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Horopters – Definition and Construction

Authors
Publisher
Croatian Anthropological Society; [email protected]
Publication Date
Keywords
  • Horopter Circle
  • Binocular Accommodative Space Curve
  • Confusion Of Disparity
  • Confusion Of Accommodation
Disciplines
  • Biology
  • Mathematics

Abstract

The feature of Horopter was studied allready since the arabic and persian school, where Aguilonius defined it in 1613 for the first time. From those times til now, horopter was investigated as a geometrical feature, but also as a physiological feature of single vision. In general, there is the geometrical or theoretical horopter (Vieth, G. 1818, Muller, J. 1823) and the empirical horopter (Wheatstone, C. 1838, Panum, P. L. 1858). Helmholtz includes cyclo-rotation of the eye and though geometrically defines the horopter as a »twisted cubic« fenomena, which accept also Schreiber, K.M. (2006). Our approach is geometrically and includes trigonometrical analysis of the visual lines and fixation points in space, but including the eye accommodation because the horopter plane in space is determined with the convergence angle of the bulbus and the accommodation sharpness of the eye near the fixation point and the whole presenting retina in the horopter space. We get the horopter with the presentation of both retinas in space, shaped as two spherical planes (calots), two semi-spheres with a common center of fixation. The width of their spacing which is the Panum's fusional area known as confusion of accommodation corresponds to the convergence angle of both bulbuae. If the fixation point is nearer, the Panum's fusional area is wider and hence the larger the disparation of imagies on the retina. The authors have mathematically estimated the radius of the horopter planes as: R = PD/2cosa.

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