# Dual-Channel Mapping-Gas Column Concentration Inversion Method Based on Multispectral Imaging
## 3 Experimental Verification
### Dual-Channel Background Radiation Mapping Experiment  
In order to eliminate the influence of target gas on background imaging during column concentration inversion, a two-channel background radiation mapping method is proposed in this paper. A background radiation image acquisition platform was built, as shown in Figure 3, which mainly included a radiation source with stable, uniform and controllable background radiation; a filter wheel that provides spectral range switching; and an optical imaging system composed of an optical lens and a detector. In the experiment, dual-spectral band imaging of the radiation source was achieved by rotating the filter wheel. The radiation source was INFRAMET's blackbody MTB-6D, and the filter wheel was an FW102C from THORLABS in the United States. The field of view of the optical imaging system was 40\({}^{\circ}\) and the F number was 1. The detector used was an uncooled vanadium oxide detector from the Wuhan Guide Company, with a resolution of 640 \(\times\) 512, a pixel size of 17 \(\upmu\)m and a working spectral band of 7-14 \(\upmu\)m. We chose SF\({}_{6}\), which has a wide range of applications and high safety, as the experimental target gas. According to the rovibrational spectrum of SF\({}_{6}\), the absorption peak of SF\({}_{6}\) is at 10.56 \(\upmu\)m; therefore, in order to fully cover the absorption peak of SF\({}_{6}\), a filter with a transmission spectrum range of 9.9-11.45 \(\upmu\)m was selected as the target spectral channel, and we selected a filter with transmission band of 7-8.75 \(\upmu\)m, which is almost not absorbed by SF\({}_{6}\), as the reference spectral channel. In order to obtain the mapping relationship between the background gray values under the target spectral channel and the reference spectral channel, the temperature of the surface source blackbody was set to 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, 60 \({}^{\circ}\)C and 70 \({}^{\circ}\)C, successively, and the surface source blackbody was imaged through the target spectral channel and the reference spectral channel. The temperature of the surface source blackbody and the gray value output by the detector underwent calibration using least squares method. The pixels of the uncooled detector will accumulate noise in the working process, which will also result in the output gray value being offset. In order to eliminate the impact of noise on the calibration accuracy, the gray image of the surface source blackbody and the low-temperature TEC (Thermoelectric Cooler) were collected by way of low-temperature correction, and the gray value difference was used as the surface source blackbody radiation at this temperature. Since each pixel in the detector has a different response to the same blackbody radiation, each pixel needs to be calibrated and fitted separately, as shown in Figure 4a,b. Figure 4a is a temperature-gray level calibration curve of the reference spectral channel, and Figure 4b is a gray level-temperature calibration curve of the target spectral channel. For convenience of display, the calibration curve of 20 \(\times\) 30 pixels in the central region of the detector is selected in these two figures, and the following parameters are analyzed by taking the mean of all pixels. Under different spectral channels, the fitting determination coefficients R2 of the calibration curves between the detector output gray level and blackbody temperature are 0.99912 and 0.9979, the average relative errors (AREs) are 0.4538% and 1.5562% and the Root-Mean-Square Errors of Cross-Validation (RMSECVs) are 2.4135 \({}^{\circ}\)C and 10.1289 gray level, indicating that both calibration curves have high fitting accuracy. According to the calibration curves under the two spectral channels, the gray mapping relationship between the two spectral channels was obtained, as shown in Figure 4c. The background gray image under the reference channel can be mapped to the gray image under the target spectral channel through the calibration curve. Figure 4: Background radiation calibration curve.