If it is assumed that the preliminary coordinates of the principal point are independently determined 
with the standard error of unit weight s' 0 the corrected coordinates of the principal point will be affected 
with a standard error of 1.2s' 0 in each direction. 
If the principal point is to be determined from fiducial marks the uncertainty of the definition and 
measurement of such points should also be included in the standard error of the reconstructed principal 
point. 
The standard error of the correction dc is calculated from 
The standard error consequently decreases with the radius r'. But because the standard error of unit 
weight s'o usually increases with the radius there must be a specific radius giving the optimum accuracy 
of dc. Assuming a standard error of unit weight determined according to the function shown in fig. 1.62:9a 
in the Appendix it is found that: 
Sdr = (4.1 - 0.0171r' + 0.000576C 2 ) 
zr 
This expression becomes a minimum for r' — 85 mm. 
Under the conditions assumed the most accurate value of the camera constant is determined from 
points on a circle of radius of 85 mm around the principal point. 
The radial distortion is the variation of the scale from circle to circle. If there are 4 points on the circle 
the weight number of the radial distortion is x / 4 and the standard error of the radial distortion is conse 
quently y . 
Similarly, the accuracy (standard error) of any other element of the interior orientation used for the 
reconstruction of the bundles of rays can be determined from the calibration procedure according to the 
grid method. The basic factor for expressing accuracy is the standard error of unit weight of the image 
coordinates. 
1.8 Tests of Photographs for Non-Topographic Photogrammetry 
In any application of photogrammetry requiring a high standard of accuracy, the interior orientation 
of the photographs to be used must be known. This was emphasized in resolution 21 of Commission Y 
at the London Congress in 1960: 
’’That all colleagues working in Commission Y pay great attention to the necessity of testing 
and calibrating their apparatus”. 
Some results from calibrations and tests of photographs from various cameras and X-ray instruments 
are shown below’. In most cases the principles, summarized in reference 1.8:1 have been used. 
Reference. 1.8:1. Hallert, B.: Determination of the Interior Orientation of Cameras for Non-Topographic 
Photogrammetry, Microscopes, X-Ray Instruments and Television Images. Photo- 
grammetric Eng. Dec. 1960. 
1.81 Close-up Cameras for Medical Purposes 
At the Division of Photogrammetry of the Royal Institute of Technology in Stockholm a great number 
of cameras for medical purposes have been calibrated according to the grid method. Some typical 
examples of the radial distortion determinations and the basic accuracy are shown in figures 1.8:1 and 
2 in the Appendix. In fig. 1.8:3 in the Appendix the basic geometrical qualities of an X-ray instrument, 
image intensifier and recording camera are shown. Measurements and computations were made by 
P. Kaasila, MSE. 
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