International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
  
  
  
  
  
R Rotation matrix considering the difference in 
LI | orientation between IMU and scanner system 
R 3D transformation matrix of the scanning 
OL | system 
U, Direction of sub-beam ray 
r Range from the origin to target point 
{y Offset between IMU and laser scanner 
IL expressed in WGS84 
t y Position of IMU expressed in WGS84 
  
  
  
  
Table 1. Description of variables in sensor equation 
(Kim et al, 2009) 
2.2.3  Ray-tracing: In order to compute an intersecting point, 
we have to identify the facet of target that encounter with sub- 
beam. However, it is not efficient to inspect whether a facet 
intersects with sub-beam or not, one by one. Thus, we employed 
ray tracing algorithm to find the intersecting facet. Figure 6 
illustrates the concept of ray tracing we used. As you can see 
Figure 6, the cell, intersected with sub-beam, can be found by 
reducing the vertical and horizontal range from one to another 
(Kim et al, 2008). 
SL. 
i ^2. 
be 
v 
  
  
Figure 6, Concept of ray-tracing algorithm 
2.3 Radiometric Simulation 
Radiometric simulation is to calculate the amount of the 
received energy of return pulse. Figure 7 represents the 
processes of radiometric simulation in this study. To calculate a 
received optical power, transmitted power should be known 
before. The intensity of laser beam is not constant across the 
range from the center axis which is the direction of the beam. It 
represents the energy profile of the laser beam in the space. In 
many previous works, Gaussian beam profile, as shown in 
Figure 8, is widely used, and its mathematical model can be 
derived as Eq. (2). Where 7 is distance from the central axis in 
the cross-section; / Üj is the maximum irradiance of the beam; 
and @ is the beam half-width (Carlsson et al, 2001). 
  
Calculate transmitted energy of sub-beam 
by beam profile 
i 
Calculate returned energy by laser range equation 
  
  
  
  
  
Figure 7. Processes of radiometric simulation 
519 
  
  
  
@) 
The returned energy is calculated using laser range equation, 
expressed in Eq. (3) (Carlsson et al, 2001). And its variables are 
described in Table 2. 
9 
  
  
  
  
  
  
  
  
  
P = -p-008(0)- EE a No G) 
P Received energy 
Pp Transmitted energy 
p Reflectance of target surface 
0 Incidence angle 
Q - Scattering steradian solid angle 
R Travel distance of sub-beam 
D Aperture diameter 
Maim | Efficient of optical system 
Hs | Atmospheric attenuation 
  
  
  
  
Table 2. Description of variables of laser range equation 
2.4 Waveform Simulation 
Waveform simulation is to generate the return signal that a 
detector of lidar receives in time domain and to detect return 
times using the simulated waveform. It mainly consists of three 
procedures as represented in Figure 9. Waveform is generated 
by summing return pulses that are generated by pulse model, 
received energies and ranges which are computed in geometric 
simulation. 
  
Merge return signals into waveform 
D 
[Insert signal random noise using NEP 
+ 
Detect return times from waveform using CFD 
  
  
  
  
  
  
  
Figure 9. Processes of waveform simulation