f correcting 
parities are 
nce d from 
the segment 
rectangular 
c presentation 
e background 
determined 
le Q for the 
kground in 
ain as the 
naged. It 
distortion 
ground is 
render the 
visual re- 
the magni- 
  
   
   
  
    
   
   
  
  
  
   
   
   
   
  
  
  
  
  
  
   
   
  
  
  
  
  
    
  
  
  
   
  
   
    
    
The fact that the correction (9) depends on h confirms that it cannot give 
a perfect subjective rendition; even so, it will often be a satisfactory solution. 
If it is the case that h is small relative to &,/(M-) then we obtain a 
result independent of h, namely, 
6 
(9a) zm 
frie 
This result was anticipated in our reference to field binoculars in the introduction. 
In practice, the problem of making the separation of the anterior modal points in 
field binoculars as large as this formula indicates does present difficulties in 
design. 
In order to exhibit the residual distortion after performing the corrections 
(9) and (9a) we present plots of the ratio Ay/Ay* against a variable elevation H 
from the background in the neighborhood of the median line (Figs. 7, 8). Here Ay 
is convergence disparity in virtual space after correction has been applied and Ay* 
in real space with the object viewed at distance d from the background. If the 
ratio Ay/Ay* exceeds unity then the object appears elongated over-all; if less than 
unity, foreshortened. In these figures we have chosen M = 6, $6 z 50m, hs dm. 
Correction (9) produces the correct over-all convergence disparity for an object 
of height h, but there are internal local distortions. At the background plane 
local convergence disparities are increased by the factor 3/2, at the near point 
of height h they are decreased by the factor 2/3. A plot of the local distortion 
of convergence disparity dy/dy* is superimposed on Fig. 7. In Fig. 8 we plot 
Ay/Ay* and dy/dy* for the correction formula (92). This correction produces the 
appropriate convergence disparity in the neighborhood of the background plane but 
produces a progressively intensified foreshortening in the proximal region. 
4, BINOCULAR VISUAL SPACE 
In the preceding sections we have discussed the distortions of the effective 
stimulus, but not the distortions of perception. If the objects in the stereoscopic 
presentation are recognized we are often able to make a mental correction for the 
distortions in perception produced by our instruments and proceed without difficulty. 
If the objects are not recognized then we are in the realm of purely binocular dis- 
criminations and the distortions to perception become significant. In order to de- 
scribe the distortions of perceptual space, we must be able to describe perceptual 
space itself in terms of the effective stimulus, and this precisely is the central 
problem of the mathematical theory of binocular vision.