The Imaging Modality of the Eye – a Summary

by Gerald Huth on August 7, 2006

The following figure showing the distribution of foveal cones is abstracted from Fig.27 of “Vision and the Eye” (M.H. Pirenne, The Pilot Press, London, 1948). Quoting Pirenne: “The mosaic of the cones in the fovea centralis of the human retina represents the bodies or inner segments of the cones arranged in curvilinear rows as a shagreen-like mosaic” (italics are mine).

Circular Fovea 2. jpg.jpg

Note that there are some 200,000+ cones in the fovea, that they are arranged in circularly symmetric fashion, and that they represent approximately 99% of all of the cones of the retina. Circular symmetry is thus at the heart of the vision process.

The light detection centers formed by cone-to-cone appositions in the fovea defines the ‘red’, long wavelength limit of the visual response of the eye. Since cone-to-cone distances are equal, the fovea responds to a single red wavelength (or at most a very narrow band of red wavelengths). Response to red is thus uniform across the fovea. At the edges of the fovea (at approximately one degree of retinal angle) rod receptors start to intrude on this regular cone matrix (forming ‘green’ detection centers) and causing a ‘falling off’ of red sensitivity.

As the density of rods increases, it is observed that he fovea is surrounded by concentric bands of ‘green’ (peaking at 7-8 degrees of retinal angle) and, finally, at angles of 15 degrees and beyond, to pure ‘blue’ sensitivity. These are bands of pure, geometrically-defined, wavelength sensitivity. This is exactly the retinal response that Edwin Land deduced must be operative in the discernment of color in vision. The center of the ‘green’ response at 8-7 degrees where rod density is sufficient to completely surround each cone geometrically defines the exact middle of the visual response band – 550 nanometers. No laboratory spectrometric measuring instrument is required.

As I have said, I believe that the imaging area of the retina extends to approximately 15-20 degrees. The primarily rod area beyond, I believe, forms a wide-angle ‘light meter’ controlling papillary constriction.

The retina is thus shown to be a diffractometric surface the only meaning that this can have is that the eye functions as a Fourier-transforming device, i.e., that he retina (specifically the fovea) is located at the focal (not the ‘image’) plane of the optics of the eye. I have shown that the Fourier transform of an ‘outline sketch’ is primarily a small central ‘dot’ as shown in the following figure from Caulfield (abstracted from the paper by Hagan referenced elsewhere in this work). An interpretation of this figure is that the small dot contains all of the information necessary to construct the ‘sketch’ image in both light intensity and phase form to satisfy the Fourier equation. Note, that the Caulfield figure is an ‘optical’ rather than a ‘Fourier’ transform. Optical transforms are images taken using photographic film at the focal or Fourier plane but do not encode light phase information for the simple reason that we do not possess technology to accomplish this as the eye does!

Rabbit.jpg

I believe that the Fourier transform performed by the fovea provides the “outline sketch” (the “Marr sketch”)of the perceived image. Since the foveal detection centers are able to process Fourier information (light intensity and phase) a complete image must result. In a sense then, the focal or Fourier plane comes into coincidence with the image plane! Remember that this image derives solely from long wavelength (red) interactions. And..I learn that this information, i.e., an actual image, is transmitted in 1:1 fashion to the visual cortex of the brain. This image, the ‘actualization’ of the Fourier transform, appears in the brain and I might propose forms the ‘basic image’ for further processing – addition of detail. color, motion, etc..

As to color I would propose that it will be found that the two other ‘pseudo Fourier transforms” that I define – the green and blue – are transmitted to the brain in the same manner and are processed to ‘overlay’ the basic sketch image. One additional step of comparative processing of the latter two transforms (around the 7-8 degree geometric center) must ensue to arrive at the hues of color in the final image. It is amazing that this scenario if it proves to be the case is the exact analogue of Edwin Land’s famous 1953 color experiments!

JUST A NOTE IN PASSING:

In reading neurobioiogical texts re: color and the brain I continually find the “where” something happens (in the brain….where color is processed etc.) but never “how” this happens..the mechanism..and there is a yawning chasm between these two descriptions. An understanding of vision in my view desperately requires input from fundamental physics and/or electrical/optical engineering. I have been amazed from the beginning of this exercise that a fundamental understanding or description of how the visual image is formed doesn’t seem to exist! It is just assumed (incorrectly) that the eye functions as some sort of ‘camera’ ..even though voluminous data taken over the years is fundamentally at odds with this idea. ????
8/9/06

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{ 4 comments… read them below or add one }

beeorchid August 29, 2006 at 2:25 am

Indeed it seems like there is no fundamental understanding or description of how the visual image is formed and that the human eye is not operating as a “camera”.

