A New View of the Interaction of Light with the Retina of the Eye and the Vision Process
April 14th, 1994 | No Comments »
A Thought Paper
by
Gerald C. Huth, Ph.D (a)
Felix Gutmann, Ph.D.(b)
Alexander G. Huth(c)
ABSTRACT
We propose a new purely geometrical view that the accepted light interaction with the outer segment of the retina of the eye can be explained in terms of an array of a unique form of “optical antennas” wherein the wavelength of interaction at a point on the retinal surface is controlled in wave optics fashion by the dimensionality between adjacent quantum confined electron spaces formed by vertical rhodopsin molecule “quantum wires”formed within the stacked thylakoid disks within the receptors. The function of the two sizes of receptors (cones and rods) can then be seen as purely spatial in nature being the determiners of the antenna interreceptor spacings and the overall geometry. With this view and using the measured densities of cone and rod receptors the plan of wavelength sensitivity of the retina can be seen as a concentric ring shaped diffractometer - long wavelength sensitive at the central fovea and extending to retinal angles of about 20 degrees. The presence of such a structure implies that the retina functions as the focal or Fourier plane of the optical system of the eye (and not the image or spatial “camera” plane) and that image detection and processing are perforce accomplished in the frequency or Fourier domain. The all-cone fovea is projected to be solely sensitive to long optical wavelengths in agreement with the classical measurements of this retinal region made by Wald. In 2-D Fourier transform terms this region can be seen as detecting and coding for the “outline sketch” (a “black and white” sketch if you wish) of the perceived image. The function of the surrounding, specifically defined, concentric transition from long to short wavelengths in the curved and optimized Fourier retinal plane is to add detail to the foveally perceived “sketch” using underlying retinal “circuitry”. In this transition region there is a distinct geometric point at a retinal angle of 7 1/2 degrees where rods for the first time are of sufficient density to completely surround cones - a region which in terms of this hypothesis is defined as having mid-band optical response. This point would serve naturally as the “fulcrum point” from which it would be possible to derive two specific “black and white lightness” signals defined in Land’s(1) color vision concept with this information being added as “detail” in the image forming process. “Detail” containing a ratio of the two wavelength derived lightnesses and “sketch” are then combined in the frequency domain and are finally presented to the visual cortex of the brain as “color”. The peripheral retina, i.e., beyond 20 degrees, consisting chiefly of smaller rod receptors (and sensitive solely to shorter wavelengths in this view) would seem to serve another function required by Land of measurement of the overall light intensity of the perceived scene. Following from the new insight of this model there is much yet that is unexplained as, for example, the reason why the ratio of the sizes of human cones and rods corresponds exactly to the visible bandwidth - leading to an “eight-around-one” retinal architecture of rods-surrounding-cones - a motif which seems ubiquitous in the visual organs of all species from bees to crabs. We now have some reason to believe that this motif corresponds to the Fourier transform of five-fold symmetry Penrose tilings - and in some sense may be the “retinal objectification” of these fascinating entities - a subject which is now under investigation. It is interesting that this model is also proving predictive and would seem to provide a basis for understanding the reason for the very large retinal receptors characteristic of the infrared vision of fish and the smaller receptors recently observed in ultraviolet-viewing lizard species. It may also explain the never explained two layered grana and stroma morphology of the chloroplast organelle characteristic of most forms of photosynthetic plants and algae (2).
(a) Direct correspondence to 4701 Grand Ave., Ojai, CA 93023
Tel. (805) 646 9607 , e-mail:
(b) Macquarie University, Department of Chemistry, Sydney, Australia
(c) Monica Ros and San Antonio Schools, Ojai, CA, Orange Grove Middle School, Tucson,AZ, and The Thacher School, Ojai,CA
(1) Edwin H. Land, “Color Vision and the Natural Image”, Proc. Nat. Acad. of Sci., Vol. 45, No.1, January 1959
(2) Huth, Gerald C., Huth, Alexander, G., “A Model for Light Absorption in the Chloroplast in Photosynthesis Based on Nanogeometrical Principles”, (manuscript in press).
