effective stimulus as the original environment from some standpoint of direct 
binocular observation. It will be found that a correction of the distortion over 
the entire visual field is not achievable by simple means. It is possible, how- 
ever, toobtain approximate corrections which will probably be found adequate 
for most practical purposes. 
In what follows we shall assume a somewhat idealized situation. So, for 
example, we presuppose that every optical system is perfectly Gaussian. Cor- 
rections for deviations from the ideal can readily be inserted in the computations 
as necessary. 
Let us consider a situation in real space wherein two photographs are 
taken from different positions for later stereoscopic presentation. We presuppose 
a background plane (e.g., the earth's surface) from which various objects (e.g., 
trees, houses) protrude. We suppose that the camera is directed perpendicularly 
to the plane and that the distance of the camera from the plane is constant. Let 
L* and R* denote the points (strictly, the anterior modal points) from which the 
pictures are taken for presentation to the left and right eyes, respectively (Fig. 4). 
We choose rectangular coordinate axis: a $£-axis perpendicular to the background 
plane and bisecting the segment joining L* and R* and an n-axis containing the 
base line between L* and R*. Let B denote half the length of the baseline from 
L* to R*. The distance of the background plane from the base line is denoted by 
€ 0° The domain 0< § < 56 between the background plane and the n-axis will be 
called real space and itis this domain which is to be mapped into the observer's 
perceptual reference frame, visual space. 
Given a point P = (§,n) in real space, let Ph and P, denote the projec- 
tions of P against the background plane from R* and L* respectively. The 
distances of these projections from their respective optical axes are denoted by 
and T,. Using similar triangles in Fig. 4 we obtain 
TR L 
T (n + PB) S 
2 
(2) qu t0-85£,4t£. 
In the two photographs, the distances TR’ TL of (2) are multiplied by a scale factor 
which we denote by k. The viewing stereoscope is usually designed so that the photo” 
graphs are placed in the common anterior focal plane of the two lenses. We shall 
assume that the optical axes of the stereoscope intersect the photographs at the points 
corresponding to the intersections of the camera axis with the background plane. 
The true binocular visual field lies in what we shall call virtual space. In 
- 6 - 
  
  
  
  
   
   
  
   
   
  
  
  
  
  
  
  
  
  
   
   
   
  
   
    
  
    
   
  
   
   
  
  
   
  
  
   
  
CI 
te 
pe 
fr 
pl 
bj 
di 
(3 
ar 
(€ 
(4 
vi 
Ir