The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
Radial distortion coefficients kj, k 2 are not given here 
explicitly. Fig. 9 shows the unbalanced radial distortion curves 
derived from these parameters. 
Unbalanced radiai distortion 
f -300 
Hassel bl ad H3D 35 m 
m (2D Calibration) 
Hassel bl ad H3D 35 m 
m (3D Calibration) 
Hassel bl ad H3D 50 m 
m (2D Calibration) 
Hassel bl ad H3D 50 m 
m (3D Calibration) 
Hassel bl ad H3D 80 m 
m (2D Calibration) 
Hassel bl ad H3D 80 m 
m (3D Calibration) 
Figure 9. Unbalanced radial distortion curves 
target: 2m, 3D test field: 5m). Focal length parameters differ by 
about 0.4% for the 35mm lens, 0.7% for the 50mm lens and 
4.0% for the 80mm lens (see Table 5). With lenses focused at 
5m, the differences are 0.2% and 1.4% (for the 50mm and 
80mm lens, respectively, see Table 6). 
PHOBA: Distance Dependent Radial Distortion 
A clear difference can be seen between the 2D and 3D 
calibration methods for all three lenses (calibration on March 
19, 2008). This is caused by the high correlation of the radial 
distortion parameters with other parameters in the bundle 
adjustment (focal length, EO parameters), especially for the 2D 
target. Errors will also propagate into the object coordinates 
(model deformation). 
20 
15 
-15 
-20 
PHOBA: Single Image Residual Plot 
Figure 10. Systematic image residuals (3D target, 50mm lens) 
We observed small but systematic errors in some of the projects 
when plotting image residuals for a single image (see Fig. 10). 
We tried to model them by distance-dependent radial distortion 
parameters (cp. Dold, 2007) in the bundle adjustment. 
As can be seen from Fig. 11, the effect of a distance-dependent 
variation of radial distortion is not very significant. Maximum 
values of 3 pm (for the 2D target) are reached, but only in the 
very comers of the image. The effect is even smaller for the 3D 
target (2 pm). 
In an additional experiment, we performed complete 
calibrations with lenses focused at a mean object distance (2D 
Figure 11. Distance dependent distortion (2D) 
Calibration results cannot be improved significantly and the 
same systematic residuals can be observed in the images. For 
the 80mm lens and the 2D target, however, results are much 
better, because we get sharp images with the focused lens. 
March 19, 2008 
Lens 
c [mm] 
x n [pml 
Yo [dm] 
Ö0 
35 mm 
35.820 
±0.0006 
-61.9 
±0.3 
278.8 
±0.3 
0.7 
50 mm 
50.585 
±0.0007 
-102.0 
±0.3 
235.1 
±0.4 
0.7 
80 mm 
85.465 
±0.0028 
-243.0 
±1.1 
256.5 
±1.6 
0.9 
Table 5. Results with focused distance 2m (2D target) 
March 19, 2008 
Lens 
c [mm] 
x 0 [pm] 
yo [ftm] 
a 0 
35 mm 
- 
- 
- 
50 mm 
50.376 
± 0.0006 
-86.3 
±0.4 
229.9 
±0.4 
1.2 
80 mm 
83.385 
±0.0010 
-112.9 
±0.8 
310.1 
±0.9 
1.0 
Table 6. Results with focused distance 5m (3D target) 
2.5 Quality check 
In order to check the quality of the calibration process, all 
calibration parameters are fixed at their estimated values in the 
bundle adjustment. The 3D test field is now used to check both 
the 2D and 3D calibration results (of March 19). Only nine 
(well distributed) control points are used, the other 383 points 
are introduced as check points to evaluate the accuracy of point 
reconstruction (see Tables 7 and 8). Only three images are used, 
i.e., one for the left, middle and right position, which can be 
seen as a “common” (not highly redundant) stereo 
configuration.