## 2 Film System Design  
### Technical Parameters  
The infrared absorption spectra of methane and ethane are shown in Figure 2. The fingerprint regions of methane are 1.653 um, 3.31 um, and 7.67 um and the fingerprint regions of ethane are 3.31 um and 6.71 um. By comparison, the absorption intensity of methane at 3.31 um and 7.67 um is much higher than that at 1.653 um, and the absorption peaks of methane and ethane overlap at 3.31 um. According to the Beer Lambert law, the energy absorbed by a beam of parallel light passing through the measured gas is related to the concentration of the measured gas and the length of the gas chamber, as shown in Equation (1):  
\[I_{t}=I_{0}e^{-alc} \tag{1}\]  
In the formula, \(I_{t}\) is the intensity of transmitted light, \(I_{0}\) is the intensity of incident light, \(\alpha\) is the absorption coefficient of gas, which varies with wavelength, \(l\) is the thickness of the absorbing substance (i.e., the length of the optical path), and \(c\) is the concentration of the measured gas. By deforming Formula (1), we can obtain:  
\[c=\frac{1}{\alpha l}ln\frac{I_{0}}{I_{t}} \tag{2}\]  
From Equation (2), it can be known that, if the absorption coefficient of the measured gas and the thickness of the absorbing substance are known, the concentration of the  
Figure 1: Structure diagram of methane and ethane gas detection and recognition system (the data in the figure are sourced from the uncooled infrared thermal imaging detection prototype developed by Changchun University of Science and Technology). measured gas can be calculated by measuring the incident light intensity and transmitted light intensity. Secondly, the detection wavelength is determined based on the infrared absorption peak of the target gas, and then the gas's absorption is obtained by querying the database to collect coefficient \(\alpha(\lambda)\), and then spectral response tests are performed on the infrared light source and infrared detector, denoted as \(S(\lambda)\) and \(D(\lambda)\), respectively. When the temperature and pressure are fixed, the gas absorption coefficient at a certain wavelength remains constant, as expressed in Equation (3). For the sake of simplicity in calculation, assuming that the bandpass filter film is an ideal case, the expression for the transmittance of the bandpass filter film is shown in Equation (4):  
\[\alpha(\lambda)= \begin{cases}\alpha_{0}(\lambda),\lambda_{0}-\Delta\lambda^{ \prime}\leq\lambda\leq\lambda_{0}+\Delta\lambda^{\prime}\\ 0,\lambda<\lambda_{0}-\Delta\lambda^{\prime}\text{ or }\lambda>\lambda_{0}+\Delta \lambda^{\prime}\end{cases}  \tag{3}\]  
\[T_{f}(\lambda)= \begin{cases}\begin{array}{c}1,\lambda_{0}-\Delta\lambda\leq \lambda\leq\lambda_{0}+\Delta\lambda\\ 0,\lambda<\lambda_{0}-\Delta\lambda\text{ or }\lambda>\lambda_{0}+\Delta\lambda\end{array}\end{cases}  \tag{4}\]  
In the formula, \(\lambda_{0}\) is the center wavelength of the target gas detection, \(2\Delta\lambda^{\prime}\) is the width of the gas absorption peak, and \(2\Delta\lambda\) is the FWHM of the bandpass filter film. So, when the light emitted by the infrared light source passes through a gas chamber with a  
Figure 2: Infrared absorption spectra of methane and ethane gases. (**a**) Methane gas absorption spectra. (**b**) Ethane gas absorption spectra (image sourced from [PERSON], [PERSON], Mallard WG.NIST Standard Reference Database Number 69 (DB/OL), 15 November 2018). concentration of \(c\) and a length of \(l\), assuming there is no interference from other gases, the transmitted light intensity \(T_{g}(\lambda)\) can be obtained from Equation (5):  
\[T_{g}(\lambda)=\left\{ \begin{array}{l}e^{-\alpha_{0}(\lambda)lc},\lambda_{0}- \Delta\lambda^{\prime}\leq\lambda\leq\lambda_{0}+\Delta\lambda^{\prime}\\ 1,\lambda<\lambda_{0}-\Delta\lambda^{\prime}\text{ {or }}\lambda>\lambda_{0}+\Delta\lambda^{\prime} \end{array} \right.