# Color CCD High-Temperature Measurement Method Based on Matrix Searching
## 4 Results and Discussion
### Comparison of Emissivity Perturbation Effects  
To explore the robustness of the solution method visually, the effect of temperature solution under the no-perturbation emissivity and perturbation emissivity models is analyzed according to the spectral emissivity model of Equations (12) and (13). The two emissivity models are used to build the search matrices, and the temperature mapping matrices are used to solve the non-perturbation emissivity model and the perturbation emissivity model. The results are shown in Figure 12.  
Figure 11: Error calculation results. Figure 12: (**a**) Results of the non-perturbative emissivity model; (**b**) results of the perturbative emissivity model. According to the solution results, both show an overall trend that the temperature of the outer flame is higher than that of the inner flame, which is consistent with the results of existing experimental studies. However, there is significant noise in the calculated results under the perturbation emissivity model, but the image has not been seriously distorted. The two-dimensional image of the solution is transformed into a statistical diagram of temperature distribution, as shown in Figure 13.  
In the figure, the horizontal axis represents the temperature, and the vertical axis represents the statistical number of temperature values that appear throughout the image. It can be seen that the spectral response curve under the perturbation emissivity model has high noise and severe oscillation in the temperature range. Generally speaking, the two have the same trend. The reason for the noise may be that when solving the perturbation emissivity model, it is necessary to calculate all the emissivity models in the range and establish the search matrix. Because the model is similar, the chromaticity values at similar temperatures are similar. According to the chromaticity search, the result is calculated as a similar temperature value on different emissivity; thus, the solution fluctuation occurs. Considering that the matrix search is to calculate the temperature of the pixel points whose chromaticity falls into the determined chromaticity range as the same temperature value, the amount of deviation of the pixel points from the given chromaticity interval in the measurement is the important reason that affects the accuracy of the temperature solution. As shown in Figure 14a, the chromaticity values corresponding to the temperatures \(T\), \(T_{pq}\), and \(T_{p+\mathcal{I}_{q}}\) will be solved at the same temperature value in the actual solution because they fall within the same divisions. However, the chromaticity of T is located at the edge of the indexing range, so its reverse search error will be minimum. \(T_{pq}\) and \(T_{p+\mathcal{I}_{q}}\) are far away from the indexing boundary, so if they are classified as temperature T, there is bound to be an error, and in theory, the farther the distance, the greater the error. Therefore, the deviation distance of the measured chromaticity from the solved chromaticity is defined as the quantity characterizing the degree of error, which is denoted by \(l\). If H denotes the three-color vector of the nearest index boundary and H\({}^{\prime}\) denotes the measured three-color vector, then \(l\) is expressed as follows:  
\[l=\left\|H-H^{\prime}\right\|_{2} \tag{15}\]  
Figure 13: Statistical distribution of temperature results from two emissivity models. Then, to characterize the robustness of the calculation method, the statistical distribution of the deviation distances calculated in the case of perturbation spectral emissivity and non-perturbation emissivity are plotted as shown in Figure 14b. It can be seen that the deviation distances trend of the two-emissivity models is the same, most of the positions coincide, with only a small amount of deviation at the most probable deviation distance position, i.e., where the deviation distance statistic is the largest. The perturbed emissivity model combined with the multi-emissivity model refines the search matrix.