\) = 8.33 \(\times\) 10\({}^{-9}\) cm\({}^{-1}\) can be obtained by the standard deviation of the fitting residuals. The experimental results indicate that the precision of cavity-enhanced absorption spectroscopy for the detection of trace gases is much improved.  
Figure 5: The OF-CEAS cavity transmitted signal optically glued onto a wedge mirror. The OF-CEAS cavity transmitted signal of M1 (black). The OF-CEAS cavity transmitted signal of M2 (red).