The discovery of the horopter

DEFINITION

The horopter is the locus of object points in space that stimulate corresponding retinal points of the two eyes when the eyes are fixating binocularly one of these object points. The horopter is a curve that passes through the fixation point and changes shape with fixation distance. Objects closer to the eyes than the horopter are seen double (crossed disparity) and objects further than the horopter are seen double (uncrossed disparity)[1].

DISCOVERY

The Arab scientist Abu Ali Al-Hasan Ibn Al-Hasan Ibn Al-Haytham (circa 965 – circa 1040) (known also by his Latinised name Alhazen) discovered[2] the horopter around 1020. Here is a reproduction of his original diagram of the horopter and a description of the experiment he performed:

  • “B” and “A” are the centres of the left and right eyes respectively.
  • The objects at “H”, “K”, “T”, and all points on “HT” would be seen as single; the line “HT” would appear as a single line.
  • The line “EZ”, and each of the diameters “AD” and “BG” would appear as double.

Here is a diagram[3] of a theoretical (“T”) and empirical (“E”) horopter before or beyond which objects would be seen as double:

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