## 2 High Dynamic Infrared (IR) Radiometry Based on a Constant Reference  
### High-Speed Calibration  
Radiometric calibration of an IR system is essential to accurately determine the target's radiance or temperature. In the outfield, it is worthy of an infrared radiometric system to provide high mobility and efficiency. Hence, the extended blackbody calibration method is adopted, which is suitable for large-aperture IR systems. The pattern of this method for a large aperture system is displayed in Figure 2. Additionally, IR radiometric systems are generally operated in a high dynamic range of irradiance. The alteration of the integration time could increase the dynamic range. The trouble with conventional calibration is that it has to be conducted at every integration time, which is  
Figure 1: Atmospheric transmission in the mid-wave infrared (MWIR) region.  
time-consuming [12]. In order to meet high-dynamic range requirements in radiometric applications, the IR imaging systems are usually calibrated at different integration times; therefore, the model of high-speed calibration that includes the integration time can be described as:  
\[G_{i,j}\ =\ t\big{(}R_{i,j}\varepsilon L(T)+G_{out}\big{)}+G_{in} \tag{1}\]  
where \(G_{i,j}\) is the gray value of the \((i,j)\)th detector in the array, and, \(t\) is the integration time in units of ms, \(R_{i,j}\) is the normalized radiation flux response, \(\varepsilon\) is the emissivity of the calibration source, \(L(T)\) is the radiance of a blackbody at temperature \(T\), \(G_{out}\) is the offset caused by the ambient temperature, and \(G_{in}\) is the offset caused by internal factors.  
\[\left(\begin{array}{ccc}t_{1}\varepsilon L(T_{1})&t_{1}&1\\ t_{2}\varepsilon L(T_{1})&t_{2}&1\\ t_{2}\varepsilon L(T_{2})&t_{2}&1\end{array}\right)\left(\begin{array}{ccc} R_{i,j}\\ G_{out}\\ G_{in}\end{array}\right)\ =\ \left(\begin{array}{ccc}G_{ij}(t_{1},T_{1})\\ G_{ij}(t_{2},T_{1})\\ G_{ij}(t_{2},T_{2})\end{array}\right) \tag{2}\]  
\[\left(\begin{array}{ccc}R_{i,j}\\ G_{out}\\ G_{in}\end{array}\right)\ =\ \left(\begin{array}{ccc}t_{1}L(T_{1})&t_{1}&1\\ t_{2}L(T_{1})&t_{2}&1\\ t_{2}L(T_{2})&t_{2}&1\end{array}\right)^{-1}\cdot\left(\begin{array}{ccc}G _{i,j}(t_{1},T_{1})\\ G_{ij}(t_{2},T_{1})\\ G_{ij}(t_{2},T_{2})\end{array}\right) \tag{3}\]  
From Equation (1), we can see that the gray value is linear with the integration time and radiance. Hence, once the integration time and the temperature have been obtained, the calibration result at a random integration time may be calculated from Equation (3) by high-speed calibration that includes the integration time:  
The observed targets are detected in the outfield in a large range of IR radiances; therefore, it is vital that the IR systems have the same high dynamic range, in order to detect the overall information of targets. Therefore, several different integration times are selected to avoid saturation of the detector. Thus, the output gray value of the detector pixel can be expressed as:  
\[G_{i,j}\ =\ t\Big{(}\tau_{atm}R_{i,j}\varepsilon_{2}L(T_{0})+R_{i,j}L_{path}+G_{ out}\Big{)}+G_{in} \tag{4}\]  
where \(\varepsilon_{2}\) is the emissivity of the target, \(\tau_{atm}\) is the atmospheric transmittance, \(T_{0}\) is the surface temperature of target, \(t\) is the integration time, \(R_{i,j}\) is the normalized radiation flux response, \(G_{out}\) is the offset caused by ambient temperature related with \(t\), \(G_{in}\) is the offset caused by internal factors unrelated with \(t\), and \(L_{path}\) denotes the path radiance.  
The radiance of the target can be calculated by:  
\[L(T_{0})\ =\ \frac{\frac{\big{(}G_{i,j}-G_{in}\big{)}}{t}-R_{i,j}L_{path}-G_{ out}}{\varepsilon_{2}\tau_{atm}R_{i,j}} \tag{5}\]  
Figure 2: Scheme of near extend-blackbody calibration method.  
where \(R_{i,j}\), \(G_{out}\) and \(G_{in}\) can be determined by high-speed calibration as proposed above in this paper.