The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
mirror and a swinging mirror. When tuning beam divergence, 
actually the lenses in the beam expander were moving. 
To calculate the effect of the errors caused by the change of 
divergence angle, a scan coordinate system was established first. 
Taking the incidence point on the fixed mirror as the origin 
point, defined the direction of flight as X axis while Y axis 
pointed to the larboard, and Z axis pointed to the opposite 
direction of the transmitted laser beam. 
Figure 1. The mechanical system of AOE-LiDAR, including a 
laser transmitter, a set of lenses, a fixed mirror and a 
swinging mirror. 
The fixed mirror Ml with normal vector M = [nt) m 2 m 3 ] was 
described by 
m l x + m 2 y + m 3 z = 0 ^ 
The beginning point of the distance measurement was defined 
as 0 = \X Y Z 1 ; the true incidence direction vector 
(7 = [zj L /']) was represented by a function of O and E, 
i=f(0,E) (2) 
The incidence point (FJ = [X, Y x Z, ]) on M1 was a function of 
E, 
P,=g(.E) (3) 
With Ml considered as a plane, the direction of the reflected 
laser beam d = [o, o, o 3 ] was given by i and M. 
This laser beam then arrived at the swinging mirror M2, and 
was reflected again. M2 swung at a certain angular velocity 
around the X axis. The position of M2 was given by the 
beginning normal vector and the swing angle co, so the 
current normal vector of M2 was N = \n n, « 1 = R ■ N 
LI 2 3-1 co 0 
where R (1) was the swing angle matrix, and the function of M2 
was 
The scan coordinate system is shown in Figure 2, Ml 
represented the fixed mirror; M2 represented the swinging 
mirror. To simplify the geometry model of the mechanical 
system, only the errors of the direction of the laser beam were 
considered. These errors caused the incidence point depart from 
the origin, which was its initial position; these departures 
composed the error vector E = [ej e 2 ]. E was on the plane of Ml, 
with the positive direction of e! was along the X axis, the 
positive direction of e 2 was along the projection of Y axis on 
the M1 plane. 
Figure 2. The scan coordinate system of the mechanic structure 
n i( x 7Y l ) + n 2 (y T,) + h 3 (z Z,)-0 
The incident laser beam of M2 was given by and O , the 
position of the incidence point on M2 was p 2 = [X 2 Y 2 Z 2 ] • The 
direction of the reflected laser beam was J = [5, s 2 s 3 ]. 
Defining P as the target point coordinate with [X p Y p Z p ], and 
the distance between P 2 and P was d, then 
P = P 2 + s - d 
(5) 
All the calculations above were processed in the scan 
coordinate system, while the measurement was done in another 
coordinate system called the ground system (which was a local 
coordinate system defined by total station), so the coordinate of 
P had to be translated into this system. The target point in the 
ground coordinate system was defined by function 
(6) 
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