One of the most curious attributes of binocular perception is that the human 
observer is seldom conscious of the double origin of his perceptions. He acts as 
though he were looking out from a single point of regard and responds to such in- 
Structions as'! 
‘arrange these points so that they appear equidistant from you'' or 
"place the points so they lie in the same direction from you" in a manner which sug- 
gests that the instructions have an unequivocal sensory interpretation. It is quite 
natural then to adopt a polar coordinate system for the sensory reference frame 
using the subjective point of regard or egocenter as the origin. Sensory radial 
distance from the egocenter will be denoted by r and sensory azimuth or angle 
measured from the sensory sagittal direction will be denoted by f. The equation 
r = constant represents a sensory circle for which the observer perceives himself 
to be at center. The equation { = constant represents a sensory ray or line of 
fixed direction of regard from the egocenter. 
The binocular sensory coordinate network is related to the physical world 
in a rather remarkable way. A typical observer in a purely binocular environment 
such as may be produced by star-like stimuli in a darkroom sets an array of lights 
at subjective equidistance from him so that, in fact, they lie very nearly on a circle 
which passes through his eyes [5]. Such a circle is physically one for which the 
observer is at the periphery rather than anywhere near the center. A circle passing 
through the eyes will be called a circumhoropter. The ideal circumhoropter is 
  
distinguished by the fact that if the eyes shift fixation from point to point along the 
curve, then the two retinal images of any point on the circumhoropter are displaced 
by equal amounts in the motion [3]. For binocularly balanced observers the circum- 
horopter is very nearly a circle upon which the convergence y of the ocular axes is 
constant. 
It is indicated by experiment that two points lie in the same subjective direction 
from the observer if in looking from one of the points to the other, the two retinal 
images are displaced equally in opposite senses. It follows that the sensory rays from 
the egocenter correspond very closely to physical curves along which the bipolar axi- 
muth is constant. 
For the binocularly symmetric observer it is permissible to equate the sensory 
azimuth $ to the bipolar azimuth 9 ,[3],[4]. For sensory distance r from the 
egocenter, however, the matter is more complex. Since r = constant on a circle 
y = constant we would expect that we may write r = f(y) where f is a numerical 
function. We know that a transformation of the form 
(11) Y! EN. 
does not alter visual perception of the stimulus. It follows that r does not depend 
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