1. Introduction
Vision research seems to have evolved two main schools regarding the fundamental mechanism for the absorption of light and optical wavelength discrimination in the retina of the eye. The most broadly accepted approach based on quantum theory posits that light in the form of photons is absorbed directly in specifically color sensitive retinal pigment molecules (such as retinal) contained within the stacked thylakoid disks within the interior of rod and cone receptors. In the spirit of the model reported herein, it should be noted that although this is certainly one correct way of viewing reality, it cannot lead to any subsequent physical interpretation of the fundamental light interaction process - it only states that “a photon interacts ….. somewhere in the chromophoric grouping of a pigment molecule and ….”.
Another approach focuses on the concept that the primary site for light absorption is still within the rods and cones themselves but extends the above thoughts somewhat in viewing these receptors as “optical lightguides” that serve an ancillary function of directing the incoming light to the retinal pigment sites. This introduces the principles of classical wave optics but in the end it offers no greater fundamental insight as to the nature of the light interaction. Both approaches essentially disregard the spaces between receptors (although the latter view does considers them in a secondary light guiding role).
Regarding the image forming process employed by the eye, and following from the above generated “fundamental vision signal”, it seems to be tacitly accepted that the eye images in the spatial domain which implies visualizing the retina as a “trichromatically sensitive photosurface” functioning essentially as a color “camera” processing image information in the same manner as a contemporary television or film camera. This in turn implies that three retinal “pigments” (long, middle and short wavelength sensitive) must be present somewhere in the retina which in turn has led to a long search for such molecular species within the retina. In the same vein, this has led to use of terminology such as defining “classes” of cone receptors and it is purported that pigment molecules in individual cones have been excited with focused light beams. Through all of this, however, it seems that only one chemical pigment specie - retinal - has definitely been identified with the existence of the other two species inferred by excitation of “color sensitive areas”. A few investigators have proposed that the eye images in the frequency domain but there seems to have been no proof adduced that this might be the case.
2. Background of Spatial Light Interaction Concepts That Form the Basis for This New Model
Our interest in the retina and vision began with a fascination with the concept that a resonant or optically interactive length (or, more precisely, “spatial dimensionality”) is involved in the interaction of light with matter. This is not an easy idea to accept as one is dealing with the historic wave particle duality of physics and the quantum (particle) approach has come to dominate thought over the past seventy five years. . It happens, however, that this is an interesting time - the beginning of concerted technological development in the “nanometer” spatial domain (dimensions of 10-8 meters or 1/100 the wavelength of light)). This is the dimensional region where optical “dipole antennas” - if they existed - would reside. Additionally there is a current ferment of new ideas and approaches to understanding the fundamental mechanism of light interaction that involve spatial extensions of mass in, for example, the nanostructural design of sub-optical wavelength cavities to be used as “thresholdless lasers”, the concept of a (necessarily spatial) “photon bandgap” and others.
Of most importance in this regard however has been a recent and most significant discovery by Canham(2) in semiconductor technology that is being termed “porous silicon”. In essence, it has been found possible to anodically etch silicon surfaces in a way that causes them to absorb and/or emit intense light of visible wavelengths. The association of visible light emission with silicon has never been predicted by the quantum energy bandgap view of the silicon crystal lattice. The new physical entity that makes this possible is a very unique “surface nanostructure” (a spatial entity) that interacts with visible light. Further, and important to the central hypothesis advancedby this paper, is that the morphology
(2) L.T.Canham, “Silicon Quantum Wire Array Fabrication by Electrochemical and Chemical Dissolution of Wafers” App. Phys., Lett., Vol. 57 No. 10, 3 September 1990
of this nanostructure is composed of very high aspect ratio (the ratio of diameter to depth) of the etched “pores” and intervening silicon “pillars” very closely resembles in this crucial aspect the morphology of the biological retina!
