3 1 7 
Commission I 
Invited Paper 
0 39 
Working üruup 1 
INTERNATIONAL SOCIETY FOR PHOTOGRAMMETRY 
COMMISSION I 
Eleventh Congress 1968 - Invited Paper 
Geometrical Calibration of Close-up Cameras 
By Kennert Torlegard, Tekn. Dr. 
VIAK AB, Gothenburg, Sweden 
Introduction 
The geometrical calibration of photogrammetric cameras is a 
procedure to determine the elements of interior orientation. When 
these data are available it is possible to reconstruct the bundles of 
rays, which belong to the pictures from the camera. 3) 4) The 
classical definition of interior orientation uses the concepts principal 
and principal distance (camera constant). This definition is sufficient 
for many applications where cameras with small distortion values 
are used. This is often the case for graphical plotting from aerial 
photographs and evaluation of terrestrial photographs taken by 
stereo-cameras or phototheodolites. 
The calibration generally includes a determination of the radial 
distortion of the camera. The reconstruction of the bundles of rays 
is very often done in such a way that the distortion is eliminated. This 
may be done by the Porro Koppe principle, by a correction in the 
diapositive printing, by using correcting plate holders in the plotting 
machine, or by numerical correction in analytical photogrammetry. 
Doing this we can say that the radial distortion is included in the 
definition of the interior orientation. 
Other regular errors of the ideal central projection such as tangential 
distortion and affine film shrinkage can be corrected for in the 
evaluation process. The corresponding parameters are then included 
in the interior orientation. It seems reasonable to state that the 
definition of the interior orientation shall contain those parameters 
that are used in the evaluation of the photographs. These parameters 
then define a mathematical model which is fitted to the geometry of 
the imaging system. If this model is expressed analytically, it is 
possible to determine the parameters by an adjustment of image 
coordinate observations according to the method of least squares. 
Then we also obtain a standard error of unit weight and standard 
errors of the parameters, which should be included in the definition 
of the interior orientation. Knowing the a priori weights of the 
observations in the adjustment, the standard error of unit weight is 
a well-defined expression of the image coordinate accuracy connected