## 2 Materials and Methods
### Image Processing
#### 2.2.2 Application of Different DAS Methods (DAS-F, DAS-f and DAS-2f)
A moderate spatial or two-dimensional Gaussian smoothing of the concentration image (e.g., \(h_{x,y}*c(x,y)\) with \(\sigma_{x}=\sigma_{y}=1.5\) mm or 3 pixels as the smoothing parameter or standard deviation) can significantly decrease the image noise. This is shown in Section 3 in more detail. In terms of leak detection, the absorption sequence in Figure 3a indicates more potential compared to the previous applied integral approach (DAS-F, see Figure 3b) to obtain an informative concentration image. This means that the simple DAS-F method is not sufficient to obtain the desired concentration information. Consequently, further image processing on the absorption sequence is applied to archive an improvement. Figure 3: **(a)** Unsmoothed absorbance sequence of methane within a 0.25 mL/min leakage scenario. **(b)** Concentration image in ppm*m based on the unsmoothed DAS-F method, including the corresponding histogram **(c)** of the concentration image. The solid and dashed red lines indicate the mean and standard deviation, respectively, of this concentration distribution, whereas the dashed black line highlights the expected ambient air concentration (9 ppm*m). * DAS-f method: In this method, a three-dimensional (3D) Gaussian smoothing \((h_{x,y,\lambda})\) is applied on the absorbance sequence according to Equation (3) for spatial and spectral smoothing: \[h_{x,y,\lambda}*A(x,y,\lambda)=-h_{x,y,\lambda}*\ln\left(\frac{I(x,y,\lambda)}{ I_{BLC}(\lambda)}\right)\] (5) The 3D Gaussian is composed of a moderate spatial smoothing of \(\sigma_{x}=\sigma_{y}=1.5\) mm (or 3 pixels) and a moderate spectral smoothing of \(\sigma_{\lambda}=0.0375\)\(1/\)cm (e.g., \(2\sigma_{\lambda}\) that corresponds to 5 frames, which is slightly below the full-width half-maximum of the absorption line). These parameters correspond to the standard deviation of the Gaussian and define the 3D Gaussian filter kernel that is convoluted across the absorbance sequence. The resulting or filtered absorbance sequence is illustrated in Figure 4a. There is a noticeable improvement in the visualization of the leak situation compared to DAS-F. In particular, the spatial and spectral aspects are clearer. Spectrally, the distinct characteristics of methane absorption are apparent, with the peak of the absorption located in the middle row and the wings of the absorption observable as a decrease in absorption value in the top and bottom rows of the sequence. Spatially, the methane anomaly near the leak (at the center of the images) and the presence of a methane gas plume at the bottom are clearly visible. Furthermore, a general methane background can be observed by the global absorbance variation of the illuminated area with respect to the wavelength. The averaged pixels within \((x,y)\ \in\ \Omega\) of the smoothed absorbance sequence (DAS-f), as depicted in Figure 4b, show a smoothed absorbance along the spectral dimension. Apart from an offset, the simulation of the spectrally smoothed absorption according to the spectroscopic parameters provided by HITRAN shows good agreement for an ambient methane concentration of 9 ppm*m. The observed offset results from the residual wings of the absorption line influencing the BLC (polynomial fit). This influence causes a slight underestimation of the absorption. Figure 4: (**a,c**) Spatially and spectrally smoothed absorbance sequence (DAS-f) and second derivative of the methane absorbance sequence (DAS-2f) of methane within a 0.25 mL/min leakage scenario. (**b,d**) Mean absorbance value (blue circle, averaged pixels \((x,y)\ \in\ \Omega\)) as the inner part of the illuminated area for each frame of the DAS-f and DAS-2f sequences shown as a function of the wavenumber in comparison with the corresponding smoothed HITRAN simulations for a methane concentration of 9 ppm*m.  
Further quantitative information about the leak situation and if the background can be linked to ambient methane from the atmosphere with approximately 9 ppm*m is given by the concentration image.