Important in the introduction of the idea of a spatial dimensionality being involved in light interaction are the prescient and original thoughts of Marks (3,4) and Bailey(5,6). We believe that Bailey particularly came very close to the truth with his concept of a two receptor “wave energy converter”. Implicit here is the idea that dimensionality is related to optical wavelength - similar to use of antennas cut to wavelength specific lengths in other regions of the electromagnetic spectrum. Marks noted that optical wavelength should be related to a dipole length corresponding to the equation lambda / 2n (where n is the refractive index of the absorber). Thus the “antenna length” for yellow light of 5,000� wavelength would be approximately 71 nanometers assuming that silicon with an index of 3.5 were the absorbing antenna medium. It is obvious from this hypothesis that long wavelengths (associated with the color red) connote longer dipole lengths with shorter wavelengths implying shorter lengths or overall smaller dimensions.
(3.) A.M.Marks, “Electrooptical Characteristics of Dipole Suspensions”, App. Optics, 8, No.7, 1397-1412, July 1969
(4.) Ibid, “Device for Conversion of Light Power to Electric Power”, U.S. Patent #4,445,050, April 24, 1984
(5.) R.L. Bailey and P.S.Callahan, “Electromagnetic Wave Energy Conversion Research” Final Report, September 30,1975, NASA 766N13591
(6.) Ibid, “Electromagnetic Wave Energy Converter” U.S. Patent # 3,760,257, Sept. 18,1973
It was from this viewpoint, and while one of the authors (GCH), was looking at the following drawing from Cornsweet’s text Visual Perception(7) showing a very old diagrammatic representation of the structure of the retina of the eye that almost at an instant the overall model presented herein became clear.
(7.) Visual Perception, Tom N. Cornsweet, Academic Press, 1970
If, as introduced above, a spatial dimension - which for the time being we will constrain to a two dimensional “length” or “nanolength” - is a function of optical wavelength in antenna fashion, then the lengths that exist between centers of individual rod and cone receptors might have meaning very much along the line of thought proposed by Bailey.
The basic principle is illustrated in Figure 1. The longest length corresponding to the center-to-center distance between adjacent larger diameter cone receptors would correspond to long wavelength response, the interim length between one larger cone and one smaller rod would correspond to midband response, and finally, the shortest length between two adjacent rod receptors to short wavelength response.
Using this simple abstract geometrical assumption one can proceed to form “arrays” and relate them to spectral response functions in a “sorting of lengths into bins” manner. This is shown diagrammatically in Figure 2 where it can be seen that an entire spectral response including total bandwidth and intervening spectral shape can be synthesized using these geometric principles.
This principle produces a number of surprising results. First, it becomes apparent that only two lengths are needed in an array to synthesize any spectral response over a two dimensional surface. Furthermore, the bandwidth of the overall spectral response function corresponds to, or is determined by, the ratio of the two lengths that are employed. These thoughts can be applied to the retina of the eye with surprising results.
First, could this be the reason behind the evolution of only major two receptor sizes - cones and rods? (one might argue that variations in the sizes of these main receptor types exist but such in our view would be secondary - there are glaringly two distinct “rods and cones”). Further, turning the process around, the bandwidth of the human visual system (from 400 to 700 nanometers corresponding to a ratio of 1:1.75 ) can be used to create a hypothetical retinal architecture with the diameters of rods and cones of whatever specific dimensions they possess being in this ratio. This abstract line of thought results in a geometrically synthesized retinal architecture that has precisely the maximum number of rods-around-cones (~ 8 1/2) as the human visible bandwidth sensitive retina. This occurs at perimetric angles of 7 degrees (8) at what is termed the “yellow spot” on the retinal surface. This implies that the entire retinal architecture of the eye can be predicted using these purely geometric principles. This is also the ratio that was used in making the drawings shown as Figure 2.
(8.) M.H.Pirenne, Vision and the Eye, The Pilot Press, London 1948
In the interest of continuing to present an overview of our hypothesis relating these geometrical considerations to retinal and vision process behaviour we will delay until later discussion of what we believe to be the physical mechanisms underlying the implied spatial or geometrical principles. Suffice it to reiterate here that we propose that it is the spaces between the outer segments of rod and cone receptors on the retinal surface that act as the primary sites for light interaction and wavelength specification.
