2 
17 
the image coordinates, expressed in terms of standard error of unit weight 
after a least square adjustment, may be regarded as fundamental for all deter 
minations of geometrical quality in photogrammetry. Because of the previously 
mentioned variation of the standard error of unit weight of image coordinates 
with the distance from the center of the image, it is always suitable to arrange 
the points to be used for the calibration at least approximately in circles around 
the principal point and to determine the standard error of unit weight for 
each circle separately. If the points are somewhat regularly located, the normal 
equations can be solved algebraically and general expressions for the geo 
metrical quality can be determined. This has been shown in some papers, see 
Hal/ert 1954 and Hallert 1960 c. From the basic standard error of unit weight 
of the image coordinates and the weight- and correlation numbers (eventually 
ordered in the usual matrix or the variance-covariance matrix) the geometrical 
quality of all elements of the interior orientation and regular errors (for 
instance the radial distortion or affine deformations) can be determined. The 
radius of the circle from which the principal distance is to be determined is 
important and is not necessarily the largest radius because of the increasing 
standard error of unit weight. From available information on the variation 
of the standard error of unit weight and the weight number of the principal 
distance, the most suitable radius for cameras with c=150 mm is about 60— 
70 mm. The standard error of unit weight itself is, for this radius, about 2,5 
microns, which can be regarded as an average value for the entire plate, as 
mentioned previously. 
For a brief demonstration of the principles of determination of geome 
trical quality of the principal distance and the principal point the results 
of the adjustment procedure in section 1 can be used. The weight number 
of the correction to the preliminary value of the principal distance is, according 
to (18), 
and the standard error of the correction is consequently 
s c =s 0 ^-]/ 2 (51) 
4a 
For the determination of the standard error of the coordinates of the principal 
point the corrections of the preliminary coordinates of this point must be 
determined. 
The corrections can be found from the differential formulas (1) and (2) 
which are computed for x=z= 0 and for the values of dx 0 , dcp, dz 0 , and d(o 
from (8), (12), (9), and (13) respectively.