f direct 
ion over 
le, how- 
dequate 
1. So, for 
an. Cor- 
mputations 
)hs are 
> presuppose 
ects (e.g., 
)endicularly 
tant. Let 
m which the 
vely (Fig. 4). 
background 
itaining the 
iseline from 
; denoted by 
ixis will be 
bserver's 
the projec- 
ely. The 
lenoted by 
a scale factor 
9o that the photo 
j. We shall 
yhs at the points 
und plane. 
| space. In 
  
     
    
   
   
  
   
    
   
  
  
    
     
   
  
    
  
   
  
   
   
  
  
    
    
   
  
  
   
  
  
  
  
   
    
     
   
  
   
    
virtual space the position of a point is defined by the place where the ocular axes 
cross in regarding it, whatever the intervening optics. We erect a coordinate sys- 
tem in virtual space in the same way as in real space. The x-axis is chosen as the 
perpendicular bisector of the base line between the eyes and the y-axis passes 
from right to left through the ocular centers (Fig. 5). The distance of the focal 
plane of the stereoscope from the axes is denoted by x, and half the baseline LR 
by b. The ocular projections into the focal plane of the images of P fallat 
distances t and t 
R L from the ocular axes projected onto the focal plane where 
(3) tg = mk rp, ti 2mks 
and m is the effective magnification of the stereoscope lens. The point P = 
(£, n) of real space is mapped onto the point (x, y) of virtual space for which 
tg = (y + b) Xe[X 
(4) 
ups (y - b) Xe/X . 
From the equations (2), (3), (4) we obtain the coordinates of the point (x, y) in 
virtual space corresponding to (£, n) in real space, namely, 
x = ips = bn 
mKBE, 7” R 
Introducing the net effective magnification M where 
M = mké /*, 
we have simply 
xat 
(5) M B 
y=bn 
B 
From equation (5) it follows that the stereoscopic presentation exactly 
reproduces the sensory effect of real space if and only if x = € and y=n. This 
means that b=ß and M= 1, a result which is plainly of little practical use. Conse- 
quently, we turn our attention to approximate methods. 
Let us choose as a specific stimulus in real space, a line segment symmetric 
tothe £-axis of length 2a lifted off the background a distance h (Fig. 6). The co- 
ordinates of the left endpoint of the segment are then given by & - 56 -h, nea. In 
virtual space such an object presents a certain convergence disparity against the 
“l=