3. The Wavelength Specific Architecture of the Retina:
It might be seen immediately that these principles result directly in the ability to define (where it did not exist before?) the site-specific optical wavelength response on the retinal surface, i.e., precisely which portions of the retina are sensitive to which optical wavelengths. But it is first necessary to introduce a few other thoughts.
Figure 3 is a generalized diagrammatic view of the outer segment of retinal receptors. This figure will be also used again below but is introduced here to indicate our view that the retinal outer segment (accepted as the site of light interaction and thus of interest to us here) possesses in the living state an exceptionally high degree of spatial order! Snyder(9) has described the outer segment as being “almost crystalline” in character. Further, it has been proposed by some investigators that the outer segment is even dynamically ordered by tactile extensions along
(9.) A.W.Snyder, P.A.V.Hall, “Unification of Electromagnetic Effects in Human Retinal Receptors with Three Pigment Color Vision, Nature, Vol. 223, August 2,1969
the vertical sides of the receptors which implies a reason for a highly ordered state. Our point here is that this view is not at all apparent in non-living, distorted, “freeze dried” retinal views obtained in the process of electron microscopic analysis. One wonders if this point has not led some investigators astray. A highly ordered (i.e., spatially ordered) outer segment is required to support our hypothesis and this seems to be the actuality of the living retina.
As shown in Figure 3, the larger diameter inner segment of the rod and cone receptors seems to provide the exquisite biological spacing for the outer segment required in our hypothesis.
In consonance with the geometric principles defined above, the proposed model agrees with (and provides verification for) the well understood fact that human vision is trichromatic, i.e., results from three separate long, middle and short optical wavelength stimuli. This model proceeds to define precisely where on the retina these stimuli interact - with very surprising conclusions.
Thus we propose that lengths corresponding to the center-to-center distances between cone receptors in the outer segment (which are the largest receptors and therefore define the greatest interreceptor separation) correspond to long wavelength response. Response in the all-cone fovea is therefore predicted by this model to be exclusively and monochromatically at longer wavelengths. In this regard, even Wald(10) noted that the fovea appeared in his observations to be “blue blind”.
(10) G.Wald, “Blue-Blindedness in the Normal Fovea”, Jour. of the Optical Soc. of Am., Vol. 57, No.11, November 1967
One can apply these spatial principles further and speculate that the reason for the conical cross section of cone receptors is to provide “broad banding” of the long wavelength response, i.e., providing a continuum of different lengths and broadening the “line spectrum” portrayed in Figure 2. In fact, orthogonal geometrical factors such as the precise shape of the cone (or rod) receptors in the plane of the retina probably also contribute to this effect.
Using the well characterized density of rods and cones of the retina from Pirenne(8), and as reproduced as Figure 4, one sees as one proceeds from the all-cone fovea (00) that rods are continuously introduced in increasing numbers to approximately 200 and thence decreasing to the periphery of the retina. Figure 5 summarizes the correspondence between the trichromatic response of the retina with the geometrical principles of our model. This indicates that, with the continuous introduction of rods proceeding from the long wavelength sensitive fovea, the spectral response shifts through the visible spectrum to the short wavelength end in the region where rods finally dominate at 15-20o. Therefore, the spectral response at any location on the retina is very simply calculable - resulting from only three primary spatial interactions.
An interesting and singular “touchstone” angle seems to be at about 7o where the density of rods (from Pirenne) is just sufficient to completely surround each cone. This point is termed by Pirenne the “yellow spot” apparently because it appears yellow when viewed microscopically. From our geometrical viewpoint this angle would correspond to mid-band (green or yellow) response. Spatially, this point appears somehow as a “fulcrum point” which may correspond to the existence of such a differentiating point as noted by Land in his anomalous color perception experiments (and discussed further below)..
It is probably not inconsequential that this geometrical view of the retina implies a design where all angles of polarization of incoming light can be detected. This mid-band geometrical structure of rods-around-cones seems to make this point very clearly.
As one proceeds to larger perimetric angles, rod density becomes predominant and by our reasoning the response of the retina becomes predominantly to short wavelengths. The continuing small density of cones in this regionprovide a small but seemingly continuous number of middle band wavelength sensitive centers in a predominantly short wavelength sensitive background continuing to the ora serrata at the periphery of the retina. Thus most of the retina is short wavelength sensitive. Near the ora serrata a statement is made that the outer segments of the cone receptors seem to be missing. This may imply sensitivity to more discrete long wavelengths. Is there any reason why such a response might be desirable at these large angles?
