## 3 Results  
### Laser Far-Field Characteristics Analysis  
Before conducting the STIL ranging assessment, we first carried out a field test to capture laser spot images and analyze the far-field characteristics of the laser spot. A high-resolution CCD camera was used, with an exposure time of 500 ms, to obtain 2048 \(\times\) 2592 pixel 8-bit grayscale images of the laser spot on the target surface. Figure 4a shows the raw image of the laser spot. Due to the limited camera angle during the test, the laser spot images exhibited distortion and aberration, making it challenging to directly derive its intensity distribution. To address this issue, a projection correction is applied to the image coordinates, aligning the optical axis of the rectangular spot with the image coordinate axis. This transformation enables the extraction of the intensity distribution along the scanning direction by reading the pixel grayscale values from a single row of the image.  
The correction process utilizes a projection transformation matrix, which maps points from the original image plane to a new projection plane, preserving the linearity of straight lines before and after the transformation. The relationship is given by the equation \([x\_y,1]^{\prime}=H\cdot[x^{\prime}y^{\prime},1]^{\prime}\), where (\(x\_y\)) are the row and column coordinates of the corrected image, (\(x^{\prime}\),\(y^{\prime}\)) are the coordinates in the original image, and \(H\) is a homography matrix. This approach effectively compensates for the angular deviation of the camera, thereby aligning the rectangular spot with the image coordinate axis. The matrix is determined by solving a system of equations using four pairs of calibration points. The initial calibration points  
Figure 3: Reflected spots of laser pulses from targets at different distances: (**a**) elliptical Gaussian laser spot formation on a target building at 1 km; (**b**) schematic of target building and STIL system positioning for long-range ranging at 6 km; (**c**) incomplete reflection of laser spot on test target building at 6 km.  
for the computation of the projection transformation matrix were manually selected by the researchers based on the rectangular features of the bricks in the image. After multiple iterations of selection and optimization, the final calibration matrix was obtained. The calculated projection transformation matrix is [1.4778, \(-\)0.0410, \(-\)0.0014; \(-\)0.0661, 1.1189, 0.0013; 0.0001, 0, 1].  
Based on the calculated projection transformation matrix, we performed projection correction on the raw laser spot images, as shown in Figure 4b. After projection correction and actual spatial scale measurement, the spatial resolution of the image in Figure 4c is 4.3 mm/pixel, and the laser spot's width at a 6 km target distance is measured to be 0.66 m. This indicates a very small divergence angle and confirming the system's excellent beam characteristics.  
The system generates a linear illumination area on ground targets, and the illumination spot width and receiver area width are calculated using the formula \(r=H\cdot tan\theta\), where \(\theta\) is the divergence angle of the laser in the scanning direction. In this study, after configuring the CCD camera and directing the detection laser toward a fixed far-field target, we measured the spot size to be \(r=0.33\) m, resulting in a calculated laser divergence angle of \(5\times 10^{-5\circ}\). The system's laser divergence angle of \(5\times 10^{-5\circ}\) ensures low beam spread over long distances, which is essential for maintaining measurement accuracy. This small divergence allows efficient laser energy use, improves long-range detection, and lowers the system's power and sensitivity requirements for distance measurement.