I was also Amazed by that, while trying to study my color blindness.

While searching for data, I came across a very interesting book – PROCESSES IN BIOLOGICAL VISION – which could be downloaded here:
http://4colorvision.com/
This book discusses many such common assumptions, unveiling severe inconsistencies!

Another interesting source which is not afraid of “exposing the naked truth” is the report/survey “Colour vision screening,
A critical appraisal of the literature” by New Zealand Health Technology Assessment Clearing House (NZHTA):
http://nzhta.chmeds.ac.nz/publications/nzhta7.pdf
Just count how many times the phrase “insufficient evidence” appears in the conclusion section…

Victor Svet September 7, 2006 at 5:25 am

Dear Dr. Gerald Huth
I like your hypothesis that an eye is a diffraction system. In any way your explanations are rather convincing and, what is an important, they are very simple and physical.
I want to make one short remark.
Yes, it correct, that light field distribution in the focus of crystalline lens is connected with initial field of object by Fourier transformation ( in a paraxial approach that is good for fovea).
It simply means that the object is placed on infinity and we can consider the incident waves as plane waves. Of course the space spectrum is building due to an interaction of light waves with phase accuracy – this is a result of their interference.
The image of object on small distance is projected not in focal plane of a crystalline lens, and in some other. But it simply means that light waves from object are spherical, not plane waves.
But again and in this case the image is formed only due to collaboration of all light waves with phase accuracy, because of their interference.
From math point of view the space spectrum could be described as the same Fourier transformation from initial field, but with exp (jkx2) under the integral instead of
exp (jkx).
This remark does not influence in any way on the final result of your “geometrical” explanation of colour vision.
Moreover this diffraction approach can very simple explain S- Crawford’s effect.
I am wondering why practically all biologists try to explain this effect by specific “waveguide” design of photoreceptors. Nobody of them measured indexes of refraction of “shell and internal structure” of such biological single mode waveguides. Only if they are different we can think something about waveguide properties of receptors..
At the same time it is very simple to estimate the diffraction (aperture) effect of each photoreceptor of finite dimensions.
The effective angle of view (on level – 3 dB) of circle aperture is approximately equal to
Δφ = 2λ/d, where d- is a equivalent diameter of rod or cone.
If d ≈ 6 µm, and λ= 0,5µm, Δφ ≈ 2 * 0,5*57 degrees /6 ≈ 10 degrees. The psychometrical experimental results give Δφ about (20-30) degrees. But I could not find the notes on values of intensities of light during experiments/ By the way on the level (-6) db the Δφ = 17 degrees, which is similar to experimental data. Then you must take into account the wavelength and possible smaller diameter of cone. It is very critical value for diffraction approach.
By the way it is reasonable to estimate directivity patterns for different combinations of rods and cones in your approach if they are working as coherent dipole arrays.
But this can be only if light coherence is existing for short time. And this is the most interesting problem as I see. Because if we can prove that light waves can keep time coherence in eye system during some time we can explain many peculiarities of human and animal vision.
Best regards
Dr. Victor Svet

ghuth September 7, 2006 at 7:31 am

Many thanks for your comments and encouragement! I think of crucial importance are your comments near the end regarding the aspect of time.I have come to the conclusion (and am writing about this just now) that explaining the ability of the eye to detect at the quantum limit (actually “count” single photons) is the key to understanding the vision process beyond the initial and simple geometric explanation that I have provided. The only answer to this ability is to invoke detection of an initial image in very short – probably picosecond – time. This is the stopping time of light in the retinal outer segments. It appears that this initial “fully formed” image is passed along to the brain via ionic, i.e., slow, mechanisms in the optic nerve. The latter probably evolved to allow perception to come into concert with nerve reaction times etc. But…no one to my knowledge has ever invoked this “two time” approach. Acquisition of the initial image in a very short (noise free) time just must be! It is the only explanation.

Again, many thanks for your comment!

ghuth September 11, 2006 at 1:17 pm

I very much look forward to the estimations that you propose.I become more convinced that the entire visual image is “there” (on the retinal surface) in some very fast , probably picosecond time. Processing in sub-retinal circuitry probably uses up a little more time before the necessary “slowing down” of the image to the slower human reaction time via ionic transport through the lengthy optic nerve bundle to the brain. I am fascinated by this apparent neurobiological finding that the entire image is transferred (coherently) to the visual centers of the brain. By coherently I mean that each pixel of the retinal image is transferred 1:1 to the corresponding image that appears in the brain. !!! One gets the feeling that the brain is “looking out” through the coherent optic nerve through the retina to the visual scene!

Gerry Huth
Tucson, AZ/USA

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