How the Inverted Retina
Enhances Vision Acuity
Amichai M. Labin and Erez N. Ribak
The visual system is one of the most complex and important biological
systems of the human body. Our eye
forms an image on the retina, which
converts it into an electrical signal.
Detection is performed by the photoreceptors, which divide into low-light-level sensitive rods and color-sensitive
cones. They are located at the bottom
of the retina, behind layers of transparent nuclei and neurons, which process
and transmit the image to the brain.
This backwards structure posed a major
problem in understanding human and
Across the neural layers run the glial
cells (also called Mueller cells). They span
the entire thickness of the retina and
open up as a funnel towards the pupil.
On the other side, they are each connected to one cone and a few rods. Until
recently, the main functions attributed
to Mueller cells were metabolism and
mechanical support for the neuron layers.
Measurements of refractive indices of
retinal tissue and recently of glial cells
show evidence of waveguide properties of
the latter. 1 Considering these facts, it is
intriguing to investigate the effect of the
array of glial cells on human vision acuity.
An analytical description of light
propagation along waveguide structures, 2 such as an irregular array of biological cells, is very difficult to apply and
unlikely to be accurate. Thus, we chose
a direct three-dimensional numerical
solution of the Helmholtz equation,
known as the split-step beam propagation method. 3
To study the glial cells array, images
of human cells were digitized to define
their width as a function of depth. These
were inserted in a data cube with their
corresponding refractive indices. A
Gaussian beam was propagated across
this volumetric description of the retina.
The output light intensity at the bottom
of the retinal structure was calculated
Exitintensity 2°,0.55mm NC 100200300400500 . 20. 4 0.60.8 1 2 4 6 8 1. 38 1. 37 1. 36 1.35mm 20 40 60 80 (a) (b) (c) (d)
a= 6°, l=0.55 mm
100 200 300 400 500
(a) and (b) A cut across the retina model. (a) Refractive index profiles of two cells and the
cross layers. (b) Tilting the cells by 2°, we illuminate with green light the right cell (C), but the
field amplitude does not leak to its neighbor (N). (c) Taken from above, now we illuminate
a number of cell funnels with a Gaussian beam at 6°. (d) After propagation, the intensity is
concentrated by a factor of nine at the cones, and the rest of the light is scattered onto the
throughout the visible regime at various
incidence angles. The latter are associated with increasingly eccentric entry
positions within the pupil. 4
The results presented a surprising
picture: For small incidence angles (up
to 5°) corresponding to a smaller pupil as
in daytime (photopic) vision, the amount
of electromagnetic field coupling into a
neighbor glial cell is low, less than 3 percent. More significant coupling occurred
for higher incidence angles, when the
pupil is wider—in other words, at night,
when we use scotopic vision. Thus, light
is concentrated into the cones during the
daytime. However, more of it is scattered
into the surrounding rods after dark.
Another significant result obtained was
that in the center of the visible spectrum
(0.5 to 0.6 µm), a lower coupling loss was
calculated, even for higher arrival angles,
thus conserving an optimal image resolution and reducing chromatic aberrations. 5
These results provide evidence for a
natural parallel waveguide array, which
almost perfectly preserves images obtained under the constraints of the pupil
diameter, eye size and refractive index.
We revealed the seemingly illogical inverted structure of the retina, long taken
as a contradiction to its optical purpose,
to be an optimal configuration for improving the sharpness of images. t
to view the video that accompanies
A.M. Labin and E.N. Ribak (
firstname.lastname@example.org) are with the Technion – Israel Institute of
Technology, Haifa, Israel.
1. K. Franze et al. Proc. Natl. Acad. Sci. 104, 8287-92
2. S. Somekh et al. Appl. Opt. 13, 327-30 (1974).
3. K. Okamoto. Fundamentals of Optical Waveguides.
4. B. Vohnsen et al. J. Opt. Soc. Am. A 22, 2318-28 (2005).
5. A.M. Labin and E. N. Ribak. Phys. Rev. Lett. 104, 158102