The following organization of this paper is listed here: 
In section 2, the basic theory is introduced including the 4MTF 
and the EZFOV model, the three kind formulas to calculate laser 
beamwidth of various scanners, as well as the dimensionless 
AMTF and EIFOV general model. 
In section 3, based on the above theory, the three angular 
resolution of terretrial laser scanner is researched, and it is 
concluded that the relationships and simplified formulas of 
scanning interval and the angular quantisation in two different 
EIFOV value, as well as the theoretical minimum E/FOV and 
the angular quantisation. 
In section 4, the laser beamwidth and angular resolution of 29 
kinds of commerical TLS systems is analysed based on the 
above theory. 
Finally, a conclusion is drew in section 5. 
2. THE METHOD OF CALCULATING BEAMWIDTH 
AND THE MODEL OF AMTF AND EIFOV 
2.4 AMTF Model 
AMTF model is computed by Fourier transfer —APSF(Average 
Point Spread Function), including the sampling AMTF,, the 
beam width AMTF, and quantisation AMTF,. The combined 
model is(Lichti, 2006; Yang Ronghua, 2011) 
AMTF,,, (u) = |sin(zAu) 2J, (wu) sin(zzu)| 
where A = scanning interval, which unit is millimeter 
W = diameter of beamwidth in the distance of S, 
which unit is millimeter 
T = angular quantisation, which unit is millimeter 
4 - frequency, which unit is 1/mm. 
  
= (1) 
| Au TWU TU 
2.2 EIFOV Model 
EIFOV model is favoured for the analysis of electric-optical 
system resolution. The appropriate expression of the EJFOV 
extends to laser scanners as it quantifies the combined effects of 
sampling, beam width and quantisation. E/FOV model is 
computed via the cut-off frequency. It is(Lichti, 2006; Yang 
Ronghua, 2011) 
EIFOV z Kd 2) 
u 
c 
where WU, - the cut-off frequency which satisfy the equation 
2 
(uu 
X 
AMTF, 
sbq 
2.3 Three Method of Calculating Beamwidth 
The point cloud angular resolution is related with the laser 
beamwidth that is affected by several factors such as the scaning 
distance, the divergence characterization of laser beam, the 
diameter of the transmitting aperture and the inclination angles 
of the objective surface, etc(Zhang Yi, 2008;Lai Zhikai, 2004). 
However, no scanner manufacturer currently provides the 
formula used to calculate the laser beam width. Most 
manufacturers keep the value of the most laser characteristics 
parameters still as secret. So it is difficult to know how big is the 
beamwidth in any distance. In here three methods are given to 
calculate different scanner's beam width: 
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 
Firstly, the diameter of the transmitting aperture and three more 
diameters in different distances are given. The formula 
is(Reshetyuk, 2009; Zhang Yi, 2008) 
W24 wi-tc^(S — Ry (3) 
where R, = the range between the beam waist and the 
transmitting aperture, which unit is meter 
W, = diameter of beamwidth in the distance of R, , 
which unit is millimeter 
C = constant variable, which unit is mm/m 
Secondly, the diameter of the transmitting aperture and the beam 
divergence angle is given, or two diameters in different 
distances are given. The formula is(Reshetyuk, 2009; Zhang Yi, 
2008) 
w=2S -tan(%-107)-10° + D (4) 
2 0 
where — 7 = beam divergence angle, which unit is urad 
D, = diameter of the transmitting aperture, which 
unit is millimeter 
Thirdly, the diameter of the transmitting aperture and the 
diameter of beamwidth in a certain distance are given. The 
formula is(Reshetyuk, 2009; Zhang Yi, 2008) 
Jie 4S - Ry. when S<2R, 
w- y (5) 
2:10(5—2R,)tan(5 -10*)+ Dyvhen S>2R, 
2.4 The Dimensionless AMTF And EIFOV Generic Model 
To make the model more practical and more simple, the AMTF 
model eq.1 and the EJFOV model eq.2 can be transformed to 
dimensionless form by using variable substitution, which 
satisfies the equation A = kw, 7=mw,u= 4 , EIFOV - Nw. 
Ww 
The dimensionless AMTF and EIFOV generic model is(Yang 
Ronghua, 2011) 
  
  
  
sin(zkU) 2J, (xU) sin(zmU 
zkU ZU zmU 
1 
N=— (7) 
QU, 
where k = the dimensionless scanning interval, which is 
the ratio of the scanning interval and the 
beamwidth 
m = the dimensionless angular quantisation, which 
is the ratio of the angular quantisation and the 
beamwidth 
U = the dimensionless frequency, which is the 
product of frequency and beamwidth 
U , = the dimensionless cut-off frequency, which is 
the product of cut-off frequency and beamwidth 
N = the dimensionless EIFOV, which is the ratio of 
the EIFOV and the beamwidth 
    
  
   
  
  
  
     
    
   
   
    
   
  
   
   
     
    
    
   
   
   
   
  
    
   
   
    
  
  
    
    
   
   
    
  
     
  
   
    
    
   
     
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