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 
backscattered echoes return to the detector. Waveform is the 
total signal of the backscattered echoes. 
  
Figure 1. Principle of generating waveform data 
In order to simulate this waveform, our main approach is to 
sample the signal echoes by dividing a laser beam into sub- 
beams. Figure 2 represents the required three simulation 
processes. 
The first process is the geometric simulation that defines the 
rays of sub-beams and computes the intersecting point between 
sub-beam and target surface. Second, in radiometric simulation, 
the energy of the each return sub-beam is calculated by laser 
range equation with the range which is computed in geometric 
simulation. Waveform simulation is to generate the return 
pulses using the computed range (return time) and energy and to 
combine these return pulses into a signal (waveform). 
  
Simulation process of full-waveform data 
  
I. Geometric simulation 
i 
II. Radiometric simulation 
| 
IIT. Waveform simulation 
  
  
  
  
  
  
  
  
  
  
Figure 2. Three processes for waveform simulation 
2.2 Geometric Simulation 
The purpose of the geometric simulation is to compute the 
locations where the sub-beams are backscattered. Its output is 
the ranges (times) from the detector to intersecting points of 
sub-beams. In this study, four steps are performed for geometric 
simulation, as follows in Figure 3. 
For the first, we defined the rays (origin and direction) of sub- 
beams in a pre-defined coordinate system with the divergence 
angle of laser beam. Next, we transformed the coordinate 
system of the rays into a ground coordinate system by geometric 
model of lidar system. Then, the intersecting point of each sub- 
beam can be computed by ray tracing, because the coordinates 
of the rays and target models are the same. In the final step, the 
ranges and the return times are calculated. 
  
Define sub-beam rays in the pre-defined coordinate 
+ 
Integrate with GPS, IMU and Scanning mechanism 
+ 
Ray tracing to search intersecting points 
i 
Compute ranges and return times 
  
  
  
  
  
  
  
  
  
Figure 3. Processes of geometric simulation 
2.2.1 Sub-beams: To define rays of sub-beams, we 
computed the footprint (coverage of laser beam) at a nominal 
distance by the divergence and the beam width. Then, we 
divided the coverage with the consistent interval which is 
computed considering the number of sub-beams. The ray of 
each sub-beam can be defined by line-equation passing the 
detector (0, 0, 0) and the centre of the divided area, as shown in 
Figure 4 (Kim et al, 2009). 
      
  
& 
Figure 4. Example of 25 sub-beams (5 by 5) 
2.2.2 Integration: The aim of integration is to transform the 
line-equation of sub-beam defined in the internal coordinate 
system to an absolute coordinate system (WGS84). And it can 
be performed by GPS and IMU sensor. Figure 5 shows each 
coordinate system of the sub-modules (GPS, IMU and laser 
scanner) and their geometric relationships. For the integration, 
the sensor equation, which is a mathematical representation of 
the position where the sub-beam is reflected, is necessary, 
derived as Eq. (1). Table 1 describes the variables of sensor 
equation. The detailed geometric modelling of lidar system 
including systematic errors is reported by Schenk (2001). 
Zw y 
i Yw INS 
coordinate 
Ga system 
* 
      
  
à Laser scanner 
coordinate 
system 
   
     
nr INL 
NN 
WGSB84 ^ 
coordinate 
system 
Zw Yo. i # "e. 
E ^". 
Xs à Target Point 
Figure 5. Geometric relationships of lidar (Schenk, 2001) 
W Wo 
P= Ry Ry Rojuy rtg fy, (1) 
  
P” | Location of target point 
  
  
  
R Rotation matrix for the transformation from 
7I! | IMU coordinate system to WGS84