# Research on the Auto-Exposure Method of an Aerial TDI Camera Based on Scene Prediction
## 2 Auto-Exposure Method  
The purpose of auto-exposure is to change the gray value of the image; therefore, by adjusting the exposure parameters, the gray value can approach the target gray value, and it is generally considered that the average gray value of the image obtained by the aerial TDI camera is more conducive to image processing when it is half full. The Auto-exposure of TDI CCD is realized by capturing images of the target scene in advance, and collecting the average gray value of the front N rows, which is used for comparison with the gray value of the target; therefore, setting the gray value of the image to approach the target value by adjusting the exposure parameters. The auto-exposure of an aerial TDI camera is a complex process. To achieve auto-exposure, an imaging link model of an aerial TDI camera is established to analyze the imaging process, as shown in Figure 1.  
In the process of earth remote sensing imaging, sunlight is the main source of illumination. The ground scene can obtain the radiation brightness by reflecting the solar illumination; however, the radiation brightness will be weakened to a certain extent through the absorption and scattering of the atmosphere, and finally be acquired by the camera lens. As can be seen from Figure 1, the solar irradiance described by \(E_{S}\) is measured on the ground by an illuminometer, whose unit is \(\mathrm{lx}\), and the relation between \(\mathrm{lx}\) and the Luminous flux (\(\mathrm{lm}\)) is:  
\[1\mathrm{lx}=1\mathrm{lm}/\mathrm{m}^{2}=1/683V(\lambda)\mathrm{W}\cdot \mathrm{m}^{-2}, \tag{1}\]  
where \(V(\lambda)\) is a normalized visual function [22], and, according to CIE 1931 [23], its value is 0.28 in the visible wavelength range \(\lambda=390\,\sim 780\) nm. The relation between irradiance \(E\) of the target and the solar irradiance \(E_{S}\) is:  
\[E=\frac{E_{S}}{683V(\lambda)}. \tag{2}\]  
In Equation (2), the unit of \(E\) is \(\mathrm{W}/\mathrm{m}^{2}\), and, according to the relation between the radiation irradiance and the radiation luminance of Lambert body, the radiation luminance \(L\) of the target is obtained by:  
\[L=\frac{E\cdot\rho_{A}}{\pi}=\frac{E_{S}\cdot\rho_{A}}{683V(\lambda)\pi}, \tag{3}\]  
where \(\rho_{A}\) refers to the average reflectivity of the ground scene. The brightness \(B\) has the relation between \(L\) and the atmospheric transmittance, that is:  
\[B=L\cdot T=\frac{E_{S}\cdot\rho_{A}\cdot T}{683V(\lambda)\pi}, \tag{4}\]  
where \(T\) donates the atmospheric transmittance, which is the ratio of the outgoing light to the incident light, and it is given by:  
\[T=\frac{I(O)}{I(I)}, \tag{5}\]  
where \(I(O)\) is the outgoing light intensity and \(I(I)\) refers to the incident light intensity. Figure 1: Imaging link model of aerial TDI camera. According to the Beer-Lambert law, the relation between the intensity of the outgoing light and the intensity of the incident light is:  
\[I(O)=I(I)\times e^{-KM}, \tag{6}\]  
where \(K\) donates the extinction coefficient and \(M\) represents the optical path length. Thus, Equation (5) can be rewritten as:  
\[T=\frac{I(O)}{I(I)}=e^{-KM}. \tag{7}\]  
A logarithm of e-based is taken on both sides of Equation (7), that is \(\ln T=-KM\), and it can be obtained \(K=-\frac{\ln T}{M}\). The horizontal visibility, described by \(P\), has the relation with \(K\):  
\[P=\frac{1}{K}\ln(\frac{1}{\varepsilon}), \tag{8}\]  
where \(\varepsilon\) refers to the minimum luminance contrast that the human eye can distinguish from a sufficiently large object at a distance, which is called the contrast perception threshold [24], and is usually 0.02.