horopter

Given a binocular system, to be seen as a model of the human eyes. The horopter ¹⁾ then, is a 3D curve that can be defined as the set of points for which the light falls on corresponding areas in the two retinas ²⁾. This definition could be equivalent to the intersection of a cylinder and a hyperbolic paraboloid (exercise is to be done).

The curve is a kind of one-turn helix around a cylinder. In the special situation that he horopter is in the horizontal plane through the eyes which contains the center of the retinas ³⁾, the horopter takes the form of a circle, named the Vieth-Muller circle, plus a line along the cylinder: the vertical horopter.
The Vieth-Muller circle is the theoretical horopter, the more general case is found in experiment.

The first to mention the horopter curve was Aquilonius (1613), but he gave the word a different meaning. He thought that monocular objects were perceived to lie in a plane, parallel to the face, containing the fixation point. It was this plane he called horopter.

The modern definition of the horopter is from Vieth, in his "Uber die Richting der Augen" (1818).

notes

1) From the Greek words horos (= boundary) and opter (observer).

2) This is called the condition of zero retinal disparity: one object seems to lay in the same direction for both eyes.
There can be confusion about the definition of this term. When when you define 'zero retinal disparity' as that objects appear to lie in the same direction, or at the same distance, you get a similar, but different curve.

3) The center region of the retina, where the light falls on when you look straight to an object, is called the fovea.

With thanks to Edgar Erwin for his remarks about the curve.