4 
the irregular errors to be expected in the image coordinates should also be 
known, primarily from statistical estimations in connection with the camera 
calibration, which must be made under operational conditions. 
1. The interpolation procedure 
An object is assumed to be located within a figure of stars (Fig. 1) and the 
image coordinates of the object and stars are measured with high geometrical 
quality in a comparator. In order to increase the precision of the measure 
ments, the settings on each point should be replicated at least three times in 
each direction and the averages of the readings computed. The standard 
deviation of the average decreases with the square root of the number of 
observations. The series of measurements can be repeated a number of times 
in order to check that no significant changes of the averages have occurred 
from series to series. Next the image coordinates are corrected for known 
non-projective regular errors, e.g. radial distortion. 
If the measured and corrected image coordinates of the stars are then 
compared with the corresponding given coordinates, discrepancies will usually 
appear, caused by sources of regular and irregular errors. The discrepancies 
are assumed to be caused primarily by the following sources of regular image 
coordinate errors (see Fig. 1). 
2 
Fig. 1. The direction toward P is to be determined with the aid of the directions to the stars 
1—4 which for the sake of clarity are assumed to be located in the corners of a square 
around the principal point.