## 2 Dark Current Measurement and Noise Correction Method Based on Focal-Plane Temperature
### Dark Current Measurement Method  
This study applies a sub-band continuum leap type (B-C) QWIP with a large spectral bandwidth and a slightly higher dark current compared to other types of QWIP [24]. The operating principle of the temperature measurement diode is to use the characteristic of the forward voltage drop with temperature when the diode PN junction is under the action of a constant-current source for temperature measurement. In the operating range, the forward voltage drop has a good linear relationship with temperature. However, there is a certain bias in the constant-current source and temperature measurement diode circuit, and to accurately obtain the relationship between the temperature measurement pin output voltage and the temperature of a certain QWIP device, a test calibration is required. The chiller calibration equation is as follows:  
\[U_{tem}=T_{dio}\times a_{ref}+b_{ref}, \tag{9}\]  
where \(U_{tem}\) is the voltage value of the temperature measurement pin, \(T_{dio}\) is the cooling target temperature, and \(a_{ref}\) and \(b_{ref}\) are the linear parameter and intercept of the relationship, respectively. By adjusting multiple \(T_{dio}\), \(U_{tem}\) is measured at different temperatures.  
The signal \(U_{tem}\) is preprocessed in the information acquisition circuit by an op-amp for linear operations. The above preprocessing can make the best possible use of the sampling range of the analog-to-digital converter (ADC) and improve the signal-to-noise ratio of the temperature measurement signal. The preprocessed temperature measurement voltage \(U_{tem\_done}\) is  
\[U_{tem\_done}=(U_{tem}-U_{tem\_sub})\times a_{tem}, \tag{10}\]  
where \(U_{tem\_sub}\) is the subtractive circuit deduction voltage and \(a_{tem}\) is the amplification.  
The temperature measurement quantization value \(g_{tem}\) is obtained by calculating:  
\[g_{tem}=\frac{U_{tem\_done}-U_{L1}}{U_{w1}}\times 2^{n_{tem}}, \tag{11}\]  
where \(U_{L1}\) is the lower limit of the input voltage interval of the ADC of the temperature measurement module, \(U_{w1}\) is the input voltage range, and \(n_{tem}\) is the number of quantization bits.  
Equation (8) is the relationship between dark current and temperature [17]. The dark current of the QWIP is easily and accurately measured using a fully enclosed cold screen and dedicated measurement equipment during the device preparation stage and before the fixed package is performed. In the temperature region where the thermal excitation effect is the dominant mechanism of the dark current, there is an exponential relationship between the dark current and temperature. Taking the logarithm of both sides of the equation of Equation (8) with a base of 10, the equation is obtained as:  
\[\lg\left(\frac{I_{dark}}{T}\right)=\left(\frac{1000}{T}\right)k_{I}+b_{I}, \tag{12}\]  
Consider the left side of the equation as the dependent variable, where \(k_{I}\), \(b_{I}\) are the linear parameters and intercepts of the linear relationship of Equation (9), respectively. The two sets of \(T\) and \(I_{dark}\) are obtained to solve for \(k_{I}\), \(b_{I}\) of the same QWIP device.  
In summary, the QWIP dark current values of the same QWIP device at any temperature under the thermal excitation effect as the dark current dominant mechanism can be measured by combining Equations (9)-(12).