An extension of the archaic Gullstrand (1911) Schematic Eye to separate the foveal model from the peripheral model. Introduces a field lens and telescope into the models in order to better represent the physiology of the human eye. The telescope supporting the foveola is shared with other animals, both arboreal monkeys and birds of prey (among others with a foveola).

1. 1
1
Schematic Eye (2016)
Extend Gullstrand beyond Petzval Surface
Support:
http://sightresearch.net/pdf/2Environment.pdf
James T. Fulton
NEURAL CONCEPTS
jtfulton@neuronresearch.net
Access slides:
http://sightresearch.net/ppt/Schematic Eye
(2016).ppt
Good Morning. I have been asked to speak with you about recent work in understanding the acuity of the
human eye beyond that provided by the previous models known as a Schematic Eye & a Reduced Eye. This
paper describes an additional lens in the eye not obvious to investigators 100 years ago. I hope my
presentation will encourage some of the younger people in the audience to pursue intriguing careers in the
visual sciences.

2. 2
2
Extends Schematic Eye
• Beyond Gullstrand Schematic Eye (1911)
• Beyond LaGrand “Reduced Eye” (1946)
• Beyond Schematic Eye of Salah (2014)
• Incorporates Physiology of Retina
• Resolves Question Re: On-axis Acuity
The Gullstrand & LeGrand models of the eye are quite old. The investigators were not trained in the optical
profession. The Salah paper is a recent and useful synopsis of the Gullstrand model created as a project when
seeking a Bachelor's degree in Optometry.
This paper will extend the Schematic Eye (1911) to include the physiology of the retina and thereby resolve the
ambiguity between the measured and predicted acuity of the human eye using the Gullstrand Model.

3. 3
3
Human Eye: Very
Sophisticated
• Combines more features than any other
optical system built by man
• Very wide field of view (+110 to –110 deg.)
• Exceptional on-axis acuity
• Fully immersed optical system
• Deformable gradient index Objective Lens
The number of optical features employed in the biological (including the human) eye is amazing. Besides its
very wide field of view (partially blocked by the nose), it offers remarkable on axis acuity. The system employs
a fully immersed system, meaning most textbook equations do not apply if they contain an expression like (n-
1). The term 1 represents the index of refraction of air. In an immersed system, the fluid exhibits an index of
refraction other than 1. The “lens” of Gullstrand was modeled as an outer capsule and an inner core. It is now
known to be more complex than that. It also exhibits a gradient in its index of refraction as a function of its
radius.

4. 4
4
Physiology of the
Human Eye
The difference in index of refraction and the curvature of the Inner Limiting Membrane constitutes an optical
lens. Where the curvature is significant, the membrane forms a concave field lens (index is higher on the right
side). A debate continues on whether the ILM is a distinct membrane or just the surface of the neural tissue.
The important point is the field lens and the main optical group forms a telescope serving only the portion of the
retina labeled the foveola. It is also important to reiterate the eye is formed as an immersed optical system.
The ocular is mounted in a azimuth-elevation gimble. When the gimble is not at its 0,0 position, a twist is
introduced around the line of sight. A third pair of muscles are provided to compensate for this rotational error.

5. 5
5
Optical System of Eye
.
The upper eye labels the parts of the eye and both the optical axis of the cornea and lens, and the visual axis,
from Salah (2014). The difference between them is 5.38 degrees. The lower ocular illustrates the very wide
field of view of the eye (limited in humans by the nose and eye brows). This eye is from Lotimer (1971).

6. 6
6
Details of Foveola of
Optical System
.
The surface of best focus of the cornea and lens combination is not a planar surface, but a spherical surface
called the Petzval Surface. As illustrated the Petzval Surface is formed just to the right of the Inner Limiting
Membrane, ILM, except in the region of the foveola where it is just to the left of the ILM but inside the center of
curvature of the ILM. The area to the right of the ILM is the quite complex neural tissue extending to the
apertures of the individual photoreceptors (the focal plane of the retina). The curvature of the ILM is
emphasized at lower right where it is labeled a field lens. In conjunction with the main lens group, a telescope
is formed as discussed below.

7. 7
7
Foveola Telescope
The presence of two lens groups, the main lens group and field lens, form a telescope that expands the image
presented to the photoreceptors of the foveola about 10 times based on the measured data provided below.
The field lens is concave. Note, the index of refraction of the neural tissue is greater than that of the vitreous
humor. It varies with location within the retina. The best acuity without the telescope is about 20 seconds of
arc at about 0.6 degrees from the point of fixation. With the telescope, the best acuity is approximately 3
seconds of arc at and near the point of fixation. The neural signals generated by these photoreceptors are
propagated to the Pulvinar of the Thalamus instead of Brodmann’s area 17.

8. 8
8
This table, from Salah (2014) has been expanded to include the appropriate parameters associated with an
extended Gullstrand Schematic. A value for some parameter have not been located in the academic or
medical literature. There is discussion in the literature whether there is a distinct ILM or whether it is merely the
edge of the neural tissue. In either case, the thickness of the ILM is negligible. It is the change in index of
refraction along this curved edge or membrane that is important. It generates the concave field lens. The
values of the photoreceptors, PC, vary significantly as will be discussed below.

