=! 
  
  
SE 
nd m 
ain the 
(16) 
ed form 
can get 
( fitting 
(17) 
From the equation (17), the relationship graph of k and m is 
ellipse, and the fitting errors of the equation (17) and m is 
Fig.5. From the plot of Fig.5, we can see that fitting errors is 
less than 0.0003. so we can think that the equation (16) is 
approximately equaivalent with the equation (17). 
  
  
T T : T 
0.0 0.1 0.2 0.3 0.4 0.5 m 
  
  
  
0.0002 —À 
0.0000 + 
-0.0002 — 
  
-0.0004 T T T ; ; 
0.0 0.1 0.2 0.3 0.4 0.5 m 
  
  
  
  
Figure 5. The rationship curve graph of fitting errors & 
(equation (17)) and m 
3.3 The Relationship & Simplified Formula of N_, And m 
With the equation (6), (7) and k=0 , we can gain the 
relationship of N... and m that is 
  
  
  
T Am 
2J, (————) sin 
C o CC 2 
———— em (18) 
7 zm 7t 
AN n ZN rin 
The equation (18) is needed to simplify using the same method 
as above. we can also get the relationship graph of N, and 
min 
m (Fig.6) and the fitting formulas of N,,, and m that is 
Na m4 t5: (m-g,) -h, (19) 
where a, — 0.82102 
b, - 1.03814 
£4 -0.0371 
h, = 0.0437 
From the equation (19), the relationship graph of k, and m is 
hyperbola, and the fitting errors of the equation (19) and m is 
Fig.7. From the plot of Fig.7, we can see that fitting errors is 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
less than 0.004. So the equation (18) is approximately 
equaivalent with the equation (19). 
  
min 
2.0 4 
(0,0.8594 
  
  
T T 
0.0 0.5 1.0 1.5 2.0 2.5 m 
  
  
Figure 6. The rationship curve graph of N,,, and m 
  
0.004 - 
0.003 + 
0.002 4 
0.001 À 
0.000 + 
-0.001 — 
  
  
-0.002 T T T T T 
0.0 0.5 1.0 1.5 2.0 2.5 M 
  
  
  
Figure 7. The rationship curve graph of fitting errors & 
(equation (19)) and m 
4. BEAMWIDTH AND RESOLUTION OF TLS SYSTEM 
The laser beam width and angular resolution of 29 
commerically available TLS systems(GIM, 2010) is analysed 
using the three methods of calculating beamwidth diameter and 
the equation (15), (17), (19). To facilitate the comparision, each 
vendor’s reported finest angular sampling interval and 
beamwith and calculated EJFOV have been reduced to linear 
spatial units at a range of 50m. The results about the 
coefficients of different scanner's beamwidth formula are given 
in Table 1, and the results about k, , &, and N,,, of different 
scanner are given in Table 2. 
From Table 1, we can see that the three methods of equation (3), 
(4) and (5) can solve the problem of calculating all TLS 
systems' laser beamwidth diameter. 
Shown as Tab. 2: 
1) The 29 systems can be classified into three groups 
according to EJFOV,... (the theoretical minimum EIFOY): 
fine resolution scanners; medium resolution instruments; 
and coarse resolution instruments. 
2) For Trimble GS. Basis Software Surphaser 25HS. Z+F 
PROFILER 5006h #1 Z+F Imager 5003: The theoretical 
minimum dimensionless EIFOV N(>1); The dimensionless 
angular quantisation(<0.545); The dimensionless scanning 
interval k, (N/A); 
in