=!
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