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Abstract

The concepts of binocular correspondence, and the horopter - the locus of self-corresponding points - have been reviewed, from the earliest records to the present day.

Since current workers in this field have restricted their investigations to two dimensions, their interpretation of their findings have been limited in at least three important respects:

1) The horopter is found to be a plane curve.

2) The deviation of the horopter, (the so-called Hering-Hillebrand deviation) can only be interpreted by assuming that the corresponding points of the two retinas are unsymmetrically disposed, an assertion that is not consistent with the recent findings of the neuro-physiologists.

3) There has been no satisfactory explanation for the experimentally determined result that this deviation changes systematically with the distance of fixation.

Using the criterion of the identity of visual directions and the techniques of linear algebra, it has been possible to extend the investigation of the horopter to the third dimension, whereupon the three anomalies referred to above have been resolved.

The horopter is not the plane curve that previous workers have indicated, but is a twisted cubic curve in space. This curve has been called the space horopter, its explicit parametric representation has been found and its properties explored in a variety of circumstances.

The chords of the space horopter are found to be self-corresponding lines, called nonius-Lines, and it is argued that it is these lines that the experimental workers have unknowingly been determining. The nonius-lines generate a family of quadric surfaces that has been named the nectilinear horopter, and its various properties have been explored.

On this basis, the horopter deviation is seen, not to imply a relative asymmetry of the two retinas. but is found to be an explicit function of the fixation distance and the angles of torsion (i.e. of cyclo-rotation) of the two eyes.

For this reason a kinematic analysis of the rotations of the eye have been included, so that the angles of torsion can be expressed in terms of known parameters.

Publication Type:	Thesis (Doctoral)
Subjects:	R Medicine > RE Ophthalmology
Departments:	School of Health & Medical Sciences > Department of Optometry & Visual Science School of Health & Medical Sciences > School of Health & Medical Sciences Doctoral Theses Doctoral Theses

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