International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
   
  
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
  
  
   
   
   
    
  
  
  
  
  
  
  
   
   
    
  
   
   
   
    
    
   
   
  
    
  
50 
45 
40 
35 
30 
m) 
25 
EIFOV (m 
20 
0 5 10 15 20 
Optech ILRIS-3D 
= Riegl LMS-Z420i - 
:* Leica FS2500 
—— Mensi GS100 
30 35 40 45 50 
À (mm) 
Figure 3. EIFOV vs. sampling interval at 50 m for four TLS systems. 
beamwidth, the Riegl LMS-Z420i and Optech ILRIS-3D, 
converge more slowly. Note also that the EIFOV is never less 
than the sampling interval under the constraint given by 
Equation 9. 
These analyses demonstrate that neither sampling interval nor 
beamwidth adequately quantify angular resolution. From 
Figure 3, it is clear that sampling interval is appropriate only 
when it equals the EIFOV, i.e. when A >> à. Beamwidth is 
equivalent to EIFOV. and thus an appropriate resolution 
measure, for one multiple of sampling interval: A = (0.5450. 
This coefficient can be estimated by setting EIFOV = à and 
solving Equation 8 for the ratio A/6. The Mensi GS100 
happens to satisfy this relationship. 
4.3 AMTF analysis 
The AMTFs for all four systems’ finest sampling interval at 50 
m range arc plotted along one frequency domain axis in Figure 
4 (for positive spatial frequencies only) together with the 
corresponding cut-off frequencies. Common to all functions is 
they equal unity at the origin and are non-negative for all 
frequencies due to the absolute value operation. They decay 
rapidly to the first zero, beyond which the secondary and higher 
side lobes have much lower amplitude than the main lobe. Both 
A and 8 govern main lobe width, which is of primary interest, 
and the locations of the zeroes, whose spacing may not be 
uniform since Equation 5 is aperiodic in W and v. The 
resolution hierarchy of the four TLS systems is clearly evident 
in the main lobe widths and cut-off frequencies shown in Figure 
4. For example, the AMTF,, of the highest resolution 
instrument, the Mensi GS100, has the broadest main lobe and 
highest cut-off frequency. The narrowest main lobe and lowest 
cut-off frequency belong to the lowest resolution instrument, 
the Optech ILRIS-3D. 
In the case where sampling interval is much larger than 
~ 
beamwidth (i.e.. A >> 5), Equation 3 governs AMTF shape (at 
     
low frequencies), since the beamwidth AMTF (Equation 5) has 
a much greater bandwidth. At the other extreme of A << à, the 
sampling AMTF function has a very broad bandwidth and so 
the combined AMTF shape resembles Equation 5. 
5. SUMMARY AND CONCLUSIONS 
Both sampling interval and laser beamwidth affect the spatial 
resolution of laser scanners. The effective instantaneous field 
of view has been proposed as a more accurate measure of 
resolution since neither sampliug interval nor beamwidth are 
adequate descriptors except under very specific conditions. To 
derive the EIFOV, the angular positional uncertainties due to 
both sampling (i.e., scene phase) and beamwidth have been 
modelled with ensemble average modulation transfer functions 
and combined into one AMTF. In essence, the EIFOV is the 
width of the average point spread function. 
Four commercially available terrestrial laser scanner systems 
have been analysed in terms of their angular resolution 
capabilities. Perhaps the important result of this process is that 
a fine angular sampling interval does not necessarily produce a 
high-resolution point cloud if the beamwidth is significant. 
Even though a small (in relation to beamwidth) feature can be 
sensed, its angular position may be biased by up to onc-half the 
beam diameter as indicated by the plumb line example. A fine 
angular resolution quoted for an instrument should be viewed 
with scrutiny unless it is much greater than the angular 
beamwidth because the actual resolution indicated by the 
EIFOV will be much larger. For example, the ratio of EIFOV 
to the finest sampling interval reached up to 21 for one of the 
systems analysed. The benefit of fine sampling interval— 
higher Nyquist frequency—may not be realised because of the 
positional uncertainty due to a comparatively large beamwidth. 
This was confirmed by the TLS system analysis, in which it was 
found that the highest resolution instrument (in terms of 
EIFOV) did not possess the finest sampling interval. 
  
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