+ b > 
Fig. 2. The relation between residual y-parallaxes and the radial distortion. 
ries of circles with varying radii r around 1 and 2. These circles will 
intersect the fundamental circles in a series of points. In these points 
the residual y-parallaxes shall be measured. Intersection points between 
for instance the fundamental circle 3 (between 20 and 3) and the other 
circles are denoted 31, 32 . . . etc. The points 51, 52 etc. are located sym- 
metrically to 31, 32 etc. with respect to the baseline. similarly the points 
41, 42 etc. are symmetrical to 31, 32 etc. with respect to the line x = 
2° More circles can be used. 
From fig. 1 it is immediately clear that the measured y-parallax in 
each of the intersection points, under the made assumptions, will de- 
pend only upon the distortion in one of the pictures, and upon the er- 
rors of the measurements, provided that the distortion is zero at the 
radius d. A zero point of a distortion curve can be chosen arbit arily in 
a wellknown manner. Due to the symmetrical locations of the points, 
four different determinations of the distortion curve will be possible. 
2. Determination of the distortion amounts from the residual y- 
parallaxes 
We define a y-parallax as the coordinate difference yo—Yy1 where y, 
and y, are the y-coordinates of corresponding details from the pictures 
2 (the right one) and 1 (the left one). See fig. 2. 
We immediately find the radial distortion dr from the residual y- 
parallax p, ata certain radius r as 
^Y 
r (1) 
7 
  
ar ==: