# Dual-Channel Mapping-Gas Column Concentration Inversion Method Based on Multispectral Imaging
## 4 Error Analysis
### Gas Column Concentration Inversion Error Evaluation  
Although the inversion accuracy detection method based on actual imaging can evaluate the inversion accuracy of gas column concentration under practical application scenarios, the error introduced in the latter half of the inversion process is ignored by using the intermediate quantity as the standard, and it is difficult to fully represent the error in the whole process of column concentration inversion. At the same time, when SF\({}_{6}\) gas is directly discharged into the atmosphere through gas cylinders, it is difficult to determine the optical path of the gas in a certain location, and it is impossible to infer the concentration of the gas column at that location, resulting in an inability to evaluate the accuracy of the inversion of gas column concentration. Therefore, gas sampling bags were used instead of gas release to evaluate the inversion accuracy. The experimental installation is shown in Figure 18.  
Figure 16: Background grayscale image comparison: (**a**) the background grayscale image taken when the target gas was not released; (**b**) the background grayscale image obtained through the mapping relationship; (**c**) the difference between (**a**) and (**b**). Figure 17: (**a**) Column concentration image calculated from the background grayscale image of the target spectral channel without gas release. (**b**) Column concentration image calculated from the background grayscale image obtained from the mapping relationship (**c**) ratio of (**a**) to (**b**). In order to reduce the influence of the gas sampling bag itself on the inversion, polyethylene with less infrared spectrum absorption was selected as the material for the gas sampling bag, and SF\({}_{6}\) gas was added to the gas sampling bag until the gas sampling bag was completely filled. The completely filled gas sampling bag was not easy to deform, and could better confirm the optical path of a certain point of the gas. After filling, the central thickness of the gas sampling bag was about 13.4 mm. In the experiment, a surface source blackbody at 40 \({}^{\circ}\)C was selected as the background. The transmittance of the polyethylene gas sampling bag was measured before the experiment, which eliminated the influence of the transmittance of the gas sampling bag in the subsequent column concentration inversion process. SF\({}_{6}\) gas at different concentrations was added to the gas sampling bag to achieve different column concentrations. The gas column concentration distribution in the gas sampling bag was obtained through the column concentration inversion algorithm, and the average column concentration in the 50 \(\times\) 50 pixel area in the center of the gas sampling bag was calculated. Since the center area of the gas sampling bag was relatively flat and the collection area was small, it can be considered that the radiation path received by each pixel was equal. The theoretical column concentration was deduced according to the thickness of the center of the gas sampling bag, and the inversion errors under each column concentration were calculated, as shown in Table 2. The mean relative error of the inversion was 4.8%. The above two experiments evaluated the error of the inversion method of dual-channel mapping-gas column concentration inversion from different angles, among which the error introduced by gas column concentration calibration in the inversion process was ignored in the dual-channel mapping error analysis experiment. The inversion error evaluation experiment with a known gas column concentration was able to calculate the actual gas column concentration according to the thickness of the inflated gas sampling