268 
Modulation Transfer Function of the WAOSS-camera as a function of optical defocusing. The pixel distance of 7um corresponds to 
a Nyquist frequency of 72 mm”! and the optimal focus to avoid undersampling is reached if the MTF at this point has only a low 
value. 
The precise alignment of the camera axis to the optical axis of the collimator is necessary for the geometric calibration. First the two 
axis of the nodal bench must put in coincidence with the optical axis of the collimator. In a second step the camera must be mounted 
in this way that the entrance pupil of the camera coincides with the center of rotation of the nodal bench and the nadir looking line is 
parallel with the vertical axis y and perpendicular to the horizontal axis x. Misalignment of the camera in the calibration facility leads 
to systematic errors in the point matching for stereo reconstruction. 
  
  
d0 di d2 d3 d4 m) m m) m m 
Inorm. Kf] A 
1.00 1.00 y 
  
0.80 08 N 
0.60 050 NNI 
040— 040 \ | 
020- 020 N S 
  
  
  
"Y 
  
  
  
  
  
  
  
  
  
  
  
  
  
NS 
LU ES d Ss 
ow |Z NN 0m mr 
00 100 200 30.0 40.0 50.0 0 X 4 60 80 100 
[um] mm-| 
Fig. 6 Dependence of PSF and MTF from the focus position Fig.7 Transformation from (x,y,z) to (x’,y’,z’ 
(measurements with camera WAOSS , 7um pixel size) 
5. GEOMETRIC CALIBRATION 
The main tasks for geometric calibration are: 
e high acurrate measurement of the interior camera orientation for determination of the image coordinates 
e Point Spread Function (PSF) measurements over the three lines 
e Computation of the Modulation Transfer Function (MTF) by Fast Fourier Transformation (FFT) 
In the measurement period of geometric calibration single pixel along the CCD-lines were illuminated by a pinhole spot from the 
collimator focus. The direction of the illuminated pixel (the pixel number is counted by the read-out electronics) to the optical axis is 
determined by the angle a (angle around x-axis, in line direction) and B (angle around y-axis, perpendicular to line direction) (fig. 1). 
It is possible but also not necessary to determine the coordinates of all pixels because the changes are very constant and the interval 
between two measured pixels can be interpolated very well. In practice it is sufficient to measure 21 pixels of a 5184 pixel line. 
The transformation from the spatially fixed coordinate system (x,y,z) to the image coordinate system (x ,y^,z^) is a simple "camera 
obscura" transformation (fig.7). The following simple relations between the coordinate systems are valid (Ohlhof): 
x zf:tang/co B; y=f tanß; 257. 
The result of the transormation is shown in fig.8. The difference between the real sensor geometry and the calculated values are less 
then 3 pixels at the end of the CCD lines. The small abreviation is caused by the remaining distortion of the optics which is not taken 
into acount. 
  
  
  
  
  
  
  
  
  
49 7 7 1 4 T T T | 
/ | 
j | a zi 
i | | 
| | | 
ar j { 5 of | = 
Le 
; | | 
: 25 - ; - 
Betaeins. i d. Ï 
1 i 1 
Betazwei, 0r ; vt e 0 - 
Betadrei. | : f : 
i j ; i i i 
RS : rtu | 4 
- 0r | i zi i | = 
; } | 
: | | 
| ee | 
| / ! 
1 1 À 1 | i | 
mo -20 0 20 40 : y a4. o3 79 5 i 15 
Righe ph niet <transformation= vhs 
Fig. 8 Result of the geometric calibration 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995