From the above, it is then possible to construct a spatially specific two dimensional map of the wavelength response of the entire retina. This response proceeds from the long wave sensitive fovea, progressing through the visible spectrum to short wavelength sensitivity at perimetric angles of about 15-20 degrees. This indicates that the retina to these angles is actually concentric ring shaped diffractometer with the remainder to the peripheral ora serrata being primarily short wavelength sensitive. This is shown diagrammatically in Figure 6. A diffractometer structure, in turn, would seem to strongly indicate as discussed in the following text that the eye actually images in the spatial frequency domain - as some investigators have proposed.
We therefore propose that the region of the retina to angles of about 15-20o is involved in the primary frequency domain imaging process with the remainder serving another probably overall intensity measurement function (as Land’s concept required).
4. How This Retinal Structure Bears on The Overall Vision Process:
The conclusion that follows from this new view of the optical response of the retinal structure is that the eye is not the spatial domain imaging detector that so many envision but rather an imaging device that must be functioning in the frequency or Fourier domain - again as shown in Figure 6. This lends support to the heretofore speculative views at least entertained by some investigators(11,12) that certain vision response measurements lead to the conclusion that a two dimensional Fourier transform is involved in the vision process in acquiring and processing information for transmission to the brain. It has even seemed logical to some investigators that a biological system would have evolved to use this more efficient information processing method.
(11.) A.L.Ochs, “Is Fourier Analysis Performed by the Visual System or by the Visual Investigator”, Jour. Opt. Soc. Am., Vol. 69, No.1, 1979
(12.) D.H.Kelly, “Spatial Frequency Selectivity in the Retina”, Vision Res., Vol. 15, Pergamon Press, 1975
The retinal surface then appears as an optical diffractometric plane. It’s finite curvature would seem to indicate that it is a highly optimized Fourier plane. Such a plane would seemingly be capable of eliminating longitudinal chromatic aberration which corroborates this surprising characteristic of the human eye.
A Fourier surface would indicate that the retina of the eye actually represents the focal and not the image plane of the overall optics of the eye. We would propose that the eye may actually possess a heretofore totally unsuspected imaging capability in that it’s focal and image planes are actually coincident.
Refer to Figure 7 which shows diagrammatically the fundamental spatial “device” that we propose is formed between retinal receptors. It consists of the high aspect ratio optical cavity between two electron confining receptors. This device is referred to generically as an “optically interactive nanostructure”. As we have proposed, the cavity is dimensionally tunable as to optical wavelength (which forms the basis for our entire spatial geometrical model) but, of note here, even in three dimensions.. This device will be discussed further in following section of this paper. We introduce the structure here to show that this perhaps dramatic capability which would seem to define a (the most fundamental?) wavelength-to-frequency or Fourier transform!
This presents the possibility shown diagrammatically in Figure 8 that the retina performs a Fourier transform at each point on the surface of the larger Fourier transform that we propose it’s diffractometer structure implies. If this were so, the overall imaging system is capable of forming a most unique spatial image and transmitting the information in this form to the brain!
5. Correspondence of This New Model of the Retina and Vision with the Anomalous Color Perception Experiments of Land
This new view of the retina and vision would seem to support the contention expressed by Edwin Land(1) that somethingbeyond the rods and cones in themselves is instrumental in detecting color - perhaps some relationship between them. This statement followed from his fascinating series of color perception experiments which indicated that the eye actually perceives color as a “contrast of lightnesses” somehow comparing bands of shorter and longer wavelengths centered around a balance or what Land termed “fulcrum” point. This point he believed could shift somewhat but would generally be located around 588 nm - the peak of the optical spectral response function in the “sunlit world”.
