Rethinking the Process of Vision

Very early in my study of the retina it became apparent that, if one assumed three classes of color sensitive cones (THAT SHOULD NOW BE APPARENT IS AN INCORRECT ASSUMPTION!), these receptors were not arranged in any logically spaced order on the retina but rather seemed to be distributed randomly. If one assumed, as vision textbooks portrayed (and still do), that the retina was located at the image (i.e., intensity-only sensitive)  plane of the optics of the eye  then  some type of spatial order would be necessary to accept the image. This situation is akin to that obtaining on the image plane of a digital camera where the silicon chip contains a logically spaced array of tri-color sensitive light detecting centers (”pixels”) to accept and electronically process the incoming image. But, the three types of cones (!) were spaced randomly!

I could not, and  still do not, understand how the vision field could reconcile this random distribution of light detection centers (or pixels) with any logical image-forming process!

(Incidentally, I do in this work  reconcile the distribution of receptors with an image-forming process explaining directly from Osterberg’s  historic retinal topology measurements, without any doubt, that the retina is the Fourier (or focal) plane of the eye with each pixel having the  necessary capability for processing both the intensity and phase of incoming light as the Fourier equation demands).

So, a dilemma -  the historically found statistical distribution versus the  logical requirement for some sort of ordered array of receptors?  ( and I didn’t even mention that in  measurements of the statistical distribution of “color sensing” receptors there is always a paucity of blue sensitive things - blue cones are very difficult to find! All of this is explained in this work.

Examples of recent work demonstrating  the statistical distribution of receptors are  the experiments of Roorda et al that I have previously referenced.(over and over!)  This group developed a method for microscopically imaging and identifying  individual retinal receptors. Their initial measurements focused on a region of the retina near one degree of eccentricity. This is a transition region where the density of cones is rapidly decreasing and where the introduction of rods is rapidly taking place . The rods being introduced crowd and fill  the spaces between the  diminishing  number of cones. (it is the statistically small number of rod-to-rod appositions that form “blue” centers that are misrepresented as cones). In summary, the centers defined as cones in this region was totally random.

(I would be derelict in my duty if I did not insert here the thought that what they found was in exact accord with my explanation! Their “red-sensitive” cones were actually cone/cone apposition centers that were still dominant in this region. What they termed “green sensitive” cones were cone/rod appositions that were beginning to statistically appear. The few (very few!) centers that they labeled “blue sensitive” were the small number of rod/rod appositions. All is geometry!).

One can read in my preceding Comments on this page where I repeatedly suggested that if the Roorda group, or some other group using their methods,  would make the same type of measurement at  a larger retina angle - near 8 degrees of eccentricity - they would find that, in their terms, “green cones” would predominate. I heard no direct acknowledgement  to my request but another group ( A paper (3832/A375) was presented at the ARVO 2008 Annual Meeting “Arrangement of the Human Trichromatic Cone Mosaic in Peripheral Retina” authored by O. Masuda, H. Hofer, J. Carroll and D.R.Williams) did make such measurements at larger retinal eccentricities. They reported  (surprisingly!) finding what they chose to term  a “clumping” of green cones in this region - in accord with what I had predicted although there was no acknowledgment of this.

This second group, apparently still seeking some spatial order buried in the random distribution, employed statistical sampling tests to locate some degree of order. -They found  none (other then the “clumping of green cones”).

In this work  the only spatial order of the retina  is  contained in the three diffractive regions  (the long wavelength limit, the exact geometrically defined midband wavelength, and the short wavelength limit).  I had assumed that these regions were circularly symmetric on the retinal surface.  I recently came upon something, however, that indicates that perhaps there may be a larger “over-arching” order to retinal structure.

In reading “THE GOLDEN RATIO” by Mario Livio (published in 2002 by Random House) about this fascinating number (1.618…..),  the author introduces the  “Wonderful (or logarithmic) Spiral”. I’ll not go into this (one can read the book), but looking at the structure of the head of a sunflower that displays such a spiral (p.36) I remembered a plate from Pirenne (VISION AND THE EYE), specifically Plate 7. This figure from a drawing by Schultz in 1866 (!) is titled the “mosaic of the cones in the fovea centralis of human retina” and is abstracted in the following:

There is certainly a spiral motif when viewed from this larger perspective.

GCH

Ojai, CA

8.25.08

From Wikipdia on the sbject of Phyllotaxis and Physics - the “Wonderful Spiral” in biology”

“Physical models of Phyllotaxis date back to Airy’s experiment of packing of hard spheres. Douady et al. also have shown experimentally and theoretically that phyllotactic patterns
emerge as self-organizing processes in dynamic systems.[4] In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis.[5] More recently (2009), Nisoli, Gabor et al. have shown experimentally and numerically that indeed that was the case, by constructing a “magnetic cactus” made of magnetic dipoles mounted on bearings stacked along a “stem”.[6] They also revealed that these interacting particles can access novel dynamical phenomena beyond what botany yields: a family of highly non local novel topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons an maxons in the spectrum of linear excitations. They named these novel phenomena “Dynamical Phyllotaxis”, as they appear in physical systems whose statics is dictated by the number theoretical laws of Phyllotaxis.”

