## 3 Results
### Single Concentration Image of the 0.25 mL/min Methane Leak Scenario  
The resulting concentration images from the three methods are depicted in Figure 5a-c, with the color scale restricted to the physically meaningful range of 0 to 50 ppm\({}^{\star}\)m. DAS-f and DAS-2f exhibit the ability to accurately locate the leak at the center of the image and to identify a gas plume for a methane leak rate of 0.25 mL/min within a single concentration image at a rate of 10 Hz. Conversely, the simple integral method (DAS-F) is only partially suitable for qualitatively and quantitatively investigating such small methane leaks. The key criteria in this context are the absolute accuracy (e.g., ambient air concentration of methane at approximately 9 ppm\({}^{\star}\)m) and the methane contrast at the source of the methane leak, including the methane plume extending towards the bottom of the image. For an area within a few millimeters of radius around the leak source in the image center, DAS-f and DAS-2f yield methane concentrations slightly below 50 ppm\({}^{\star}\)m, while the gas plume exhibits concentration values around 20 ppm\({}^{\star}\)m. These values are significantly higher than both the background methane concentration in the ambient air and the spatial variation in the concentration values within the image. The latter can be estimated to be approximately 2 ppm\({}^{\star}\)m for DAS-f and DAS-2f.  
Based on these criteria, it is evident that DAS-F exhibits an underestimation of the ambient air concentration in significant parts of the image, including negative concentration values, as well as a larger dispersion of concentration values. Consequently, identifying the leak position and leak plume becomes much more challenging with DAS-F. The correspond  
Figure 5: (**a–c**) Methane concentration images at the 10 Hz frame rate using the DAS-F, -f and -2f methods within a 0.25 mL/min methane leakage. The color scale is restricted to the physically meaningful range between 0 and 50 ppm\({}^{\star}\)m. (**d–f**) The corresponding histograms represent the methane concentration distribution of the upper concentration images of DAS-F, -f and -2f. The dashed black line highlights the expected ambient air concentration of 9 ppm\({}^{\star}\)m, and the solid red line highlights the mean value.  
ing histograms representing these methane images can provide additional information, as shown in Figure 5d-f.  
Considering that the methane leak rate of 0.25 mL/min is quickly diluted in the ambient air, most of the concentration image is dominated by ambient methane at approximately 9 ppm*m. Therefore, the most frequent value in the image or histogram (referred to as the mode value) is expected to be around 9 ppm*m. From this perspective, the baseline-free implementation of DAS-2f demonstrates remarkable absolute accuracy, as the mode value aligns with the ambient air concentration of methane. The ability to measure ambient methane with a sufficient spatial signal-to-noise ratio documents the performance capability of DAS-f and, particularly, DAS-2f. A methane anomaly can only be detected at the leak origin or the associated gas plume, which constitute a relatively small portion of the image. The higher methane concentrations around the leak origin and corresponding gas plume align with a positive skew in the distribution of concentration values in the histograms.