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amplitude of angular motion and 
the relation of integration time 
and CCD-clock with the cut- off 
frequencies of the disturbances. 
We assume a terrain, 
characterised only by its 
maximum terrain height z_, and 
an isotropic distribution of height 
variations. Then it is possible to 
discuss all effects of the real 
imaging process only using the 
projection of the image lines on 
the plane zz z,,. The ideal 
imaging is done with a constant 
flight velocity (x-direction), with a 
constant altitude H. Each 
exposure of the CCD-line in a 
vanishing integration time 
produces an image of the 
underlying terrain with central 
projection. The extension of the 
imaged terrain cut in flight 
direction B depends on the 
altitude H, the terrain heights z, 
the focal length f and the width of 
the sensor line dp. 
B(z)=(H-2)*dp/f (1) 
B is varying in swath direction 
because z is varying. B is minimal 
for z= z__. The ideal scan must 
not have gaps. This is true if the 
sensor moves between two 
  
  
  
  
exposures over a distance B 
Fig. 1 Nadir and forward looking images without geometric corrections 
H=4000 m , Harz Mountains Bz(H-z,, )* dp/f (2) 
Of course this sampling produces oversampling if z < z___ but this has to be considered in a resampling procedure. 
This is the best scan under the made assumptions. The images are central projections onto the plane 
z=z__. So, all disturbances can be discussed analysing their consequences in this projection plane. 
A nadir looking sensor line is placed at the centre of the focal plane parallel to the y-axis. A stereo line is shifted by the 
distance d in the focal plane. This produces the stereo angle o: 
tan(o) = d/f (3) 
The stereo images differ only by geometrical reasons even in an ideal scan. The parallaxes make differences and if the 
ratio d/dp is not an integer value, we have a shift between the two ideal lattices of projected scan lines. The gradient of 
terrain height changes the images too. The extreme case is a slope near by d/f . 
Real scanners have a finite exposure time. This produce a motion blur. Modern scanners can change the integration 
time. This has the advantage, that the right integration time can be found for example as an optimum value comparing 
motion blur and s/n ratio and it can be tuned with respect to the illumination conditions (Jahn/Reulke, 1995). 
The consequence of finite exposure times is, that camera position and velocities influence the imaging process. 
At least 12 quantities are necessary to describe the geometry of imaging process: Three attitude angles, the vector of 
angular velocity c, the vector of camera position R and the vector of linear velocity v. The six degrees of freedom lead 
to other degrees of freedom of a vector r in the projection plane: two components of translation, one angle of rotation 
and the new degree of freedom: The dilatation. Each pixel can be characterised by its viewing direction vector b : 
b = (d, i*dp,f)" i=-(N-1)/2....0.....+(N-1)/2 N = number of pixels (4) 
This vector is given in the camera fixed co-ordinate system. (z-axis down). The pixel position in the focal plane is given 
by its number multiplied with the pixel spacing dp. In order to calculate the positions of each vector in the projection 
plane the following vector equation can be used: 
IAPRS, Vol.30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995