The infrared radiation characteristics of the aerial target usually refer to the infrared radiation characteristics of aircraft in the flight state. It is an important combat technique indicator for evaluating the stealth performance of aviation weapons and equipment. Before conducting infrared radiation characteristics testing of aerial targets, infrared calibration is required. The traditional calibration method takes the average response value of the entire infrared detector focal plane array for calibration, without considering the calibration non-uniformity in the image spatial domain, which reduces the calculation accuracy. To improve the calculation accuracy of infrared radiation characteristics, we propose a computation model for calculating the infrared radiance of extended aerial targets, which is based on each pixel calibration of the focal plane array in refrigeration infrared systems. The model obtains the gain coefficient matrix and bias matrix of all focal plane arrays by each pixel independent calibration, which can correct the errors caused by calibration non-uniformity. The computation model can provide references for the measurement and theoretical research on the infrared radiation characteristics of aerial targets.

Firstly, each pixel calibration method for refrigeration infrared systems is proposed and the linear relationship between each pixel response value of the infrared focal plane array and the radiation amount of blackbody is established. The calculation formulas of gain coefficient matrix and bias matrix are also derived. Then, we put forward a computation model for calculating the infrared radiance of extended aerial targets based on each pixel calibration of the focal plane array in infrared measurement systems. The model obtains the calculation formula for the infrared radiance of the target by subtracting the sky background gray value from the target gray value and acquires the environmental parameters by adopting atmospheric parameter measurement equipment and MODTRAN software. Finally, large-caliber blackbody calibration experiments and field verification experiments are conducted to verify the model correctness and accuracy.

Firstly, the calibration gain coefficient and bias of the refrigeration infrared system at different temperatures are compared (Fig. 3). The calibration bias of the refrigeration infrared system increases linearly with the temperature, but the gain coefficient does not change much with temperature and remains basically unchanged. Secondly, the large-caliber blackbody calibration experiment is conducted based on the near-extended-source method. The traditional calibration method and the proposed method are employed to calibrate the refrigeration infrared system, with a wavelength range of 3.7 μm to 4.8 μm and an integration time of 2000 μs. The blackbody temperature is set at five temperature points including 40 ℃, 50 ℃, 60 ℃, 80 ℃, and 100 ℃ (Fig. 4). The area with a size of 30 pixel×30 pixel in the blackbody image at T1 temperature, center at random pixel x,y is considered as the measurement target. The annular region in the blackbody image at T2 temperature, which is beyond the area with a size of 30 pixel×30 pixel and within the area with a size of 34 pixel×34 pixel, is considered as background (Fig. 5). The theoretical value of blackbody at T2 temperature can be considered as the infrared radiance of background and the theoretical value of blackbody at T1 temperature can be the theoretical value of the measurement target. The atmospheric path radiation Lpath is 0 and the transmittance τatm is 100%. Comparisons show that our method is correct and has a certain improvement in calculation accuracy (Table 1). Thirdly, the field verification experiment is conducted to verify the model accuracy, which considers atmospheric path radiation and transmittance measurement errors. The blackbody is moved to a distance of 420 m from the measurement system (Figs. 7 and 8), and set at five temperature points of 90 ℃, 110 ℃, 130 ℃, 150 ℃, and 200 ℃. The atmospheric path radiation Lpath is 0.2917 W?m-2?sr-1 and the transmittance τatm is 0.738, which are calculated by atmospheric parameter measurement equipment and MODTRAN software. By employing the same method as above (Fig. 5), the infrared radiance values of the measurement target are calculated by the traditional method and our method (Table 2). The calculation results are closer to the true value of the target.

The results show that the computation model can reduce the infrared-radiance average error of an even expand target by 8.58% and the average degree of calculation error deviation by 0.60 without considering atmospheric measurement errors, which is compared with traditional methods. Considering the measurement error of atmospheric path radiation and transmittance, the infrared-radiance average error of even expand target is reduced by 7.23%, and the average degree of calculation error is reduced by 2.25. The calculation results are closer to the true values of the target, but the overall calculation accuracy of the model is limited by the measurement accuracy of atmosphere parameters. In subsequent research, it is necessary to further evaluate the overall accuracy of the model based on the measured data of aerial targets and verify the universality of the calculation model. Our paper provides references for studying infrared radiation characteristics of aerial targets and promoting the development of target characteristic measurement technology.