# A Calibration Method for Time Dimension and Space Dimension of Streak Tube Imaging [PERSON]
## 2 Coupling Mechanism  
Different from other types of lidars, our approach features detection data (i.e., streak images) containing both time and space information. Ideally, the streak contains some illuminated pixels on the CCD. The position of the streak on the time axis is used to calculate the time when the echo signal reaches the detector, and the distance of the target can be calculated based on the propagation speed of light in the air. Generally, we obtain the position of the streak by calculating its centroid on the time axis [10]:  
\[x_{j}=\frac{\sum_{i=1}^{N}(i\times I_{i})}{\sum_{i=1}^{N}I_{i}} \tag{1}\]  
Figure 1: The schematic of the STIL system. (**a**) Schematic diagram of the data collection process. (**b**) The work principle of the streak array detector. (**c**) The streak image on the CCD. where \(x_{j}\) is the centroid of the pixels of the jth row, \(N\) is the number of pixels in the time dimension of the CCD, and \(I_{i}\) is the gray value of the \(i\)th pixel. Afterward, we obtain the distance of the point on the target by  
\[R_{j}=\frac{1}{2}c\left(\alpha x_{j}+t_{d}+t_{inth}\right) \tag{2}\]  
where \(R_{j}\) is the distance of the point corresponding to the pixels of the \(j\)th row, \(\alpha\) is a coefficient used to indicate the time represented by one pixel, \(t_{d}\) is the gate delay of the detection system, and \(t_{inth}\) is the inherent delay of the lidar. However, in practice, coordinates on both axes have components on the time axis and space axis. Two main reasons for this result are (1) the angle difference of the direction of the sweep electric field and the direction of the time-resolved channels on the CCD and (2) the diffusion of the optical imaging system and electronic imaging system. The effect process of the first reason is shown in Figure 2. When there is an angle difference between the direction of the sweep electric field and the direction of the time-resolved channels on the CCD, a deviation of the dynamic streak occurs, which is shown in Figure 2a. The streak image recorded by the CCD is shown in Figure 2b. Without the action of sweeping voltage, the position of the streak (called static streak) is as shown in Figure 2a. While the sweeping voltage is applied, the streak (called dynamic streak) is displaced along the opposite direction of the electric field. If the direction of the electric field is parallel to the time-resolved channels of the CCD, the dynamic streak is as shown in the thin green line in Figure 2a. If, however, a deflection of the direction of the electric field occurs, the dynamic streak shifts not only in the time-resolved direction but also in the space-resolved direction. As shown in Figure 2b, one pixel of the static streak is marked with a darker color and moved to the position of the pixels marked with the color red or green under the influence of the electric field. The green pixel corresponds to the black pixel when the electric field is parallel to the time-resolved channel, and the red pixel corresponds to the black pixel when there is an electric field angle. We find that when the red pixel is displaced on both the time-resolved and space-resolved channels, difficulties arise when deconstructing the position of the streak into time and space information. Another factor leading to components on the time axis and space axis is the diffusion of the optical imaging system and electronic imaging system. An experiment was conducted to demonstrate the impact process. A laser beam with upright incidence was directed at a flat target, and the laser spot on the target could be transformed into a small point with a  
Figure 2: The coupling caused by angle difference. (**a**) The angle difference of the direction of the sweep electric field. (**b**) The streak image on the CCD. size of 1 mm \(\times\) 1 mm by adjusting the optical emission unit.