manner as for calibration but on the next day and after sufficient 
zoom action. This time, the 3D co-ordinates were "traced back" 
to the image co-ordinates using all the calibrated parameter 
values. These image co-ordinates were then compared with the 
"measured" image co-ordinates to derive root mean squared 
errors. These are shown in Table 3. We can say that this r.m.s.e. 
is attributed to the error of repeatability, the error of the 
calibrated parameters and the error of target image location. If we 
take off the latter part from the RMS., the repeatability ranges 
from 0.17 to 0.35 pixel (RMS). 
Table 3. Repeatability over Zoom (pixels) 
5.4 
10.8 
Focal Settings (mm) 
16.2 
21.6 
43.2 
RMS:c 
0.37 
0.33 
0.17 
0.18 
0.27 
RMSy 
0.33 
0.21 
0.17 
0.18 
0.37 
RMSc 
0.35 
0.28 
0.17 
0.18 
0.33 
8.2 Repeatability test using a single target 
A simple method had in fact been implemented to assess zoom 
repeatability before the above experiment was performed. The 
method used a single stable target. The stable camera imaged the 
targets many times and before each time the zoom was adjusted 
away and back. The repeatability was computed as standard 
deviation of the target image position. Results for the tested focal 
settings were shown in Table 4. Since only a single target was 
used in this method, the results should only be interpreted as 
indictive. Nevertheless, the inconsistency between Table 3 and 
Table 4 somehow indicates that the repeatabilities at various focal 
settings do not repeat themselves very well and that the factors of 
repeatability are complex. 9 
Table 4. Repeatability over Zoom by Single Target (pixel) 
Focal Settings (mm) 
5.4 
43.2 
RMSx 
0.11 
0.19 
RMSy 
0.09 
0.27 
RMSc 
0.10 
0.21 
9 CONCLUSIONS AND FUTURE WORK 
The repeatability of the calibrated zoom camera system against 
zooming is about 0.4 pixel (gross with assessment error). This 
level meets the requirement of the terrestrial image based system 
for which the camera system is employed. This level of accuracy 
for zoom cameras is believed to be also satisfactory for many 
measurement applications. This will enable zoom lens cameras to 
gain a better share in photogrammetric application, which is now 
much dominated by fixed lens cameras. 
The radial lens distortion is very significant, especially for short 
focal lengths. It can amount 0.2 pixels at 43 mm focal length to 
1.7 pixels at 5.4 mm focal length. This amount is fortunately 
compensatable with the three radial lens distortion terms. The 
decentering lens distortion is much smaller than the radial type, 
but still significant compared with the 0.08 pixel random error 
level of the calibration. The magnitude of lens distortion 
normally does not pose problems in practice. What really matters 
is the calibratability or stability of the distortion. 
The camera-on-theodolite calibration method has proved very 
effective and efficient for calibrating zoom CCD cameras. In 
particular, it has proved to be very suitable for calibrating this 
camera-theodolite combined unit. As the combined unit was 
calibrated in exactly the same set-up as it will be employed for 
measurement application, the 0.4 pixel repeatability figure can be 
taken for the prediction of the accuracy level achievable by the 
system. 
By the time of writing, experiments are still going on to obtain 
more data at more focal settings. Modelling the orientation 
parameters with focal length will be attempted. Constrained 
calibration with fewer free parameters, fewer images and a single 
target will be experimented. 
Fully automated calibration is not yet realised by the time of 
writing, but it remains one of the goals of the project. This is of 
importance considering the fact that the zoom mechanics tends to 
ware and more frequent calibration is required for a zoom camera 
than for a fixed lens camera. Thanks to the camera-on-theodolite 
calibration method, which lends itself to automation, the date for 
reporting a full automatic calibration should not be long. 
ACKNOWLEDGEMENT 
The authors would like to thank Measurement Devices Limited 
for lending the camera, and colleagues Jim Dudley, Ms Daoxiang 
Gong, and Darryl Newport for assistance during the experiments. 
REFERENCES 
Brown, D.C., 1971. Close-range camera calibration. 
Photogrammetric Engineering, Vol. 37, No.8, pp. 855-866. 
Fryer, J.G., 1986. Distortion in zoom lenses. Australian Journal 
of Geodesy, Photogrammetry and Surveying, 44, pp 49-59. 
Huang, Y.D. & Harley, I. 1989, A new camera calibration method 
needing no control fields. Optical 3-D Measurement Techniques, 
Edt. Gruen & Kahmen, pp 49-56. 
Huang, Y.D. & Harley, I. 1990, CCD camera calibration without a 
control field, International Archives of Photogrammetry and 
Remote Sensing, Zurich, Vol. 28, Part 5/2, pp. 1028-34. 
Huang, Y.D. 1992, 3-D measurement based on theodolite-CCD 
cameras. International Archives of Photogrammetry and Remote 
Sensing, Vol XXIX, Part B5, pp. 541-544 Washington. 
Wiley, A.G. and Wong, K.W., 1990. Metric aspects of zoom 
vision. International Archives of Photogrammetry and Remote 
Sensing, Zurich, Vol. 28, Part 5/1, pp. 112-118. 
Wiley, A.G. and Wong, K.W., 1995. Geometric calibration of 
zoom lenses for computer vision metrology. Photogrammteric 
Engineering and Remote Sensing, Vol. 61, No. 1, pp. 69-74.