Following my Comment yesterday applying the geometric principles of this work to define the visual characteristics of cats, I have found a reference Topographical characterization of cone photoreceptors and the area centralis of the canine retina (Mowat et al) measuring the distribution of cone and rod receptors on the retina of canines that leads to similar predictions about the vision of this species.

Again, I will let the paper speak for itself (omitting the references):

“The dog has two discrete cone subtypes; the two cone opsins are sensitive to long/medium wavelength light (555 nm spectral sensitivity; red/green or L/M-opsin) and short wavelength light (429 nm spectral sensitivity; blue or S-opsin. Previous studies have examined cone density in retinal cross sections Unlike the detailed characterization of cone distribution in other species, cone subtype distribution in retinal flatmounts has only been examined qualitatively in dogs, and the location of the area centralis has not been accurately defined.”

There is much to be written here but I thought the conclusion to be sufficiently important to summarize in the following.

The authors present views of the cone and rod distribution in what they term the area centralis of the dog’s retina in their Figure 1. It is clear that receptor distribution in this region is similar to the cat retina with no evidence of the tight packing (hexagonally arrayed) of cones as characteristic of the human retina. This eliminates, in the context of this work, any long wavelength sensitive region (i.e., a “fovea”).

Therefore, and as stated in their remarks above, the vision of dogs will be dichromatic. This means (refer to the discussion in yesterdays Comment) that there can be no central geometrically- defined, “fulcrum” from whence the hues of “color” may be synthesized.

I propose that dogs, therefore do not see the hues of “color” in the same sense that humans do. What they do see is visual image of the world composed of two very discrete wavelengths that are defined by two geometric lengths. I cannot emphasize enough the narrow discrete character of this light detection process.

I would believe that dogs see an image synthesized in a band between these two discrete wavelengths but that image in my view must be some sort of grayscale image.

I would expect that experiments with dogs would find an ability to discern the difference between these two wavelengths but this does not mean that they see color.

I emphasize again the difference that has been muddled through history between the detection on the retina of: a.) discrete wavelengths (the three in the human are termed “primary”) an, b.) the subsequent synthesis of the hues that we term “color” – that follows from the presence of central geometrically-defined mid band fulcrum and color vision teaching of Edwin Land.

Now what will be confusing – using traditional (and incorrect) thought, the authors attribute detection of the two wavelengths to the existence of “two discrete cone subtypes” (from the above) and associated opsins etc. I assert that these are not different types (or traditionally, “classes”) of cones but different discrete geometric spacings. As I have proposed, the different opsins represent “structural cages” that hold the ubiquitous retinal molecules in the the differentially sized rod and cone receptors.

Respectfully submitted,

GCH

Ojai,CA

8.18.09

I have said repeatedly in this work that, given a measurement of the distribution of receptors on the retinal surface of any specie, the fundamental principles uncovered for the human eye would allow precise definition of the visual characteristics of that specie. I have searched for such data and a paper  The Distribution of Rods and Cones in the Retina of the Cat (Felis domesticus) Roy H. Steinberg, Miriam Reid, Paula L. Lacey. Comp. Neur., 148, 229-246, provides a test for my proposal.

A quote from the introduction to that paper :

“Although a large amount of physiological research is currently being carried out on the cat retina, little information concerning the distribution of receptor densities is available…”.

The reader might first familiarize himself/herself with these principles applied to the human retina in the Comment that I wrote on 7.31.09  “A PRIMER ON GEOMETRY AND VISION” and, if necessary, repeat over and over the phrase that “cones do not detect color…cones do not detect color…and on”. It would be useful in the context of this work to cease using the terms “cones” and “rods” with all of the  baggage that they carry and substitute “large or small diameter receptors”. For clarity in the following, however, I will continue to use the old terms.

First to be noted is that the receptor distribution of the retina of the cat as measured in the Steinberg paper can be seen to reflect , in an overall sense, the general plan of the human retina. The cat retina has with a central region (their “area centralis”) that contains, as does the human retina, the highest density of cones. The distribution of rods also mirrors that of the human  but, as will be noted, of much greater density. In essence, the result is that there is no hexagonally arrayed,  tightly packed all-cone region on the cat retina  - the fovea in the human.

The central region of cone density (or, in the cat, cone/rod and rod/rod appositions) is the area where the image is acquired.  In the cat it would seem that the  image acquired will be more diffuse than human reflecting the spread (or diffuseness) of cones in the central region (I suppose that this might be termed visual acuity). Again, in cursory reading, I find that this seems to have been noted as characteristic of cat vision.

