## 2 Materials and Methods
### Image Processing
#### 2.2.1 Preprocessing for DAS  
A preprocessing of the raw images is required to apply the BLL (\(I=~{}I_{0}\,exp(-A)\)) in an appropriate manner. The detected or backscattered light intensity is given by \(I=I(x,y,\lambda)\) and includes ideally only the signature of a methane absorption \(A(x,y,\lambda)\), as well as the intensity modulation of the laser during the line scan \(~{}I_{0}(\lambda)\). A suitable preprocessing method is described in detail in Appendix A and shown in Figure 2a. It clearly shows a local absorption signature of the 0.25 mL/min methane leak in the middle row of the image sequence, as well as a global intensity modulation of the laser during the line scan. It yields a three-dimensional representation of the BLL as follows:  
\[I(x,y,\lambda)=~{}I_{0}(\lambda)\,exp(-A(x,y,\lambda)). \tag{1}\]  
A first spectroscopic analysis of the image sequence is shown in Figure 2a, where the mean intensity value of the inner part of illuminated area is determined for each image (\(I(\lambda_{i})=<I(x,y,\lambda_{i})>\) for \((x,y)~{}\in~{}\Omega\), cf. Figure A1a). A simulation with the BLL \(I(\lambda)=I_{0}(\lambda)\,exp(-A(\lambda))\), including the spectroscopic parameters of HITRAN [6] for the methane absorption \(A(\lambda)\) around 3057.7 cm\({}^{-1}\), is in line with the measured values. Furthermore, a methane absorption concentration of 9 ppm*m was assumed at the standard temperature and pressure (STP). The laser intensity modulation during the scan was estimated as the linear function around the methane feature by  
\[I_{0}(\lambda)=<I_{ref}>-\eta\,\left(1/\lambda_{i}-1/\lambda_{ref}\right) \tag{2}\]  
Figure 2: (a) Reflectivity image sequence (contrast-corrected), including a local absorption signature of the 0.25 mL/min methane leak in the middle row of the sequence and a global intensity modulation of the laser during the line scan. (b) The mean intensity value of the inner part of the illuminated area (\((x,y)~{}\in~{}\Omega\)) for each image is shown as a function of the wavenumber, including a simulation of the Beer-Lambert law (BLL) for a methane concentration of 9 ppm*m. (c) Baseline-corrected methane absorption for 9 ppm*m as a function of the wavenumber in comparison with the corresponding HITRAN simulation.  
where \(<I_{ref}>=1\), \(\eta\)\(\approx\) 0.25 1/cm\({}^{-1}\) and \(1/\lambda_{ref}\)\(\approx\) 3057.44 cm\({}^{-1}\). The spectral resolution or spacing between two frames of the image stack was estimated as 0.015 cm\({}^{-1}\). In this context, the wavenumber calibration was estimated using the characteristic methane absorption line and assuming a linear tuning behavior around the absorption maximum. A spectrally good agreement between measurements and simulations of the BLL and the corresponding absorption \(A=-ln(I/I_{0})\) can be shown in Figure 2b,c, respectively. The estimated methane concentration of 9 ppm*m corresponds to the ambient concentration of methane. The background concentration of methane in this case is given by the distance between laser, target and camera, which is around 2 \(\times\) 2.25 m (see Figure 1), multiplied by the methane concentration of ambient air of approximately 2 ppm. Up to now, it has been observed that the DAS concept principally works in this setup, but it is impossible to distinguish between the fugitive methane emissions of small leaks and methane in the ambient air without a high spatial resolution. From this point of view, a pixel-by-pixel determination of the methane concentration in ppm*m is required for a powerful methane leak detection and quantification in this challenging methane leak scenario.