The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
335 
coordinates by adding the effect ei and e 2 , the calibrated point 
coordinates were shown in Table 5. 
No. 
1 
2 
3 
4 
5 
X(mm) 
1701.6 
1698.5 
1695.4 
1692.4 
1689.4 
Y(mra) 
-37911.6 
-33929.9 
-29978.3 
-26057.9 
-22163.6 
Z(mm) 
-213991.2 
-213924.7 
-213847.9 
-213778.5 
-213705.5 
6 
7 
8 
9 
10 
11 
1686.4 
1683.4 
1680.5 
1677.6 
1674.7 
1671.8 
-18295.9 
-14446.9 
-10619.4 
-6807.7 
-3010.4 
774.5 
-213647.4 
-213568.6 
-213507.9 
-213439.8 
-213372.2 
-213314.4 
12 
13 
14 
15 
16 
17 
1668.9 
1666 
1663.2 
1660.3 
1657.5 
1654.7 
4550.6 
8319.2 
12082.6 
15843.6 
19604 
23366.9 
-213241.7 
-213171.4 
-213113.6 
-213047.8 
-212975.2 
-212917.1 
18 
19 
20 
21 
22 
23 
1651.8 
1649 
1646.2 
1643.4 
1640.5 
1637.7 
27132.7 
30906.3 
34688.3 
38481.5 
42288.4 
46111.2 
-212834.9 
-212775.2 
-212707.9 
-212640.1 
-212574.1 
-212506.4 
24 
25 
26 
27 
28 
29 
1634.9 
1632 
1629.1 
1626.3 
1623.4 
1620.5 
49952 
53816.7 
57699.9 
61611.9 
65552.7 
69525.8 
-212436.1 
-212381.4 
-212300.6 
-212232.9 
-212165.3 
-212099.4 
30 
31 
1617.5 
1614.6 
73532 
77573.8 
-212028.4 
-211951.4 
Table 5. Point coordinates calibrated by et and e 2 
In Figure.5, the true values (point coordinates measured by total 
station) were represented by data set 1; the raw data (point 
coordinates calculated without considering ei and e 2 ) were 
represented by data set 2; the calibrated data (point coordinates 
calculated considering ei and e 2 ) were represented by data set 3 . 
Figure 5 . The errors caused by change of beam divergence 
angle before and after calibration 
4. DISCUSSION 
accuracy of AOE-LiDAR is required to be O.lmRad; that means 
at the distance of 200m, the errors on X axis and Y axis were 
less than 20mm. Before calibration, the residuals were dx = 
±21.5mm, dy = ±35.5mm, dz = ±5.2mm. After calibration, the 
residuals reduced to dx = ±1.2mm, dy =± 0.8mm, dz = ±1.6mm. 
That satisfied the pointing accuracy of AOE-LiDAR. 
In future research, an improved calibration method will be 
studied, which contained the error factors in a general 
mathematic model. The relativity between the error factors is 
complex; the general mathematic model would help to increase 
the LiDAR data precision. 
5. CONCLUSIONS 
When tuning the beam divergence angle (which changed the 
footprint size), 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. From 
formulae (1) ~ (9), the optical axis shifting errors were 
calculated in the ground experiment. After calibration the 
system error caused by vector E was removed, the pointing 
precision of AOE-LiDAR increased obviously, which was 
increased from ±0.2mRad to ±0.01mRad. 
REFERENCES 
Baltsavias, E.P., 1999a. A comparison between 
photogrammetry and laser scanning. ISPRS Journal of 
Photogrammetry and Remote Sensing, 54, 83-94. 
Baltsavias, E.P., 1999b. Airborne laser scanning: basic relations 
and formulas. ISPRS Journal of Photogrammetry and Remote 
Sensing, 54, 199-214. 
Burman, H., 2000. Calibration and Orientation of Airborne 
Image and Laser Scanner Data Using GPS and INS, PhD 
dissertation, Photogrammetry Reports No. 69, Royal Institute of 
Technology, Stockholm, 107p. 
Luis Gon^alves-Seco, David Miranda, Rafael Crecente and 
Javier Farto. Digital Terrain Model generation using airborne 
LiDAR in a forested area of Galicia, Spain. 7th International 
Symposium on Spatial Accuracy Assessment in Natural 
Resource andEnviromental Sciences, 169-180. 
Nora Csanyi May, Charles K. Toth, 2007. Point Position 
Accuracy of Airborne LiDAR Systems: A Rigorous Analysis. 
International Archives of Photogrammetry, Remote Sensing and 
Spatial Information Sciences, 36, 107-111. 
Wehr, A., Lohr, U., 1999. Airborne laser scanning - an 
introduction and overview. ISPRS Journal of Photogrammetry 
and Remote Sensing, 54, 68-82. 
From the data above, obvious system errors were found when 
tuning the beam divergence of LiDAR; actually the errors were 
caused by the shift of the optical axis. It was hard to make the 
incidence point on the mirror immobile when tuning beam 
divergence. From the experiment, shift of the incidence point 
was calculated, error vector E was added to formula (6), the 
errors of recalculated scan points were reduced. The pointing 
ACKNOWLEDGEMENTS 
The authors would like to thank the LiDAR Department, 
Academy of Opto-Electronics, Chinese Academy of Sciences 
for having supported LiDAR data acquisition.