The actual disturbed direction vector x d is related to the 
undisturbed by a rotation matrix M. 
xy = M-xJ (3-2) 
M contains the disturbance of the flight path: roll, pitch and 
yaw, as described before. In the example (Figure 2) the 
angle B corresponds to the pitch of the aeroplane and the 
angle a is the stereo angle. 
2. Back projection from the intersection point with the ref- 
erence plane into the image plane of the camera moving 
on an ideal (undisturbed) linear flight path. 
The simplest approach is the projection of the object point 
into the image space or focal plane on an ideal flight path 
not affected by disturbances. By this procedure the data 
will be sorted and corrected. 
The back projection procedure only works for some well 
known, but simple, flight trajectories. It is necessary to find 
a functional dependence for the projection point of the vec- 
-tor on an ideal flight trajectory x (see Figure 2). So for 
the whole measured swath the number of parameters for 
describing the external orientation can be reduced, and 
they are determined by the flight parameters such as 
  
velocity v and height h;. 
The aircraft has linear uniform motion v - « on a track at an 
altitude of z = hs. The question is, which pixel in the row i 
and in the column j of the image strip sees the point x; on 
the reference plane. We have the three equations 
  
xko| —x$0 
= yk tt 20 (3-3) 
h, zd 
- XE (J) projection point of the vector on an ideal 
flight trajectory 
- x) (i) viewing angle without disturbances 
with the unknown parameters t and (i,j). 
Because of the ‘push broom’ principle the numerical order 
of the lines results from the movement of the aircraft in the 
object space. The counting of the pixels in a CCD-line will 
be performed in the image space. 
  
Figure 3 Aircraft correction of the image in Figure 1 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
   
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