The thinking here is summarized in Figure 9. As expressed above it is our view that the retina at small angles to 15-20o around the fovea represents the region engaged in the primary image detection function. The “outline sketch” of the perceived image is detected by the all-cone, solely long wavelength sensitive, foveal region. Higher frequencies detected in the surrounding concentric rings provide both: 1.) the information required to fill in the “photographic detail” of the image that we perceive, and simultaneously, 2.) the two contrasting short and long wavength “lightness records” required by Land. It is crucial to note as indicated in Figure 9, and as Land implies, that the concept of “color” is not directly detected on the retinal surface - color is in actuality a “perception of the brain”. The only perceptions of the retina itself are outline line sketch detail and two records (”black and white” if you wish!) which when intensity normalized and contrasted provide color and image detail information.
A question then is what function might the remainder of the retinal surface serve? As noted in the previous section, we project that this larger retinal surface must be characterized by shorter wavelength sensitivity. We further note that rods in this region are connected as assemblages or groups which might indicate that they are not acting in a direct imaging function. We then propose that this region of the retina may be acting as a large solid angle, high sensitivity light intensity measurement function (or “light meter”) whose function would be to obtain the opposing “lightness” signal that Land required.
There is also yet another possible symmetry point at retinal angles of about 7o (Pirenne’s “yellow spot”) which is at about the mid-point of the retinal image forming diffractometer. This point would seem to have geometrical meaning as this point where for the first time sufficient rods are present to completely surround each cone - a unique geometrical fulcrum-like situation. Further, it would be sensitive at mid-optical band which agrees with Land’s requirement.
Land proceeded from his color perception measurements to formulate his “Retinex” theory to explain them. The ideas contained in this theory are tedious to work through but one observation is that the theory is certainly phenomenological in nature - working backwards from his observations to attempt to describe in overall and general terms how the eye must function to achieve the results that he has experimentally measured. It may be that the new model for the retina and the eye described herein indicate specifically how the eye might accomplish how Land’s results indicate that it should function. A great deal seems to fit.
6. On the Nature of Light Interaction in The Interreceptor Spaces of the Retina
The most fundamental definition of the interaction of light with matter is expressed in the discipline of quantum electrodynamics (”QED”) and summarized so elegantly by Richard Feynman(13), simply as the “coalescence of a photon and an electron” (with the photon representing light and the electron the absorbing mass). This is represented as one of the truly fundamental interactions in nature. Moreover, Feynman states that the development of quantum electrodynamics solves the historical dilemma in physics of the observed dual wave-particle nature of light. Science and technology have over the years, however, not yet truly “gathered in” this new concept and still in practical terms use both the classical wave and quantum particle views of reality. Optical instruments, lens etc., are still designed using classical wave optics principles. The development of new semiconductor light emitting devices, photovoltaic solar cells, etc. is still based on the pure quantum (energy bandgap) theoretical approach. No one would argue that either of these approaches have not been successful - they are.
(13.) R.P.Feynman, “QED - The Strange Theory of Light and Matter”, Princeton University Press, 1985
At this time in our technological development we are entering a new era - the era of “nanotechnology” with the ability to measure and manipulate in atomic and molecular dimensions - and most importantly at dimensions at, or smaller than, the wavelength of light. Powerful new discoveries such as atomic force and electron tunneling microscopes allow visualization of even single atoms and organic molecular configurations. What will these new methodologies tell us?
For one, we believe as noted on the introduction that spatial dimensions - “nano” spatial dimensions - will be found to have meaning in the interaction of light. The premise of this paper is that in this regard we ought to look at how nature has evolved photosynthetic apparati - from this new perspective of the nanoscale - and see what this may tell us.
The insight of this paper is that - in the nanoscale - the biologically evolved retina of the eye appears to treat light classically but in a unique configuration immediately adjacent to what appear to be quantum confined electron spaces. Thus it might be said that in the nanoscale these two divergent views of reality seem to exist side-by-side.
