## 3 Dark Current Measurement Based on Focal-Plane Temperature and Dark Current Correction Experiment
### Long-Wave QWIP Dark Current Noise Correction Experiment  
First, the detection system was turned on, and after the chiller stabilized the focal-plane device at the target cooling temperature of 41 K, 1000 frames of image data were \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter Name** & \(\mathbf{U}_{tem\_sub}\)**V** & \(\mathbf{a}_{tem}\) & \(\mathbf{U}_{L1}\)**V** & \(\mathbf{U}_{wt}\)**/**V** & \(\mathbf{n}_{tem}\) \\ \hline
**Parameter Values** & 0.9 & 27 & \(-10\) & 20 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the temperature measurement module. Figure 6: Dark current values in the range of 40–50 K.  
acquired continuously facing the 300 K surface-source blackbody. As shown in Figure 7, the image data were processed, and the right side of the vertical axis is the mean response of the detector surface array pixels \(\overline{g}_{det}\), the left side of the vertical axis is the acquired temperature response \(g_{tem}\), and the horizontal axis is the sequence number of the frames. It can be clearly seen that the values of \(\overline{g}_{det}\) and \(g_{tem}\) are strongly correlated in the order of frame F. This also confirms that very small temperature fluctuations can cause changes in the dark current in the focal-plane. Next, the calibration process is described. In the paper, the pixels coordinates were defined using the format (CH, i), where CH is the spectral channel and i is the spatial dimensional coordinate. The data of four pixels from different spectral channels were extracted and used as the target data for calibration. The \(\Delta T_{set}\) of this system at a \(T_{set}\) of 41 K is 0.2 K. The \(\Delta I_{dark}\) in this temperature interval (40.9-41.1 K) was found to be \(3.35\times 10^{-13}\) A according to Equation (12). The parameters of the target signal preprocessing module in the information acquisition circuit are shown in Table 4. According to the system operation mode, the \(T_{int}\) of Equation (2) was obtained as \(1.42\times 10^{-2}\) S and \(C_{int}\) is \(5.60\times 10^{-13}\) F. According to Equations (2), (13) and (14), the response voltage variation value corresponding to this temperature interval can be obtained, the response voltage variation value \(\Delta U_{det\_done}\) after preprocessing is \(2.77\times 10^{-2}\) V, and the quantized value of response voltage after preprocessing \(\Delta g_{det}\) is 56.79. According to Equation (15), \(a_{dark}\) is 4.96. The target data were corrected according to Equation (16), and the corrected data were obtained. As shown in Figure 8, the response values \(g_{det}\) and \(g_{det}^{\prime}\) before and after correction using this method are compared; the horizontal axis is the serial number of the frame, the red curve is the response value after correction, and the black curve is the response value before correction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter Name** & \(\mathbf{U}_{det\_sub}\)**/**V** & \(\mathbf{a}_{det}\) & \(\mathbf{U}_{12}\)**/**V** & \(\mathbf{U}_{w2}\)**/**V** & \(\mathbf{n}_{det}\) \\ \hline
**Parameter Values** & 1.68 & 0.73 & 0 & 2 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Information Acquisition Circuit’s parameters. Figure 7: The relationship between \(\overline{g}_{det}\) and \(g_{tem}\) regarding the serial number of the frames (time order). By comparison, the fluctuation in the pixel response was significantly reduced after correction using this method, and the temporal noise was reduced. The following is a quantitative analysis of the temporal noise reduction value and its proportion by examining the noise value of the pixel response. The noise reduction effect of this method was examined by comparing the temporal noise before and after the correction of imaging pixels [30].