The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The target points on the wall were marked by retro-reflectors, 
as shown in Figure 4. And a total station was used to measure 
the footprint on the wall accurately. 
Figure 4. The retro-reflector placed on the wall 
In the experiment, there are two steps continuously collecting 
data. In the first step, the beam divergence angle was set to 
0.3mrad; the incidence point on Ml was defined as the origin in 
Figure. 1. Set the scan angle to a fixed value, the coordinate of 
the point could be calculated from the recorded angle and range 
of the target. 
In the second step the beam divergence angle was set to 
0.8mrad; set the scan angle to the same value as before. For the 
errors caused by movement of the incidence point on Ml, the 
true coordinate of the point was changed. The footprint 
movement direction on the wall was observed by infrared 
observer. This helped to make sure that the tuning of beam 
divergence affected the laser pointing accuracy. 
3.3 The Experiment Data 
In the experiment, 31 points were set from -15° to 15° with a 
gain of 1°. Two groups of data were recorded in order to 
calculate the error vector E. 
One group was the target point coordinates recorded by AOE- 
LiDAR (with errors caused by the change of beam divergence 
angle). The scan angle and range recorded by AOE-LiDAR are 
shown in Table.2. 
No. 
1 
2 
3 
4 
5 
Angle (°) 
-7.5 
-7 
-6.5 
-6 
-5.5 
Range(mm) 
222235 
221296 
220425 
219631 
218906 
6 
7 
8 
9 
10 
11 
-5 
-4.5 
-4 
-3.5 
-3 
-2.5 
218269 
217679 
217175 
216731 
216358 
216058 
12 
13 
14 
15 
16 
17 
-2 
-1.5 
-1 
-0.5 
0 
0.5 
215811 
215632 
215532 
215489 
215505 
215601 
18 
19 
20 
21 
22 
23 
1 
1.5 
2 
2.5 
3 
3.5 
215739 
215966 
216254 
216604 
217026 
217517 
24 
25 
26 
27 
28 
29 
4 
4.5 
5 
5.5 
6 
6.5 
218071 
218712 
219396 
220168 
221010 
221934 
30 
31 
7 
7.5 
222925 
223990 
Table 2. Scan angle and range recorded by AOE-LiDAR 
If the errors caused by the change of beam divergence angle 
were not considered, the point coordinates were calculated as 
shown in Table 3. 
No. 
1 
2 
3 
4 
5 
X(mm) 
1679.7 
1676.7 
1673.7 
1670.7 
1667.8 
Y(mm) 
-37947.6 
-33965 
-30014.3 
-26093.3 
-22199.3 
Z(mm) 
-213984.4 
-213914.5 
-213842.3 
-213771.3 
-213700 
6 
7 
8 
9 
10 
11 
1664.9 
1661.9 
1659.1 
1656.2 
1653.3 
1650.5 
-18331.4 
-14482.5 
-10655.1 
-6843.2 
-3046.1 
738.9 
-213641.7 
-213564 
-213505.3 
-213436.4 
-213372.3 
-213312.2 
12 
13 
14 
15 
16 
17 
1647.6 
1644.8 
1641.9 
1639.1 
1636.3 
1633.4 
4515 
8283.6 
12047.1 
15808.1 
19568.5 
23331.4 
-213240.3 
-213170 
-213113.1 
-213047.5 
-212976.7 
-212918.7 
18 
19 
20 
21 
22 
23 
1630.6 
1627.7 
1624.9 
1622 
1619.1 
1616.3 
27097.2 
30870.8 
34653.1 
38446 
42252.8 
46076 
-212837.2 
-212778 
-212713.6 
-212643.8 
-212577.7 
-212513.2 
24 
25 
26 
27 
28 
29 
1613.4 
1610.4 
1607.5 
1604.6 
1601.6 
1598.6 
49916.5 
53781.2 
57664.4 
61576.9 
65516.9 
69490.6 
-212442.1 
-212387.7 
-212307.4 
-212242.9 
-212172 
-212109.6 
30 
31 
1595.6 
1592.5 
73496.6 
77538.8 
-212038.1 
-211963.1 
Table 3. Point coordinates calculated without considering errors 
caused by ei and e 2 
The other group was the coordinates measured by total station. 
The true coordinates of the target point measured by total 
station were shown in Table.4. 
No. 
1 
2 
3 
4 
5 
X(mm) 
1700 
1697 
1696 
1694 
1690 
Y(mm) 
-37913 
-33929 
-29977 
-26058 
-22164 
Z.(mm) 
-213987 
-213921 
-213848 
-213780 
-213709 
6 
7 
8 
9 
10 
11 
1687 
1682 
1679 
1677 
1677 
1670 
-18296 
-14449 
-10620 
-6809 
-3010 
773 
-213652 
-213568 
-213507 
-213440 
-213373 
-213316 
12 
13 
14 
15 
16 
17 
1667 
1667 
1666 
1661 
1658 
1657 
4550 
8319 
12083 
15844 
19602 
23367 
-213242 
-213171 
-213111 
-213044 
-212973 
-212915 
18 
19 
20 
21 
22 
23 
1650 
1648 
1645 
1643 
1641 
1637 
27134 
30907 
34690 
38481 
42288 
46112 
-212834 
-212775 
-212706 
-212641 
-212574 
-212506 
24 
25 
26 
27 
28 
29 
1633 
1632 
1629 
1626 
1624 
1620 
49952 
53818 
57700 
61612 
65554 
69525 
-212438 
-212384 
-212301 
-212231 
-212163 
-212101 
30 
31 
1619 
1617 
73532 
77576 
-212030 
-211952 
Table 4. Point coordinates measured by total station 
Use these two groups of data, the errors were calculated by the 
formulae (1) ~ (9). 
3.4 Results 
From Table.3 and Table.4, the errors ej and e 2 described in 
chapter 2 were calculated. Since the values of the errors were 
usually small judged by experience, the initial values of ej and 
e 2 were set to zero. After several times of iteration, ei and e 2 
were calculated as ej = 0.036793040994718 (mm), e 2 = 
0.066471918809104(mm). Recalculate the scan point