background and a disparity in azimuth between its ends. Our method of correcting 
the subjective distortion is to adjust the constants in (5) so that the disparities are 
equal to those obtained when the object is viewed binocularly at a distance d from 
the background. This is a precise correction only for the endpoints of the segment 
but it can represent a great improvement over-all, as we shall see. 
First we write the angular coordinates (y, 0) in terms of the rectangular 
coordinates (x, y). To a good approximation [5] we have 
_ 2b cos^g 
(6) tan Q = x 
.. 
x I< 
We shall suppose that the total visual angular extent of the stereoscopic presentation 
is sufficiently small that we may assume convergence is constant on the background 
plane; in other words that cos’ ^^]. The distance d in real space is determined 
by the condition that an observer at d obtains the same azimuthal angle 4 for the 
endpoints as in virtual space: 
(7) tan 9 = 
al 
a 
d-h" 
From (5) and (7) we obtain the value of d, namely, 
1 
(8) d= hu C - h) 
Using y=2b/x and matching convergence disparity Ay against the background in 
virtual space with that in real space at the viewing distance d, we obtain as the 
condition for the correction of the visual distortion 
where Xo is the distance in virtual space at which the background is imaged. It 
follows from (5) and (8) that in order to employ this method of correct distortion 
we must satisfy 
(9) B eps M 
b TT(OM - Tt, 
Consequently, if the optics is given and the distance 56 from the background is 
prescribed, equation (9) dictates the length of the baseline required to render the 
convergence disparities within the object in approximately the correct visual re- 
lation. The correction may be achieved in the stereoscope by changing the magni- 
fication of the instrument. 
  
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