I 
I 
35 
In Fig. 6 we have a co-ordinate system with origin at the center point defined 
above. The principal point has the co-ordinates x r y r in this system. They are 
assumed to be small in relation to other image co-ordinates. With symbols as 
shown in Fig. 6 we obtain the radial distortion as 
dr' = F(r) 
where 
r = |/(.x—x r ) 2 + (y—y r ) 2 
The distance between the center and principal points is 
r o = ]¡Xr 2 + y r 2 
and the radial distortion of the center point is dr o. The rotation /? in the #—y- 
plane is assumed positive in a clockwise direction. The polar co-ordinates of 
the principal point are /?<>, r\. From similar triangles in Fig. 6 we obtain 
dt r o sin (/9—ftp) 
dr' r 
7.2.1 
Fig. 6. 
Assymetric radial distor 
tion and so called tangen 
tial distortion can be cau 
sed by an eccentricity of a 
central target in relation 
to the principal point. See 
text.