LASER FOOTPRINT SIZE 
AND POINTING PRECISION ANALYSIS FOR LIDAR SYSTEMS 
Xu Bin a , Li Fangfei a , Zhang Keshu a ’*, Lin Zongjian b 
a Academy of Opto-electronics, Chinese Academy of Sciences, 95, Zhongguancun Road East, Haidian District, Beijing, 
China, 100080 - xub@aoe.ac.cn 
b Chinese Academy of Surveying & Mapping, 16 Beitaiping Road, Beijing, China, 100039 - lincasm@casm.ac.cn 
WG 1/2 - SAR and LiDAR Systems 
KEY WORDS: LiDAR, Data, Accuracy, Analysis, Laser scanning 
ABSTRACT: 
Laser footprint size and beam divergence angle tuning was found to affect LiDAR data accuracy and measurement precision because 
of beam axis shifting. The laser beam divergence angle is generally tunable in modem LiDAR systems in order to adapt to different 
application scenarios. Beam divergence angle can either be switched from one position to the other (i.e. 0.3mRad / 0.8 mRad), or be 
tuned continuously (i.e. 0.3 to 0.8 mRad). In either case, mechanical moving parts have to be introduced into the optical systems. As 
a result, the movements of mechanical parts make the optical axis shift and the laser pointing direction shift as well. In other words, 
switching laser beam divergence angle makes the laser pointing accuracy degrade. A mathematic model was developed to improve 
the LiDAR data accuracy when the laser beam divergence angle was changed in surveying practice. Experiments were designed and 
carried on to verify the calibration model. A calibration method and procedure was introduced to handle these issues. 
1. INTRODUCTION 
In the last few years, some of the weaknesses of 
photogrammetry have been overcome by using airborne LiDAR 
(Light Detection And Ranging) (Baltsavias, 1999a), which 
proves that laser altimetry is now a mature technology for the 
determination of accurate DTMs. The term airborne LiDAR or 
Airborne Laser Scanning (ALS) refers to an airborne laser 
system consisting of a laser scanner, a geodetic-quality GPS 
receiver and an inertial measurement unit (IMU), which provide 
data about the scan angle and the aircraft coordinates and 
attitude (Wehr and Lohr, 1999). Based on this data and on the 
distances measured, point coordinates are calculated (Baltsavias, 
1999b) and stored in digital format in the onboard computer. 
LiDAR systems are widely used in modem surveying projects 
due to its accuracy, informative signals and good resolution. 
People are interested in acquiring higher accuracy in measuring, 
pointing, more return signals and better resolution of intensity. 
Laser footprint size and beam divergence angle tuning was 
found to affect LiDAR data accuracy and measurement 
precision through its influence on laser beam pointing. 
Besides the consideration of human-eye safety, laser power, 
flying altitude, point cloud distribution etc., the geometric 
feature of survey targets is the primary factors determining the 
LiDAR’s beam divergence angle. For city survey projects, it is 
desirable to get accurate 3-D models of the buildings, streets, 
rivers and so on. The edges of models should be as sharp as 
possible when they are extracted from the LiDAR shots cloud. 
Small footprint size and high shot cloud density are the 
precondition for this purpose. In the forest survey, laser beam 
should have a small divergence angle to get the hierarchy, 
multi-return signals and high penetrability. In electric wire 
survey, bigger footprint should be used to detect the small 
targets. 
The laser beam divergence angle is generally tunable in modem 
LiDAR systems in order to adapt to above application scenarios. 
Beam divergence angle can either be switched from one 
position to the other (i.e. 0.3mRad / 0.8 mRad), or be tuned 
continuously (i.e 0.3 to 0.8 mRad). In either case, mechanical 
moving parts have to be introduced into the optical systems. As 
a result, the movement of mechanical parts made the optical 
axis shift and the laser pointing direction shift at the same time. 
In other words, switching laser beam divergence angle made the 
laser pointing accuracy degraded. Taking AOE-LiDAR system 
as an example, 0.1 mm offset at the emission point (about 
0.218mRad offset) of laser beam expander caused 0.28m of 
error in 1000 meters distance and 0.56m in 2000 meters away. 
Moreover, the offset did not occur just along the x or z axis, it 
occurred in any direction. 
There are several error sources that can degrade the accuracy of 
the derived ground coordinates (Nora Csanyi May, Charles K. 
Toth, 2007), such as, errors in the navigation solution (position 
and attitude errors), range measurement errors, scale and offset 
errors of scan angle, etc. In addition, the effect of the errors is 
influenced by the flight parameters (flying height, flying speed, 
etc.). Usually, the basic errors such as range measurement 
errors, scale and offset errors of scan angle were calibrated in 
lab calibration, the navigation errors were calibrated in flight. 
Because of the complex error sources, it is hard to separate the 
error brought by the change of beam divergence in flight 
calibration; and because of the limited space in lab, this error 
can not be calibrated in lab either. A better method to calibrate 
the laser pointing error was a calibration experiment on field. 
2. METHODOLOGY 
As shown in Figure 1, the optical system of typical LiDAR 
system includes a laser transmitter, a set of lenses, a fixed 
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