## 2 Materials and Methods
### STIL Ranging Data Processing  
According to the ToF ranging principle, the ranging distance \(d\) is expressed as:  
\[d=\frac{c\times t_{range}}{2n} \tag{1}\]  
where \(c\) is the speed of light, and \(n\) is the refractive index of the atmospheric medium. The ranging time \(t_{range}\) in the proposed STIL system refers to the duration between emitting and receiving a laser pulse. This ranging time can be described as follows:  
\[t_{range}=\left(t_{\textit{streak\_camera\_trigger}}+t_{\textit{streak\_echo}}+ \tau_{\textit{streak\_camera}}\right)-\left(t_{\textit{optical\_trigger}}- \tau_{\textit{PIN}}\right)-\tau_{\textit{env}} \tag{2}\]  
The designed STIL measures the time delay of the optical trigger \(t_{optical\_trigger}\) and the streak camera trigger \(t_{\textit{streak\_camera\_trigger}}\) using two independent channels of TDC and records the echo intensity changes with time \(t_{\textit{streak\_echo}}\) through the streak camera. \(\tau_{\textit{streak\_camera}}\) represents the intrinsic delay between the trigger of the streak camera and the generation of the output image. This delay is determined by the inherent characteristics and design of the streak camera. \(\tau_{\textit{PIN}}\) refers to the inherent delay in the optical path between the PIN diode trigger pulse and the emission of the fan-shaped laser pulse. This delay is influenced by the laser emitter's components and configuration. \(\tau_{\textit{env}}\) is the propagation delay of the laser pulse during atmospheric transmission, which is influenced by environmental factors such as visibility. For short-term measurements, this delay is treated as a constant. Based on this ranging principle, the system ranging time is described by the model:  
\[t_{range}=\Delta t_{\textit{trigger}}+\Delta t_{\textit{streak\_echo}}+\tau \tag{3}\]  
The ranging accuracy of the system is influenced by several factors: the temporal characteristics of the laser output pulse, TDC time measurement errors, the temporal calibration accuracy of streak camera, and the accuracy of echo time feature extraction from streak images. To improve ranging precision, it is essential to use high-stability and high-resolution lasers and TDC units, precisely calibrate the temporal characteristics of the streak camera, and employ efficient streak image processing algorithms to extract echo temporal features. In the processing of streak images, the centroid point of the echo is extracted by row as the time axis coordinate of the echo at that spatial angle:  
\[n_{echo}(m)=n_{con}(m)=\frac{\sum_{n\in I_{(m)}}\left(n\cdot I_{(m,n)}\right)}{ \sum_{n\in I_{(m)}}I_{(m,n)}} \tag{5}\]  
3. \(\quad\) Streak echo temporal information extraction  
\[\Delta t_{streak,echo}(m,n_{echo}(m))=M_{t}(m,\lfloor n_{echo}(m)\rfloor) \times(1-b)+M_{t}(m,\lfloor n_{echo}(m)\rfloor+1)\times b \tag{6}\]  
Combining the calibration time matrix \(M_{t}\) and the coordinates of the echo centroid points \((m,n_{echo}(m))\), we interpolate and extract the temporal information to determine the temporal relative values \(\Delta t_{streak,echo}\) of the echo lasers recorded in the streak image, where \(b=n_{echo}(m)\cdot\lfloor n_{echo}(m)\rfloor\), the time values \(\Delta t_{streak,echo}\) of the echoes are obtained by linearly interpolating the column directions of the calibration matrix \(M_{t}\). 4. \(\quad\) Ranging Data Fusion  
The STIL system operates by conducting pulse measurements at a specific repetition frequency. For the detection pulse \(k\), the fusion of ranging pulse time \(\Delta t_{\text{TDC}}\) from the TDC with echo time information \(\Delta t_{streak,echo}\) extracted from multiple streak images is essential. This calculation depends on the high synchronization between the TDC data and the streak images, ensuring precise determination of the relative time \(t_{range}^{*}\) for the current pulse:  
\[t_{range}^{*}(k,m)=\Delta t_{trigger}(k)+\Delta t_{streak,echo}(k,m,n_{ echo}(m) \tag{7}\]  
5.