e 9 
The problem could be solved by renouncing the geometrical property of the unknown and 
using a system of orthogonal functions. This, on the other hand, would convert the analytical 
photogrammetry into a black-box system, that will introduce quite a lot of other problems. 
I have used another method, that until now have been working quite satisfactorily. By 
analysing the a priori knowledge of the orientation parametres it will be found, that some 
parametres, for instance the principle distance of the camera, are a priori pretty well-known 
and can be given a fairly well-approximated value, while other parametres, especially the 
exterior orientation elements, often have approximated values diverging quite a lot from the a 
posteriori values. In a least square adjustment, this varying accuracy of the approximated values 
is not taken into account, and after the first adjustment the unknowns are not really improved by 
the ascribed corrections. The errors of the exterior orientation elements are transferred to the 
interior elements, and the second adjustment will often have approximated values far worse than 
the approximated values of the first adjustment. 
This insufficiency of the adjustment can be overcome by letting all the orientation 
elements that have good approximated values appear as constants, while at first the orientation 
elements with poor approximated values appear as unknowns. I have given the interior orientation 
elements constant values, that is, the principal-point located in the center of the picture, the 
principle distance that can be calibrated from the distance setting of the cameralens and, further- 
more, the camera is taken as distortion-free, leaving only the exterior orientation parametres 
as unknowns. By making three or four iterative adjustments with this set of unknowns, the 
knowledge of the exterior orientation will normally be quite good. 
In the next step, the exterior orientation and c, xd 
unknowns, the distortion parametres as well as the angles « and B are given constant values of 
zero. In this way the approximated values of all the unknowns are encumbered with the same 
error, and the correlation between w and ve ,9 and xg will not disturb the adjustment. e © 
3 
The result of this last adjustment will give the most favourable values for the orientation 
elements if the picture is to be compilated in an analogous instrument. The reducial error of the 
adjustment gives an idea of the accuracy to be obtained by an analogous compilation. 
and y, are all incorporated as 
The next step is to introduce the radial distortion as unknown in the adjustment. As all 
other orientation elements after the first two steps have very good approximated values, the 
adjustment can be stopped after one or two iterations. The results of the adjustment correspond 
to a camera with a well-centred optic, and a stable camera housing. Normally this will be the 
last adjustment in the calibration procedure. In cases where bellowcameras are used, the angles 
a and f can be introduced in a fourth adjustment step, but normally this adjustment will not 
improve the results compared with the other adjustments. 
Finally it should be mentioned, that a laboratory calibration should be done over more 
than one picture, making the adjustment for all pictures at once. Variations from picture to 
picture in emulsion shrinkage and picture flatness will not be seen if the calibration is done from 
a single picture only. Especially for metric cameras, where the interior orientation elements 
are used as constants in the compilation, it is important that these constants are not compilated 
from one picture only. By calibrating over several pictures the number of testfield points can 
be brought down, and as Kälbl [ 8] has shown, it is possible to avoid geodetic measurements of 
the testfield points. If cameras without fiducial marks are used, the pictures must all be exposed 
on the same photographic plate to insure a constant interior orientation. 
We have been working with numerical photogrammetry along these lines for the last 
6 years, solving problems ranging from underwater photogrammetry [6 ] to time series measure- 
ments in hydraulic laboratories. In most cases we have done the actual photographing and 
compilation ourselves, but in the last two years it has become possible to let the professionals 
involved take care of these two operations. It is our experience that numerical photogrammetry 4 
can be developed to a degree, where most of the traditional problems of orientation, error- 
finding and accuracy evaluation can be solved by a computing program, leaving only the problems E 
of control point measurement, photographing and coordinate measuring in the stereocomparator. e - 
Using numerical photogrammetry the process of photographing is quite uncomplicated, and Ss 
training a person for compilation in a stereocomparator can be done in a few days compared to 
months in an analogous instrument, 
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