# Color CCD High-Temperature Measurement Method Based on Matrix Searching
## 2 Method  
### CCD Temperature Measurement Theory  
According to the blackbody radiation theory, the directional spectral radiation intensity of a blackbody satisfies as follows [21]:  
\[I_{b}(\lambda,T)=\frac{2 hc_{0}^{2}}{\lambda^{5}\{\exp[hc_{0}/(\lambda kT)]-1\}} \tag{1}\]  
It represents the spectral radiation intensity of the unit solid angle. Where \(h\) = 6.626 \(\times\) 10\({}^{-34}\) J/K, \(k\) = 1.381 \(\times\) 10\({}^{-23}\) J/K, respectively, Planck constant and Boltzmann constant, \(c_{0}\) = 2.998 \(\times\) 10\({}^{6}\) m/s, is the speed of light in vacuum, T denotes the absolute temperature of the blackbody. For the thermal radiation of non-black matter, the radiation signal is modulated by the spectral emissivity \(\varepsilon(\lambda)\), and the absorption of the transmission medium during the transmission process is considered. If the absorption coefficient of the transmission medium is represented by \(\kappa(\lambda)\), and the radiation and transmission distance are represented by \(l\), the CCD camera lens indicates that the received radiation intensity should be expressed as follows:  
\[I_{\rm c}=\varepsilon(\lambda)I_{b}(\lambda,T)e^{-\kappa(\lambda)l} \tag{2}\]  
The radiation intensity reaching the photosensitive surface of the detector is affected by the detector lens and the spectral response characteristics of the detector. Finally, the gray values of each channel of the pixel are expressed as follows [22]:  
\[H_{i}=\left[P(f,d)g_{i}(I)\int_{380}^{780}s_{i}(\lambda)\varepsilon(\lambda)I_ {b}(\lambda,T)e^{-\kappa(\lambda)+}d\lambda-D\right]^{\frac{1}{7}}\quad(i=r,g,b) \tag{3}\]  
where \(s_{r}(\lambda)\), \(s_{g}(\lambda)\), and \(s_{b}(\lambda)\) are the spectral responsivity functions of the red, green, and blue signals of the CCD camera, respectively, and their specific expressions will be given by the calibration process. \(D\) is dark current noise, \(g_{i}\) (\(I\)) is the grayscale curve of each channel, which characterizes the transfer relationship between thermal radiation intensity and gray level [3], \(\gamma\) is the gamma value representing the nonlinear acquisition degree of the device [20]. Because the CCD detector range is visible light band, the integral domain covers the visible light band. \(P(f,d)\) is the instrument parameter affected by the focal length \(f\) of the lens and the aperture \(d\). If \(m\) is used to represent the magnification, \(\rho\) is used to represent the aperture magnification of the asymmetric lens, and \(\Delta t\) is the exposure time. In the case of long-distance quasi-spherical thermal radiation signal acquisition, it can be expressed as follows [23]:  
\[P(f,d)=\Delta t\cdot\pi(\frac{4f^{2}}{d^{2}}(1-\frac{m}{\rho})^{2})^{-1} \tag{4}\]  
Equation (3) can obtain the relationship between the gray value of each channel and the actual temperature of the object to be measured. Normalize the RGB three-channel signal to the following relationship:  
\[R_{j}=\frac{H_{ij}}{\sum\limits_{r,g,b}H_{ij}}\quad G_{j}=\frac{H_{ij}}{\sum \limits_{r,g,b}H_{ij}}\quad B_{j}=\frac{H_{ij}}{\sum\limits_{r,g,b}H_{ij}} \tag{5}\]  
At this time, corresponding to the determined R value and G value, the unique B value can be determined, and the unique temperature value T can be determined. The mapping relationship between the temperature T and the normalized channel output signals R and G will be obtained by substituting the temperature T from the Draper point [2] with a sufficiently small step \(\Delta T\) (\(\Delta T\) will directly determine the temperature measurement accuracy), the mapping relationship between the temperature T and the normalized channel output signals R and G will be obtained. Taking R and G values as horizontal and vertical coordinates, the temperature mapping surface in R and G space is calculated by using the nearest neighbor difference algorithm [24].