June 2022
Volume 63, Issue 7
Open Access
ARVO Annual Meeting Abstract  |   June 2022
Nodal Points and the Eye
Author Affiliations & Notes
  • Michael Simpson
    Simpson Optics LLC, Arlington, Texas, United States
  • Footnotes
    Commercial Relationships   Michael Simpson Simpson Optics LLC, Code E (Employment)
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    Support  None
Investigative Ophthalmology & Visual Science June 2022, Vol.63, 3072 – F0544. doi:
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      Michael Simpson; Nodal Points and the Eye. Invest. Ophthalmol. Vis. Sci. 2022;63(7):3072 – F0544.

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

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Purpose : The very concept of “nodal points” probably originated with the eye, because they are only distinct when the refractive index is different on one side. Johann Listing described this in 1845, and the points belong on a paraxial “cardinal point” drawing (Fig 1), though they are often misleadingly sketched alone as the axial intersections of 2 parallel rays. They are meaningful only for small angles, yet it has recently been confirmed that the nodal point can scale the pseudophakic retina at large angles for other reasons. The evaluation is extended here to the phakic eye.

Methods : Raytracing software was used to model an average older eye with a gradient index lens. Input chief ray angles were compared to angles leaving the exit pupil, relative to the visual axis. A 70 year old eye was used because this is a typical age for cataract surgery, where recent questions about “negative dysphotopsia” and “far peripheral vison” have not yet been fully resolved.

Results : The phakic eye was found to have broadly similar properties to the pseudophakic eye, with input chief ray angles being rescaled by a fairly constant factor of 0.81 at the exit pupil over more than 70 degrees (Fig 2). These are actual rays, with angles relative to the visual axis that is rotated 5 degs from the optical axis (angle alpha). They identify image locations on the retina, though the overall image may be slightly defocused and astigmatic. Lines are not drawn to the 2nd nodal point (NP2), to maintain clarity, but a ruler parallel to an input ray can be used to confirm that in addition to the angular rescaling at the pupil, angles from NP2 are approximately the same as input angles to the eye, and that the input angles do not all meet at a single point.

Conclusions : The eye has a remarkably linear relationship between input angle and image location on the retina, with the cornea curving around toward light entering at an angle, and the retina curving around to meet the image. These optical properties have nothing directly to do with the traditional nodal points, which are described for very small angles using a sketch that has only straight lines. At large angles, the relationship comes from ray bundles that pass through the center of the pupil. This discussion also has relevance to fundus cameras, and to wide-field imaging of the retina.

This abstract was presented at the 2022 ARVO Annual Meeting, held in Denver, CO, May 1-4, 2022, and virtually.




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