# Color CCD High-Temperature Measurement Method Based on Matrix Searching
## 2 Method
### Temperature Measurement Realization  
The actual temperature measurement process based on the CCD temperature measurement principle can be summarized into two stages, which are the preparation stage and the solution stage. The relationship and steps of the two stages are shown in Figure 1.  
The preparation stage is marked by the blue box in the figure. This stage is completed before the measurement starts, and its ultimate goal is to generate a temperature mapping matrix for a specific temperature measurement environment. In this stage, the specific environment of temperature measurement is first determined, including the spectral response curve of the selected camera, clear imaging focal length and aperture, channel gain, emissivity model of the material to be measured, absorption model of the transmission medium and radiation transmission length, etc. Then, according to the determined temperature measurement environment, the integral equation representing the relationship between the three-channel signal and the temperature described in Formula (3) is constructed. Finally, the appropriate temperature step \(\Delta T\) is set from the Draper point and substituted into  
Figure 1: Flow chart of temperature measurement. the established integral equation to obtain three-channel signal values corresponding to different temperatures. The normalized three-channel signal values corresponding to each temperature are calculated by Formula (5) to obtain the distribution of temperature T in R-G space. The appropriate sensitivity factors \(p\) and \(q\) are selected by Formula (6) to calculate the channel signal step \(\Delta R\), \(\Delta G\) to establish the search address. Finally, the temperature T is added to the corresponding address, and the temperature mapping \(T_{map}\) is established. The solution stage is marked by the red box in the figure. The ultimate goal of this stage is to obtain the temperature solution of the corresponding position of the pixel (specific or global). At this stage, firstly, the temperature field images collected in the measurement are analyzed. As shown in Figure 2, the color images collected by the equipment are analyzed as grayscale images of three primary colors, which are stored in the form of a matrix with the same dimensions as those of the collected images. Three-channel matrices are recorded as _ImageR_, _ImageG_, and _ImageB_, respectively. Use Formula (5) to normalize the three-channel signal and, respectively, construct two normalized matrices _ImageRnorm_ and _ImageGnorm_, with the same dimension as the image frame. The matrix elements are normalized R value and G value of the corresponding pixel, and each vector corresponds to the pixel position one by one. For the image of r \(\times\) c dimension, the image normalized matrix _Imagenorm_ is expressed as follows:  
\[\textit{ImageR}_{norm}= \begin{pmatrix}R_{11}&\cdots&R_{r1}\\ \vdots&\ddots&\vdots\\ R_{1c}&\cdots&R_{rc}\end{pmatrix} \quad\textit{ImageG}_{norm}= \begin{pmatrix}G_{ 11}&\cdots&G_{r1}\\ \vdots&\ddots&\vdots\\ G_{1c}&\cdots&G_{rc}\end{pmatrix}  \tag{9}\]  
\(R_{mn}\) and \(G_{mn}\) are, respectively, the normalized R value and the normalized G value of the pixel in the m-th row and the n-th column. Then, the quotient operation is performed on the matrix element of each pixel position, and \(\Delta R\Delta G\) is set in the preparation stage to obtain the mapping matrix search addresses \(I\) and \(j\) corresponding to each pixel as follows:  
\[\frac{1}{\Delta R} \begin{pmatrix}R_{11}-R_{\min}&\cdots&R_{r1}-R_{\min}\\ \vdots&\ddots&\vdots\\ R_{1c}-R_{\min}&\cdots&R_{rc}-R_{\min}\end{pmatrix} = \begin{pmatrix}i_{11}& \cdots&i_{r1}\\ \vdots&\ddots&\vdots\\ i_{1c}&\cdots&i_{rc}\end{pmatrix}  \tag{10}\]  
\[\frac{1}{\Delta G} \begin{pmatrix}G_{11}-G_{\min}&\cdots&G_{r1}-G_{\min}\\ \vdots&\ddots&\vdots\\ G_{1c}-G_{\min}&\cdots&G_{rc}-G_{\min}\end{pmatrix} = \begin{pmatrix}j_{11}& \cdots&j_{r1}\\ \vdots&\ddots&\vdots\\ j_{1c}&\cdots&j_{rc}\end{pmatrix}