4-2-3 
7 CALIBRATION RESULTS 
Figure 5. Image location accuracy assessed using the subpixel 
shift method. Standard deviation=0.04 pixel 
5 DISTORTION MODEL 
The parameters to be calibrated include the camera exterior 
orientation parameters with respect to the telescope of the 
theodolite, the camera interior orientation parameters, and the 
parameters in the error function model below: 
Sx = A■ y + x(K/ + K 2 r 4 + K/) + P x (r 2 + 2x 2 )+ P 2 (2xy) 
Sy = B-y + y(K t r 2 + K 2 r 4 + K/) + P x (2 xy) + P 2 (r 2 + 2/) 
where ^ and B are the affine deformation parameters, Ks the 
radial lens distortion parameters and Ps the decentring lens 
distortion parameters (Brown 1971). 
6 WARM-UP EFFECT AND STABILITY TEST 
The camera and a target were set stable. A frame of image was 
captured and the target image in it were located every 5 minutes 
from switch-on. The x and y co-ordinates are graphed against 
time as in Fig. This shows that the warm-up period is about 1 
hours and after that the x and y stay stable to 0.04 and 0.02 pixel 
respectively. 
In order to minimise the warm-up effect, the camera was always 
switched on at least two hours before the experiments. 
Calibration were carried out at five identifiable focal length 
settings. These focal length settings are coded which represent 
nominal focal lengths of 5.4 (minimum), 10.8, 16.2, 21.6, 43.2 
(maximum) mm respectively. The calibrated values and the root 
mean squared residuals (RMS) for image co-ordinates are shown 
in Table 1. 
Table 1. Calibration Results 
Focal Settings (mm) 
Parameters 
5.4 
10.8 
16.2 
21.6 
43.2 
X() mm 
-0.39 
-1.66 
-3.46 
-2.47 
9.23 
Y() mm 
28.96 
28.30 
20.91 
9.98 
-9.22 
Z() mm 
55.32 
55.52 
57.31 
56.89 
61.04 
CO 
1.57376 
1.57364 
1.57458 
1.57653 
1.55807 
<P 
.45041 
0.77979 
-1.11973 
-1.33119 
1.05899 
K 
-2.01235 
2.34151 
-0.44200 
-0.23107 
-2.62046 
X0 
312.01 
312.86 
314.08 
315.82 
347.95 
yo 
413.19 
412.55 
418.86 
423.52 
454.18 
c 
901.91 
1048.07 
1240.01 
1490.79 
3112.96 
Ki lo-u 
0.316 
0.187 
0.155 
0.106 
0.041 
K2 10-21 
-0.305 
-0.215 
-0.588 
-0.360 
-0.059 
K3 10-21 
-1.03 
-0.671 
0.957 
0.480 
0.322 
P] io- 9 
-0.649 
-1.88 
-1.83 
-1.92 
-0.332 
P2l0- 9 
-0.132 
0.398 
-1.01 
-1.18 
0.123 
A 10- 6 
-0.997 
3.17 
4.87 
0.947 
3.80 
B 10-4 
-0.344 
-0.336 
-0.369 
-0.306 
-0.305 
RMSx 
0.086 
0.078 
0.091 
0.121 
0.144 
RMSy 
0.081 
0.082 
0.084 
0.127 
0.236 
RMS 
0.084 
0.080 
0.088 
0.124 
0.190 
In order to 
assess the 
effect of 
lens distortion, RMSs from 
calibrations using no lens distortion parameters, using radial lens 
distortion parameters only and using both radial and decentering 
lens distortion paramters are shown in row 1 through to row 3 of 
Table 2 respectively. It is quite evident that the radial lens 
distortion is very significant at all focal settings. The shorter the 
focal length, the greater the radial lens distortion. It ranges from 
0.2 at maximum zoom to 1.6 pixels at minimum zoom. 
Comparatively, the decentering lens distortion is less significant, 
only showing a 0.02 pixel improvement. It is, however, worth 
considering. 8 
Table 2. Significance of lens distortion parameters 
Focal Settings (mm) 
5.4 
10.8 
16.2 
21.6 
43.2 
No lens parameters 
1.748 
0.963 
0.556 
0.400 
0.416 
Radial lens par. 
0.094 
0.119 
0.122 
0.154 
0.268 
Radial+Decentering 
0.090 
0.086 
0.094 
0.133 
0.266 
8 REPEATABILITY OF CALIBRATED VALUES 
8.1 Repeatability of the whole parameter set 
The calibrated parameter values for each focal setting should 
remain valid to certain accuracy whenever the lens returns to this 
focal setting after zooming in or out. Repeatability here refers to 
this accuracy. In order to assess this repeatability, data were 
collected again for each calibrated focal setting in the same 
manner as for calibration but on the next day and after sufficient