9. 9
9
Positions of
Refractive Elements
.
The first six positions of the refractive elements are as calculated by Salah. The last three are just estimates
based on the figures in this presentation. They will be refined.

10. 10
10
Radii of Curvature
.
This table has been expanded from Salah (2014) to include the field lens curvature, r7. Note the curvature of
this surface is an order of magnitude smaller than any other optical surface in the eye. It should be noted the
cornea is a paraboloid. Only its paraxial sector can be considered to have a fixed radius of curvature.

11. 11
11
The Schematic Eye of Gullstrand or the Reduced Eye of LeGrand, are technically based on a paraxial optical
analysis. This paraxial analysis only applies to angles less than 1.0 degrees from the optical axis. However,
the paraxial analytical technique is frequently used to get an estimate of the real case. With the foveola 5.38
degrees from the optical axis, the estimate of acuity by the paraxial technique is poor. As a result, actual
measured data is preferred when discussing acuity. This graph is a composite taken from the literature. It
shows an acuity (dashed line) that would be expected from the eye based on the Gullstrand or LeGrand
models. However, the measured acuity in the foveola is significantly better than predicted by a single simple
lens group, by a factor of about seven. There is no way for the main lens group to exhibit a narrow spike at the
visual axis. This can be accounted for by the formation of a telescope as described above, formed by the main
lens group and the Field Lens combined.

12. 12
12
Dimensions of the
Foveola Region
This figure illustrates the complexity of the neural tissue behind the ILM of a monkey. It appears to be quite
similar to the right eye of the author based on recent optical computer-aided tomography, OCT. The physical
content of the neural tissue varies significantly with location. Only the sector of the concave lens below the 350
micron dimension is used by the telescope. The area below this sector is devoid of acuity limiting ganglion
and bipolar cells. The sector projects an expanding cone of light downward toward the aperture of the
photoreceptor cell array where the broad cone is brought to a focus. The index of refraction of the ganglion
and bipolar free region below the sector is unknown. It has not been reported in the literature.

13. 13
13
Right Eye OCT Scan
This recent OCT scan of the Author’s eye shows the typical shape of the retina in the foveola region between
the Inner Limiting Membrane and the Basilar Membrane of the RPE. The approximate location of the Focal
Plane of the retina (the location of the photoreceptor cell outer segment apertures) is also shown. It is
approximately 100 microns between the depth of the pit and the F.P. It is difficult to estimate the curvature of
the lower sector of the pit using a circular template. The two circles (distorted by the scales used in the OCT
equipment suggest the radius is between 500 and 1000 microns (in general agreement with that of the previous
slide). This curvature provides a magnification on the order of seven-to-one, broadening the image presented
at the F.P. The sloping sides of the pit (represented by long dashed lines) act as prisms, moving the images at
the F.P. adjoining the foveola outward to make room for the expanded central image. The OCT scan was
horizontally through the point of fixation.

14. 14
14
Left Eye OCT One Year
After a Detached Retina
.
One year after surgery for a detached retina, the OCT scan of the left eye Shows a much shallower foveola pit,
with the radius of curvature in the lower sector of the pit estimated at between 1000 and 3000 microns. The
dashed lines also suggest less prismatic action than in the right eye. The result is a lower magnification of the
image presented to the photoreceptor cells of the foveola and less movement of the part of the image outward
when projected onto the F.P. adjacent to the foveola. These actions agree with what the author perceives; a
significant reduction in the size of the image at the foveola (estimated at 30% of normal) and a reduction in the
size of the immediately adjacent image to about 85% of normal. The thickness of the photoreceptor cell layer
straddling the F.P. is less than half its normal thickness. The nature of the extraneous layer left of the foveola
has not been investigated. This OCT scan was vertically through the point of fixation.

15. 15
15
Options Related to
Petzval Surface & PCs
The acceptance angles of the photoreceptors are larger than the cone angle of the incident optical bundle. The
outer segments operate as very efficient waveguides. Once the incident light is captured, there is very little
cross-talk between outer segments. In the absence of the waveguide mechanism, the cross-talk would be very
large as suggested by the sloping dashed lines. The diameter of the outer segments is at least three times the
longest wavelength of light they are designed to absorb.

16. 16
16
Indices of Refraction of
Photoreceptors
The indices of refraction within the photoreceptor vary considerably and are not known with high precision. The
rationale for the presence or absence of an ellipsoid is not understood. The value of 1.41 for the index of the
outer segment is probably an average value. The indices of interest relate to the disks and the inter-disk matrix
individually (when illuminated axially).

17. 17
17
Summary
• Fulton’s Schematic Eye (2016) replaces
Gullstrand (1911) & LeGrand (1946) eyes.
• Schematic Eye (2016) expands model
Separates Peripheral from Foveola models
Introduces a telescope into Foveola model
• Continues to use paraxial analysis
.
• Thank You for your attention