Journal of Vision - The surface of the empirical horopter, by Schreiber, Hillis, Filippini, Schor, & Banks

Kai M. Schreiber	School of Optometry, University of California at Berkeley, CA, USA
James M. Hillis	Department of Psychology, University of Glasgow, Glasgow, UK
Heather R. Filippini	UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of California at Berkeley, CA, USA
Clifton M. Schor	School of Optometry, University of California at Berkeley, CA, USA
Martin S. Banks	School of Optometry, Psychology, Wills Neuroscience, University of California at Berkeley, CA, USA

The distribution of empirical corresponding points in the two retinas has been well studied along the horizontal and the vertical meridians, but not in other parts of the visual field. Using an apparent-motion paradigm, we measured the positions of those points across the central portion of the visual field. We found that the Hering–Hillebrand deviation (a deviation from the Vieth–Müller circle) and the Helmholtz shear of horizontal disparity (backward slant of the vertical horopter) exist throughout the visual field. We also found no evidence for non-zero vertical disparities in empirical corresponding points. We used the data to find the combination of points in space and binocular eye position that minimizes the disparity between stimulated points on the retinas and the empirical corresponding points. The optimum surface is a top-back slanted surface at medium to far distance depending on the observer. The line in the middle of the surface extending away from the observer comes very close to lying in the plane of the ground as the observer fixates various positions in the ground, a speculation Helmholtz made that has since been misunderstood.