The horopter is defined as the locus of the points in space whose retinal images fall on corresponding points of the two retinae. In a general way the horopter is three-dimensional, a surface that passes through the fixation point and through any other point whose images fall on corresponding retinal points.
The simplest approach to the study of the horopter is the longitudinal horopter, the line of intersection between the horopter surface and a plane through the point of fixation and the foveae of the two eyes. In the following, discussion will be limited to the longitudinal horopter and to the special case of symmetrical convergence.
Early writers on the subject attempted to ascertain the shape of the horopter from geometrical considerations. Those attempts were given a final form by Helmholtz1 (1910). He based his calculations on the following assumptions, derived mostly from experimental data found by Volkmann.
HALLDÉN U. An Optical explanation of Hering-Hillebrand's Horopter Deviation. AMA Arch Ophthalmol. 1956;55(6):830-835. doi:10.1001/archopht.1956.00930030834009