The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
930 
334 mm at the edge of the image format. Another large 
correction of note is the 400 mm rangefinder offset. Little or no 
improvement is gained by adding the two empirical parameters 
in case 4 except in range, for which there is slight improvement. 
RMS 
% improvement 
Case 
X 
(pm) 
y 
(pm) 
P 
(mm) 
X 
y 
P 
1 
11 
8 
171 
- 
- 
- 
2 
10 
7 
160 
9 
12 
6 
3 
6 
5 
50 
45 
38 
71 
4 
7 
5 
46 
36 
38 
73 
Table 2. RMS of self-calibration residuals and % 
improvements 
Focusing on case 3, the overall precision as measured by the 
RMS of residuals is quite good in both x and y at 6 pm and 5 
pm, respectively, which represent 0.15 and 0.125 of the pixel 
size. This indicates that 1) the lens-system correction model 
was effective and 2) the image point measurement method of 
intersecting best-fit edge lines was very precise. At 50 mm, the 
range results are somewhat less impressive, though. This is 
most likely the due to the target design in which the observed 
distance was interpolated at the boundary between the white 
and black target components. Range biases were found between 
these two differently-coloured materials, which cased severe 
inflation of the range residuals. They can be seen in Figure 4 as 
the recessed rectangles in the range image. The magnitude of 
the bias can also be seen to vary with distance to the target. 
Note, however, that the gradual curving of the planar surfaces is 
expected in a range image. 
Figure 4. Range image showing biases due to the different 
target components as recessed rectangles. 
This effect has also likely caused the estimated parameters, in 
particular the rangefinder offset, to be biased and, due to the 
high dispersion of observational errors, to be estimated with 
low precision (±2 mm for do in case 3). The resulting high 
dispersion of the range residuals for case 3 can be seen in 
Figure 5 as a function of range. It is planned to use a circular 
target design for future calibrations. 
4.3 Rangefinder Error Examples 
Figure 6 shows the range residuals from case 3 excluding the 
cyclic error terms d 6 and d 7 to show the effect of this systematic 
error. Clearly a large-magnitude, periodic error exists. The 
nominal wavelength is 1.875 m, one-quarter of the unit 
wavelength. Lindner and Kolb (2006) report a systematic 
deviation from the sinusoidal pattern of the cyclic errors at 
close range. No such effect was found in these data, though this 
may be due to the slightly-larger minimum range mentioned 
earlier. 
Figure 7 shows the effect of excluding the e 2 clock-skew error 
term from the case 3 self-calibration solution. The result is a 
very strong linear trend in the range residuals as a function of 
the y image co-ordinate. 
p(m) 
Figure 5. Range residuals vs. range for case 3. 
250 
onn 
-200 
-250 1 ‘ 1 1 ' 
1 2 3 4 5 6 7 
p(m) 
Figure 6. Range residuals vs. range for case 3 excluding the 
cyclic error parameters d^, and d 7 . 
Figure 7. Range residuals vs. y for case 3 excluding the clock- 
skew parameter e 2 .