## 6 Sensor Sensitivity  
The sensor sensitivity is the minimum concentration that can be detected by the system. This implies that the sensitivity is the concentration for which the signal to noise ratio (SNR) is equal  
Figure 7: **(a,c)** Measured channel signals showing the effect of varying the light intensity. (**b,d**) calculated depth of modulation showing that it is unaffected by light intensity variations. For (**a,b**) the C\({}_{2}\)H\({}_{2}\) concentration was 9% and for (**c,d**) it was 40%.  
to unity (\(S=N\)) [26]. Afterwards, considering that the sensor output has a linear behavior, therefore, it is possible to rewrite the relationship \(S=N\) as \((\Delta D_{M}^{\text{E}}/\Delta C)C=\sigma\), where \(\sigma\) is the standard deviation over the time of the depth modulation signal. Here, as our sensor has a nonlinear output, therefore, we grouped the measurements into four intervals that can be fit by a linear function \(D_{M}^{\text{F}}=mC+n\); the details of each range and their corresponding function constants are listed in Table 1. Moreover, the depth of modulation as a function of time was recorded and its corresponding average value and standard deviation were calculated. This procedure was performed for one concentration level within each range. For instance, the depth of modulation as a function of time for a \(C_{\sigma}=9\%\) concentration is shown in Figure 8a, which has an average value of 0.522 and a standard deviation of \(2.9\times 10^{-3}\). By using these values, it is possible to estimate that the system sensitivity is 521 ppm for a concentration range from 0 to 20%. The sensor sensitivity for different concentration ranges are given in Table 1. Furthermore, it is important to comment that the sensor response can be faster by reducing the order of the low pass filter process, however, it will reduce the sensor sensitivity. For instance, in Figure 8b, the transition region is shown in detail and an appreciation can be gained in how the \(D_{M}\) changes when the concentration is varied and considering two different low pass filters (LPF1 and LPF2). For this work, LPF1 was a high order low pass filter that was used to remove the sensitivity of 521 ppm. LPF2 was a first order low pass filter, which makes it possible to reduce the response time (Figure 8b), however, it has a penalty in the sensitivity since it increases up to 2578 ppm. Therefore, depending on the combination of required parameters such as the response time and the sensitivity, the gas cell and the low pass filter parameters can be adjusted. Finally, it is important to point out that our tunable optical fiber laser is capable to be finely tuned over different spectral windows where absorption lines due to different molecules can occurs. By means of the VOA, spectral windows between 1530 and 1565 nm can be selected and these can be scanned by changing the temperature of the silicon wafer. Moreover, other wavelength windows of the telecommunications region can be achieved by changing the laser gain medium. This is useful for spectroscopy applications since there are different molecules that can be detected in this spectral region. Also, the overall cost of the system is relatively competitive since it can be implemented with standard optical telecommunication components.