stabilizing the interior orientation has often been done, but if you want a camera with the same 
accuracy as a metric camera, the modifications can be rather expensive and difficult, 
Another approach which this paper will be dealing with, is to leave the mechanical 
system of the non-metric camera untouched and calibrate the interior orientation along with the 
exterior orientation for every single picture. This method has one draw-back. You have to place 
and measure more controlpoints than ordinary on the object, but on the other hand the method 
has many advantages. 
Defining the camera's orientation parametres 
  
With no fiducial marks in the camera the usual definition of the exterior orientation is 
not possible. The principal point in the picture can be defined from any other point in the picture, 
and as a new principal point is calibrated in every picture, the image of one or more control 
points can be used as reference for the fixation of the principal point. Having fixated the principal 
point in the picture, the interior and exterior orientation parametres can be defined in the usual 
way. 
    
PRINCIPAL POINT OF CAMERA 
Fig. 1. Definition of the angles & and B. 
For cameras with a stable housing, a stable and repeatable focal frame and a symmetri- 
cally placed lens, this description of the orientation parametres is sufficient. The optical axis 
of the cameralens will be very nearly perpendicular to the picture plane, and as long as the 
deviation is less than one degree, the error stemming from defining the lens-distortion from the 
principal point will be negligible. 
In many cases these mechanical properties are not at hand. The camerahousing can be 
a flexible bellow, the focal plane frame can be so poor, that the pictures will have varying angles, 
and many cameras with replacible lenses will not have a sufficient fixation and orientation of the 
lens. 
To overcome these stabilization problems, the optical axis of the lens is introduced. 
The exterior orientation is defined from the orientation of the optical axis. The radial lens- 
distortion is defined from the same optical axis. The picture-plane may not be perpendicular to 
the optical axis, but the introduction of 2 angles, a and f will describe the difference between the 
optical axis and the picture- NORMAL, so that the camera geometry of a flexible camera can be 
sufficiently described analytically. 
Lens-distortion can be analytically described with varying degree of sophistication. In 
my work I have only taken the radial distortion into account using the known polynomen of 
3 9 7 
dr = 83.17 -285.r"-d8g9.Lnr'. 
This relatively simple expression will of course not satisfy the distortions of every lens, 
1