==== Angular Resolution ====
**I. Definition**\\
**Angular Resolution** refers to the angle formed between the lines connecting the ranging center to two adjacent detection points in either the horizontal or vertical direction within a LiDAR-generated point cloud. Depending on the axis of measurement, it is categorized into **Horizontal Angular Resolution** and **Vertical Angular Resolution**.
|  {{ :yanding:成像质量评价:工具:激光雷达:激光雷达1.png?580 |}}  |
^  Figure 1[1]:  Schematic of LiDAR Angular Resolution  ^
**Horizontal Angular Resolution: **: The angle formed between the lines connecting the ranging center to adjacent detection points along the azimuth direction. It reflects the sampling density in the horizontal plane, affecting the acquisition of lateral contours and fine details of a target.\\

**Vertical Angular Resolution: **: The angle formed between the lines connecting the ranging center to adjacent detection points along the elevation direction. It reflects the sampling density in the vertical plane, affecting the acquisition of vertical contours and height information of a target.\\

Taking Figure 1 [1] as an example, at a detection range of 30 m, a horizontal angular resolution of 0.10° results in a horizontal spacing of approximately 5 cm between adjacent points; a vertical angular resolution of 1° results in a vertical spacing of approximately 50 cm. This demonstrates that at a constant distance, a smaller angular resolution value leads to smaller spatial intervals between points and a denser point cloud, enabling more comprehensive sampling of target contours and details.\\


**II. Influencing Factors **\\
**(1) Scan Channel Configuration** \\
Angular resolution is affected by the synchronization between the scanning mechanism (motor/micro-mirror) and the laser point frequency. If the step angle (sampling interval) is too large, the point cloud distribution will be too sparse, causing small distant targets to fall into the gaps of the point cloud, resulting in information loss and perception blind spots; if the step angle is too small, it will lead to data redundancy and cannot effectively improve resolution when exceeding the physical limit. Testing must ensure that the actual step angle is consistent with the theoretical design to ensure the uniformity of spatial sampling.\\
|  {{ :yanding:成像质量评价:工具:激光雷达:通道数.png?500 |}}  |
^   Figure 2: Point Cloud Comparison of 16/64/128-Channel LiDAR  ^
As shown in Figure 2 [2], increasing the number of channels typically increases the number of vertical sampling lines, resulting in a denser point cloud that reveals more object and scene details.\\

**(2) Beam Divergence** \\
Beam divergence affects the spread of the laser beam and the resulting spot size during propagation. The spot size increases proportionally with the detection distance. When a spot covers multiple targets or a target edge, the received echo may contain reflections from various sources, hindering target discrimination and measurement accuracy. Consequently, the actual spatial resolution of a system is determined not only by the angular sampling interval (which dictates sampling density) but also by the beam divergence (which influences spot size and the ability to resolve fine target details).\\
|  {{ :yanding:成像质量评价:工具:激光雷达:角分辨率.png?400 |}}   |
^  Figure 3: Schematic Comparison of Beam Divergence  ^
As illustrated in Figure 3[3], for an aircraft at an altitude of 1000 m, a beam divergence of 0.7 mrad results in a ground spot diameter of 0.7 m, whereas a divergence of 0.3 mrad results in a diameter of 0.3 m. This indicates that at the same detection distance, a larger beam divergence increases the spot size, which may degrade the resolution and detection capability for small or closely spaced targets.\\

**III. Measurement Methodology**\\
Angular resolution is a core performance indicator of automotive LiDAR, directly determining the density of the point cloud and the ability to extract target geometric features. The following details the test conditions, operational procedures, and determination methods for angular resolution in accordance with the relevant provisions of GB/T 45500-2025. {Note: This test method is not applicable to LiDAR using MEMS technology.}\\

**(1) Test Conditions:**\\
**Environment Setup:**\\
|  {{ :en:yanding:imaging_basics:imaging_systems:lidar:angluar_resolution-1.png?600 |}}  |
^  Figure 5: Angular resolution test setup  ^

**Equipment Recommendation**\\
The Automated Automotive LiDAR Testing System, independently developed by Yanding, is designed to comply with the GB/T 45500-2025 standard. It provides a one-stop standardized verification process—from device control and data acquisition to report generation—for metrics including ranging and angular resolution. Core components used in this test, such as the 90% diffuse reflection board, automatic target switching bracket, and linear motion guide, are fully integrated into this system.

|  {{ :yanding:成像质量评价:工具:激光雷达:90_反射图卡.png?400 |}}  |  {{ :yanding:成像质量评价:工具:激光雷达:图卡切换.png?400 |}}  |  {{ :yanding:成像质量评价:工具:激光雷达:移动导轨.png?460 |}}  |
^  90% Diffuse Reflectance Target  ^  Automatic Chart Switching Bracket  ^  Moving Guide Rail  ^


**Parameter Requirements:**\\
|  {{ :en:yanding:imaging_basics:imaging_systems:lidar:angular_resolution-2.png?600 |}}  |
^   Figure 6: Angular Resolution Test Parameters   ^

**FOV Partitioning (9 Regions)**\\
|  {{ :yanding:成像质量评价:工具:激光雷达:jgld_视场.png?400 |}}  |
^   Figure 7: Angular Resolution Field-of-View (FOV) Partitioning   ^

**(2) Operational Procedure **\\
|  {{ :en:yanding:imaging_basics:imaging_systems:lidar:ang-3.png?600 |}}  |
^  Figure 8: Operational Schematic for Angular Resolution Testing  ^

(a) Install the LiDAR on a high-precision rotary stage according to the setup in Figure 5. Place a 90% diffuse reflection board (recommended size: 1 cm $\times$ 1 cm) perpendicular to the ground at a horizontal distance of $(d_{\text{Nmin}} + 1\text{ m})_{-5}^{+5}\text{ cm}$. Connect the LiDAR to a point cloud visualization device for real-time data monitoring.\\

(b) Rotate the LiDAR around the ranging center to bring the reflection board into a specific FOV region. Slowly rotate the LiDAR horizontally and record the angle traversed by the rotary stage when the point cloud on the left or right edge of the board transitions from the "2nd point/column" to the "3rd point/column" (i.e., the transition from Scenario A to Scenario B, as shown in Figure 8).\\

(c) Repeat the above measurement at least 5 times. The average of these measurements shall be taken as the horizontal angular resolution for that FOV region.\\

(d) Execute the same procedure by rotating the LiDAR vertically. Record the angle traversed by the rotary stage when a single point or column of the point cloud transitions at the upper or lower edge of the reflection board. Repeat the measurement at least 5 times; the average value is the vertical angular resolution for that FOV region.\\

(e) Repeat steps (b) through (d) to measure the horizontal and vertical angular resolutions for all other FOV regions.\\
  
 
**  (3) Result Analysis**\\
The system is considered compliant with the standard if the difference between the measured angular resolution and the nominal value does not exceed 0.25 times the nominal value.\\

**Image Sources:**\\
[1] https://www.analog.com/en/resources/analog-dialogue/articles/lidar-for-autonomous-system-design-object-classification-or-object-detection.html\\
[2] https://inertiallabs.com/wp-content/uploads/2024/09/Screenshot-2024-09-10-162547.jpg\\
[3] https://www.researchgate.net/figure/llustration-of-LIDAR-beam-divergence-Horizontal-and-vertical-distances-are-drawn-in_fig2_237372271\\
[4] https://www.researchgate.net/figure/An-example-of-point-cloud-distortion-correction-a-The-point-cloud-before-correction_fig13_331102582\\