I would note again that, as I propose,  the visual image is acquired both in  human and cat in the Fourier domain, i.e, implying that the retina lies at the focal (or Fourier) plane of the optics of the eye. To satisfy the Fourier equation receptor appositional light detection centers possess  the ability to detect both the  intensity and phase of incoming light for the image formation process.

A place to begin is to reproduce their Figure 13a comparing the densities of cone receptors in the human and cat retina. These densities both peak at zero degrees but the density of cones in the human retina reaches 150,000 / mm2 while in the cat this value is only 25,000 / mm2.


Figure 13b from their paper shows the distribution of rod receptors in both the human and cat retina. It is readily apparent that the overall shapes of the two curves are similar in shape. The cat retina, however, contains a maximum rod density of almost 500,000 / mm2 while the value for the human variety is only 150,000 / mm2.. It becomes immediately obvious why the cat retina does not contain a central tightly packed all-cone region.


This is shown clearly in their Figure 2 with photomicrograph 1 depicting the array of receptors at the point of maximum cone density (i.e., near zero degrees eccentricity).

For comparison, the following is Osterberg’s classic measurements  published in 1935 of  the distribution of cones and rods on the human retina. I would note that these are the measurements upon which this entire explanation of light interaction on the retina is based. A simple calculation of the number of receptor appositions as a function of eccentricity reveals the three wavelength peaks that underlie the trichromicity of vision and all that follows. Refer here to my geometric “Rosetta Stone” diagram in the original paper.
I have proposed that an admixture of retinal receptors of two sizes on the retina is required to elicit the sensation that we term “color”  in vision. In such as admixture (as on the human retina) I have noted that there is geometrically-defined center (a rod-to-cone apposition) that defines an exact mid-band wavelength from which the sensation of color is obtained. This center (at 8-9 degrees on the human retina) provides the wavelength reference from which other wavelengths can be quantified.  On the human retina this corresponds to, if the entire band lies from 400-700 nanometers, 550 nanometers.  I wonder if anyone has yet appreciated the profound nature of this finding - the wavelength of light is geometrically defined.

This wavelength reference must undoubtedly be the “fulcrum” that Land deduced from external measurements must be present. The sensation of “color” is then synthesized by the eye or brain somehow from what Land termed “lightness records” deriving rom light interaction on either side of the fulcrum reference point.

Humans see color therefore because their retina possesses three discernible  light interaction regions and a resultant “fulcrum” central wavelength reference point. As taught by Land, any specie that senses what we term “color” must have three differential light interaction regions on it’s retina.

On the human retina these regions are: a.) a central all-cone fovea composed of hexagonal tightly packed cones providing long wavelength interaction and, that in  fact defines the long wavelength limit of the visual band, b.) the mid-band fulcrum reference defined by an admixture of two sizes of receptors, and finally to, c.) the region sensitive to short wavelengths primarily rod-containing  region beyond that defines the short wavelength limit of visual response.

From the Steinberg paper, the sizes of cone and rod receptors of the cat are generally similar to the human variety with rods of about 1 micron diameter and cones slightly large than human as measured at 2 microns. (they find that as one approaches the peripheral retina the size of rods slightly increases for which  I will propose a tentative explanation in the following). The ratio of the sizes of cones to rods in the human retina  is ~1.8:1. In the cat, therefore, according to this work, this ratio is ~2:1 reflecting the slight increase in cone diameter. Thus human and cat rod receptors are of approximately the same diameter with the cone receptors of cats being slightly larger than the human variety.

In support of this the rod-around-cone motif observed for the cat retina (see Figure 2 above) contains, perhaps primarily, the eight-around-one motif of the human retina (and most other species - ref) but also a sizeable number of nine-around-one centers that would follow from the larger size of the cat’s cones. I would note again that these motifs are the only ones that are geometrically possible using the above ratio values.

For those who have not read this work - this ratio of the sizes of receptors exactly determines the visual band of the specie.

Although the cat retina contains an admixture of two sizes of receptors (as does the human retina) an entirely different situation obtains. It is seen from these measurements that the density of rods greatly overwhelms the density of cones in the area centralis. This precludes the formation of a tightly packed all-cone “fovea” as in the human specie.

Cat vision therefore sees only two wavelengths  instead of  the three that we see! The necessary third, long wavelength sensitive region provided by the all-cone human fovea is missing in the cat retina.  The cat retina does not detect the three “primary” wavelengths necessary to synthesize the hues of color, nor does it contain a geometric “fulcrum” point necessary to accomplish this.