We consider that the first and fundamental wavelength specific interaction of light occurs in the interreceptor spaces in the retina and that this interaction is defined by classical (but unusual - see below) wave optics principles.This region can be characterized as an optical lightguide cavity formed with an exceedingly high aspect ratio (diameter to vertical dimension). The walls of this cavity are defined by the higher refractive index matter of the two adjacent receptors forming it, i.e., the individual rods or cones. It is proposed in turn that these receptors themselves act as quantum electron confinement regions ( or “quantum wires”). The role of the lightguide region is then to guide light to specific regions of three dimensional nanospace where photons can “coalesce” with quantum confined electrons constrained therein. This effects the fundamental light detection process as defined by Feynman. It will also be readily apparent that this process can be run in reverse with “injected” electrons causing light to be emitted.
The interaction of light in an optical lightguide configuration that very closely mimics the interreceptor spaces of the biological retina has actually been very well described by McIntyre(14) and to some degree by Snyder and Hall(15). McIntyre’s analysis considers the power loss between adjacent optical fiber lightguides having dimensions and separation distances of the order of or less than the wavelength of light.
(14) P.D.McIntyre, A.W.Snyder, ‘Power Transfer Between Optical Fibers”, Jour. Opt. Soc. of Am., Vol. 63, No. 12, December 1973
(15) A.W.Snyder, P.A.V.Hall, “Unification of Electromagnetic Effects in Human Retinal Receptors with Three Pigment Color Vision”, Nature, Vol. 223, August 2,1969
In general terms when fiber lightguides are reduced to these dimensions they tend to “leak” radiation into adjacent fibers and intervening spaces. We believe it very straightforward to propose that the reverse of this power loss - with light introduced between adjacent optical lightguide fibers represents the signal that we invoke in our model.
A great deal of additional teaching is contained in the McIntyre analysis. In addition to defining the dimensional parameters of the lightguide cavity they show, for instance, that light of different wavelengths is “ducted out” at specific depths in the high aspect ratio optical structure. This forms the basis for our proposal that the basic nanostructure formed by adjacent retinal receptors and the intervening space is able to perform three dimensional color wavelength discrimination. Therefore, in addition to the overall structure possessing the capability for being specific wavelength “tuned” by altering it’s dimensions, it also possesses the ability for wavelength discrimination in depth. This leads to the concept of a very unique color receptor indeed - one that when arrayed in a curved plane can conceptually eliminate the two forms (longitudinal and lateral) of chromatic aberration in an optical system. The eye is the only optical system that is known to be free of this ubiquitous form of aberration present in all lens optical systems.
Perhaps providing more detail as to the optical design of the central optical lightguide retinal nanostructure, the analysis of Thornton(16) was directed towards optimized solar absorption surfaces is also of note. Thornton’s analysis defines the effects of the gradient of refractive indices that exist laterally (inthe plane) of surfaces comprising the proposed nanostructures - from interreceptor fluid through the membrane surrounding the rod or cone receptor and finally into the thylakoid disk structure.
(16.) B.S.Thornton, “Limit of the Moth’s Eye Principle and Other Impedance Matching Corrugations for Solar Absorber Design”, Jour. of Opt. Soc. of Am., Vol. 65, No. 3, March 1975
Regarding the electron quantum confinement region, i.e., the function ascribed to the structure of the retinal receptors themselves, this region must: a.) first thermalize the electronic energy induced by the light interaction and, b.) then provide an “energy sink” wherein this energy can finally be absorbed - and the primary vision signal generated.
We propose that the bilipid membrane structure of the thylakoid disk with it’s contained opsin and retinal molecular species is ideal for effecting the above functions. Central in this regard is very probably the elegant “photon funnel” experiment of Kuhn(17). In that experiment which used self-organized bilipid membrane structures similar to that of the thylakoid disks, it was shown that the energy from the interaction
(17.) H. Kuhn, Kuhn’s “Photon Funnel” experiment is well summarized by Blinov in Russian Chemical Reviews., Vol. 52, No.8, 1983
of a single photon is transduced over hundreds of molecular distances before final absorption. Thus the general principle of spatial translation of energy from light interaction is demonstrated.
A group of us have proposed (18,19) that the energy transduction mechanism in the photon funnel (and thus in the thylakoid disk structure) involves the lossless soliton physical entity. The final endpoint electronic energy absorption site in the vision receptor seems undoubtedly to be central molecular opsin/retinal membrane-spanning entity with the isomeric translation of this molecule generating the vision signal that is transmitted further along the optical image formation logic chain.
