Mathematical Definitions 
Inner orientation: 
The position in space of the image plane 
relative to the projection center. 
The term inner orientation, when used for 
instruments may refer both to the image 
and the camera. In the mathematical ideal 
case, the two concepts are identical. 
Physical Definitions 
Inner orientation of a camera: 
The position in space of the registering 
plane relative to a lens with a given dis- 
tortion. By it, an unequivocal relation is 
established between the radial distances in 
the registering plane and the object angles, 
and the camera function thereby realized. 
     
     
   
  
    
    
   
   
    
  
   
   
    
     
   
    
   
  
    
     
    
    
    
Data of inner orientation are the deter- Data of inner orientation are the deter- 
minants necessary for fixing the inner minants necessary therefor. They may be 
orientation, and may be diversely selected, diversely selected. 
| 
i e.g.: The coordinates of the principal point 
in a coordinate system fixed in the image 
plane and the image constant. 
On the basis of the equation: 
7 =c..tanı +4r, | 
the following data are frequently used: 
Position of the principal point H’ relative 
(1118 to the fiducial center M’. 
Il Camera constant c, for a given zero dis- | 
tance 7, | 
Distortion 4+” as a function of +’. 
  
Fig. 3 
Inner orientation of am image 
he inner orientation of an image is the geometrical relation whereby the object-side 
principal ray bundle is reconstructed from the radial distances of the image and therefore 
the image function is realized. For this purpose: 1) the image must be changed into a 
central projection (so that the distortion is eliminated) and 2) this distortionless image 
must be brought into a certain position in space relative to a projection center. 
These two measures may be fused into one by bringing the image into such a position 
relative to a lens with such distortion as to bring by means of the optical image formation 
the radial distances of the image and the corresponding object angles into a relation 
identical to the image function. 
In any case, the inner orientation of an image can be determined by the following data: 
Position of principal point H’ relative to fiducial center M’. 
Image constant c for a given zero distance y 
Distortion 47^ as a function of +. 
  
Photogrammetric mage : 
Photogrammetric image : 
An image of known inner orientation. 
An image of known inner orientation. 
  
In the ideal case here premised, it repre- 
It need not represent a central projection 
sents a central projection. 
and may therefore have a distortion which, 
I however, must be known. 
i 
INNER ORIENTATION OF AN IMAGE