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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
TTS al 
  
  
  
  
  
  
  
Figure 7. Two push broom views (forward and backward). 
Another version shows a series of “line imaging events”. Each 
event is shown by four lines only: 
e À straight and horizontal line in the object space, 
e Two imaging rays for the extreme points 
e The sensor line. 
In this case the flight path and the rotation angles are modelled 
by a second order polynomial. There is no object shown and no 
image. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
‘. 
K « » »\Chart1 / calculation / Shee | «| | P 
B C D E F G 
2 param Uo Vo Wo kap(gr) phifgr) om(ar) 
3 3 ao 220 10 300 0 0 0 
B 4 al 3 0 0 -0.3 0 0.4 
|5 32 0 0 a 0.005 ü| -0004 
6 C 150 sû: 60 smax: 120|  imured:]3 
  
  
  
  
  
Figure 8. Push broom imaging events and parameters 
There were no macros made to handle the parameters in this 
version, as the speed of changes in zero order, first order and 
second order terms is incompatible. A better choice of the units 
could probably overcome this problem, but there are much 
more changes foreseen: It should become an imaging version 
and also restitution with changed parameters should become 
possible. The concepts and layouts are ready since some time, 
but the time to implement it was not available so far. I hope to 
be able to show it at the congress. The transformation from 
object to image is not straight forward in that case, because the 
orientation parameters to be used depend on the image line, in 
which the point is imaged. This requires iterative calculation or 
higher order rational polynoms. Iterative calculation with three 
iterations will be used. This should give satisfactory results. To 
allow all possible constellations, the restitution will make use of 
concise formulas for the intersection of the rays such, that the 
joining line of the resulting points on each light ray is 
perpendicular to both light rays. 
U; uU u 4 
Viz E, ptt v, (4) 
W. Ww. Ww, 
1 2 1 
f uy —iu, (v-w,—w-v) r= 
Li=lv, -v (m-m-mue LV, -V, 
0 
1 745 (4 V, Yi 15) W : ET W 
where U;, Vi, W; = object coordinates of the restituted point, 
calculated from image i 
Ui, Vj, W; = vector in image i from projection center to 
image point in the object coordinate system 
Unis Vois Woi = coordinates of projection center (i) 
; = scale factors 
i = index of the image (1 or 2) 
OTHER GRAPHICS 
Orbiting Satellite 
35 4 
  
  
-35 
  
a 
en 4 
m 
-15 
m 
a 
-35 
25 35 
Figure 9. orbiting satellite and globe (showing The Netherlands) 
This graphic shows a spherical globe and a circular satellite 
orbit. The following parameters can be changed “continuously” 
by macros: all viewing parameters, the radius of the globe and 
its speed of rotation, the height and the inclination of the orbit, 
the position of the satellite at time "zero", the (angular) speed of 
the satellite, the swath (angle), the forward and the sideward 
look angle, the “time”(in minutes). 
When the time changes, then the globe rotates and the satellite 
moves, both according to the speeds specified.