Stereopsis, cyclovergence and the backwards tilt of the vertical horopter

It is generally recognized that the vertical horopter has a backwards tilt such that it passes through the fixation point and a point near the feet of the observer. The basis of the tilt has been attributed to either a shear in binocular retinal correspondence along the vertical meridian or the presence of cyclovergence eye movements. In an attempt to determine empirically the mechanisms underlying the tilt of the vertical horopter, retinal correspondence along the vertical meridian was investigated as a function of viewing distance. In addition, binocular measurements of torsional eye position were made in the same observers under similar viewing conditions. The vertical horopter was determined using two criteria. In the first instance, increment depth discrimination thresholds for both crossed and uncrossed disparities were measured as a function of retinal eccentricity along the vertical meridian, up to 5 degrees superiorly and inferiorly, and the horopter was defined by the region in space which had the lowest stereo-threshold. Secondly, subjective alignment of dichoptically presented nonius lines defined the horopter by identical visual directions. Both criteria were used to determine the horopter at 2 m while only the criterion of identical visual direction was used at the nearer distance of 50 cm. The vertical horopter showed a backwards tilt that decreased from an average of about 12 degrees at 2 m to 3 degrees at 50 cm, with some variability between observers. Torsional eye position did not change significantly between fixation distances. These results confirmed the geometric relation between the backwards tilt in the vertical horopter and fixation distance and support Helmholtz's original contention that the tilt is a consequence of a shear in retinal correspondence in the vertical meridian.