The cat can therefore not see the hues of “color” that we see! Here I ask the reader to repeat again that “cones do not detect color”………). What the cat must see from this explanation is an image, that must in some sense appear as black-and-white, viewed within the bandwidth from 400-600 nanometers.
In “human color terms” cat vision would be sensitive from blue to perhaps green-yellow. Even a cursory exploration of the literature on cat vision seems to bear this out. From a  Wikipedia entry  “The Senses of Cats”

“Cats can see some colors, and can tell the difference between red, blue and yellow lights, as well as between red and green lights.[3] Cats are able to distinguish between blues and violets better than between colours near the red end of the spectrum.[4][5]

The emphasis is mine. Also, I would disagree with the sentence that “cats can see some color,…”. More properly stated this sentence should read: “cats are able to discern some wavelengths in the visible band”.

At the start of my thinking on this paper I imagined, since I vaguely believed that cats possess excellent night vision, that their retina would necessarily possess larger cone receptors for night viewing (larger center-to-center distances between receptors extend wavelength sensitivity into the near infrared). In first glance at the paper this seemed to be so. But, the analysis does not at all bear this out as described above. I would believe that the excellent night vision of  cats follows from the seemingly much larger physical size of the structure of their eye. I have not had time to look into this, but the huge density of rod receptors  on the cat retina (3-4 times greater than the human retina), and the seeming fact that the rods on each retina are of the same size, foretells a much larger eye structure. I would appreciate comments on this subject.

In analogy to my view of the functioning of the human retina, the combination of  a higher density of rods distributed over a larger area  (almost the total area) of the retina in the cat functions as a (very!) wide angle light meter controlling pupillary constriction and light entrance into the eye. This combined with the seemingly larger  (ref) eye of the  cat functions to acquire a much greater amount of light than the human eye.

The finding of the paper that the size (diameter) of rod receptors increases near the  peripheral retina and the ora serrata. I vaguely recollect that this may also be true on the human retina. Remember that it is the diameter pf rods that determines the exact short wavelength end of the visible band of the eye. This is an important diameter as this region abuts the potentially biologically-damaging ultraviolet region. It might be therefore that nature employs larger rod size as a protective measure to “bend the band upward” toward slightly longer wavelength interaction in this sensitive region.

I conclude that this analysis concludes that cats cannot detect “color,” as humans do,  and correspondingly, that we must begin to realize the distinction between detecting optical wavlengths and detecting color.

Respectfully submitted,
GCH
8.17.09

This story is based on the well known measurements made by G. Osterberg, “Topography of the Layer of Rods and Cones in the Human Retina”, Acta. Opthalmologica (suppl.) 6, 1-103, 1935 and repeatedly used everywhere

I find myself standing at the center of a shallow bowl shaped arena.  A bright light shines down from a dome above and it must be sometime around noon because the light emanates from that position in the sky overhead.  The floor under my feet seems to be composed of an array of round  transparent glass-like tiles that I note randomly emit flashes of red light between them. These flashes do not come from any single tile but seem to connect pairs of the circular tiles that comprise the floor.  I further note that all of the flashes seem to be of exactly the same shade of red.

I am in a mood to explore, so I proceed to walk outward along what must be a radius of my  broad  concave environment.  At first, all of the tiles under my feet continue to be of the same diameter emitting the same random red flashes of light. Upon close inspection I see that the light does not come from the interior of the tiles but rather emanates from the periphery. In the tiles themselves there seems to be a “dance of particles” as is iron filings were continually being jostled  by a magnetic field.  After walking a distance, however, I encounter here and there the same type of random flashes but these are green in color!  The green flashes emanate from one of the round tiles I mentioned before and a new smaller tile that is being introduced at random into the array.

Continuing my walk I note that the green flashes are increasing in number in the still preponderant sea of red. Finally,  I reach a point where all flashes are green and the red has completely disappeared. Stranger still, I note that flashes of blue (!) light are appearing here and there, triggered by the, what has become obvious, even rarer encounter of two of the smaller tiles.   Continuing my journey toward the edge of the bowl, I find that the number of green flashes now begins to diminish with the blue variety beginning to dominate until, finally, the floor is composed of an almost complete sea of blue flashes.

Summarizing my experience in traversing the retinal surface, I have passed through three somewhat overlapping regions starting from an initial red at the center, through a region of green to, finally, a periphery that is entirely blue. I recall that these are what I was taught as being the “primary” colors from which the other hues of color are synthesized. Focusing on the green region that I have passed through, I reason that the increase and then decrease in the density of green flashes as I walk outward from the center must represent an intensity peak of this color. I reason that since the bowl of the retina is circularly concave each of these regions must represent concentric rings of the three colors on the retinal surface. I reason therefore that this surface cannot be, as has for so long been thought, the analogue of the film plane of a camera or any of the other contemporary imaging devices that we use that would comprise some sort of ordered array of color centers to detect an image. Rather, it seems that the retina must certainly be a diffractive surface.

To be continued………

GCH