May 2006
Volume 47, Issue 13
ARVO Annual Meeting Abstract  |   May 2006
How to Calculate the Orientation of the Eye in Any Gaze Position
Author Affiliations & Notes
  • R.S. Jampel
    Ophthalmology, Wayne State University, Detroit, MI
  • D.X. Shi
    Ophthalmology, Wayne State University, Detroit, MI
  • Footnotes
    Commercial Relationships  R.S. Jampel, None; D.X. Shi, None.
  • Footnotes
    Support  None
Investigative Ophthalmology & Visual Science May 2006, Vol.47, 2486. doi:
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      R.S. Jampel, D.X. Shi; How to Calculate the Orientation of the Eye in Any Gaze Position . Invest. Ophthalmol. Vis. Sci. 2006;47(13):2486.

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      © ARVO (1962-2015); The Authors (2016-present)

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Donders’ Law: "The orientation of the eye as a whole is determined by the position of the fixation line. Each time the fixation line returns to the same point, no matter by what trajectory, the eye always reassumes the same orientation." This paper confirms Donders Law by defining the orientation of the eye for each gaze position (? for the first time).


The apparatus allows the head to move freely while maintaining the retinas and the brain in synchrony during and following head movements, i.e., the eyes remain in, or return to, the same place in the orbit in all head positions. VOG clips of eye trajectories are recorded under diverse gaze conditions.Video frames are measured and analyzed with graphic algorithms.


In maximum brow–up and chin–down gaze the trajectory of the eye projects on to a frontal plane as an elliptical arc (Fig. 1A). This observation is confirmed by a frame by frame computer analysis (Fig 1B). The slope of the 3 to 9 o’clock corneal meridian in maximum circumgaze can be calculated at any point on the trajectory by using the formula for the derivative of an ellipse. For less than maximum intermediate tertiary gaze positions the angle of the slope can be calculated by comparing the slope in the primary position (zero slope ) with the slope in tertiary gaze positions. In figure 1C the slopes are calculated along the 45° meridian. Figure 1D is from Tscherning and shows the position which after–images assume when a cross is projected on a concave surface of a hollow hemisphere. [Tscherning’s Physiologic Optics, The Keystone Publishing Co, Philadelphia, 1924, p352, Fig. 179.]


The derivative m=b2x/a2y of an ellipse calculates the slope of the 3 to 9 o’clock corneal meridian for any gaze position when projected on to a frontal head plane. If the transverse radius of the eye ‘a’ (which is a constant), the altitude of the eye 'b', and the tangent of the angle of the meridian are known the orientation of the eye (the slope) can be calculated for any gaze position. For example, on the 45° meridian at 20° elevation the slope is about 6°. Slope angulation is not a true wheel motion. Note the similarity between the after–image projections in figure 1D and trajectories in figures 1A and 1B.  

Keywords: eye movements • eye movements: recording techniques • ocular motor control 

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