SOME ASPECTS OF STEREOPSIS 99 



lain region of external space containing the point of fixation. 



There are doubtless other possibilities, but whatever they are, 

 they must provide for the fact that a slight disparity or none leads to 

 a unitary cortical representation, different representations differing 

 according to the magnitude and direction of the disparity. In other 

 words, the three-dimensional character must be present, whether in 

 a spatial fashion or otherwise. The occurrence of anomalous fusion 

 in some cases of strabismus may seem to invalidate this argument 

 (Brock, 1940). However, it can be questioned whether a real fusion 

 occurs here, and it seems simpler to suppose that a quite different 

 mechanism is at work, with the factor of conditioning playing a pre- 

 dominant role, much as it must do in monocular depth judgments. 



If to each point of one retina there is a unique "corresponding" 

 point on the other retina, the lines joining any pair of these to the 

 nodal points will generally be skew and fail to intersect in any point 

 in space. For any given fixation of the two eyes the locus of points 

 in space where pairs of corresponding lines do intersect is called the 

 horopter. There is at least one such point, the fixation-point, and in 

 general the horopter is a curve in external three-space (Helmholtz, 

 1896). Consider the situation in which, the head being upright, the 

 visual axes are horizontal. The horizontal plane containing the visual 

 axes does not necessarily contain any part of the horopter except the 

 fixation-point and other isolated points. However, if we take any 

 point Q L on the intersection of this horizontal plane with the left 

 retina, there will be a point Q' R of the intersection of this plane with 

 the other retina which is closest of all these intersections to the true 

 corresponding point Q R , and the point Q in space which projects Q L 

 and Q' R lies somewhere on this plane. The locus of the point Q in the 

 horizontal plane of fixation we shall, for the present, refer to as the 

 horopter. 



It is evident that in symmetric convergence this horopter-curve 

 should be symmetric with respect to the subject's medial plane. If 

 each eye were symmetric about the fovea, so that corresponding points 

 were at equal distances from the two foveas, it is easy to see that the 

 horopter would always be a circle. Actually it is found empirically 

 that for a suitably located fixation-point the horopter is a straight 

 line, while for nearer fixation it is an ellipse, for more distant fixation 

 a hyperbola, either conic passing through the nodal points of the two 

 eyes (Ogle, 1938). 



Now granting the existence of a rectilinear horopter and the 

 anatomical fixity of the corresponding points, that the other horop- 

 ters are conies of the sort described follows from elementary projec- 

 tive geometry, and furthermore the equations of these can be deduced 