(18.) Huth, G.C., Gutmann, F., Vitiello, G., “Ring Solitonic Vibrations in Schiebe Aggregates” , Phys., Lett., 140, 339, (1989)
and referencing this model:
(19.) Christianson, P.L., Eilbeck, J.C., Enol’skii, V.Z., Gaididei, Ju.,B., “On Ultrasonic
Davydov Solitons and the Henon-Heiles System”, Phys.. Lett., 166, 129-134, (1992)
7. The Morphology of Other Biological Photosynthetic Structures and Their Possible Correspondance with This Model
It seems well understood that the optical receptors found in the retina of fish are generally much larger in diameter than those found in the human eye - sometimes being over seven times greater in diameter (20). The reason for this size differential seems never to have been explained. Moreover, the visual range of fish species is generally thought to be in the near infrared, i.e., at longer wavelengths than human vision. This would seem to be consistent with this model with the center-to-center distances between such large receptors corresponding to longer wavelength dimensional spacings.
(20.) J.K.Bowmaker, Y.W.Kunz, Ultraviolet Receptors, Tetrachromatic Color Vision and Retinal Mosaics in the Brown Trout (Salma Trutta): Age Dependent Changes, Vision Res.Vol.27,1987
We must note that although the receptor morphology presented in the above reference describes cones which are some seven microns in diameter (thus we believe supporting this hypothesis) the remainder of their conclusions are based on attempted measurement of traditional “visual pigments within cones” leading to the conclusion concerning “tetrachromatic ultraviolet response”. If this latter were fact there may be shorter wavelength sensitive lengths actually existing within these very large diameter receptors. Nonetheless, it seems generally true that the receptor sizes in fish are larger than in human retinas.
At the other end of the visual spectrum, a recent article in Nature(21) reports that species of
(21.) Fleishman, L.J., Loew, E.R., Leal,M., “Ultraviolet Vision in Lizards”, Nature, 365, 397, 30 September 1993
anoline lizards possesses vision in the ultraviolet. They report that “four classes of cones have been identified in these species with absorption peaks at 565, 495, 450, and 365 nanometers”. Using the sense of the arguments presented herein, we would predict that the visual receptors characteristic of these species would be smaller than the human variety in consonance with shorter wavelength vision. In personal communication with one of these investigators (Fleishman) he indicates that this is indeed the case.
In perhaps the most predictive use of this model, it would seem to be consistent with the heretofore unexplained “grana” and “stroma” morphology of the photosynthetic chloroplast organelle of plants and algae. Indeed if one set out using our principles to design the morphology for a photosynthetic structure that would absorb in two distinct peaks as chloroplasts do while simultaneously possessing high energy conversion efficiency (implying large area) one would end up with precisely such a two (and only two) layered structure. An electron micrograph showing the two layered grana and stroma morphology of the chloroplast of spinach and corresponding absorption spectra of the blue and red absorbing chlorophyll a and b are shown in Figure 10. We would note again that the sample preparation procedures for such an electron micrograph involving freeze fracturing etc.undoubtedly degrade the spatial detail of the structure. It seems extraordinary that the remaining detail so well displays the distinctly two separations characteristic of the structure. As is well known chloroplasts absorb in the far blue and red ends of the visible spectrum reflecting the midband green radiation to the eye - as indicated in the figure. We feel that a correlation along these lines will be found, and should be searched for, between the morphology of the chloroplasts of other species of plants and algae and their particular optical absorption characteristics.
8. Summary
This new model specifically defines where light interacts on the retinal surface. Longer wavelengths in the visible spectrum interact at cone-to-cone appositions - and thus predominantly within the fovea. Mid-band wavelengths interact at cone-to-rod and shorter wavelengths at rod-to-rod appositions. This defines that the retina acts as a concentric ring shaped optical diffractometer extending to retinal angles of about 15 degrees. This in turn would indicate that the retina acts as a Fourier, frequency transforming surface (with the qualification noted below). The fundamental organization, i.e., the overall scene view, of an image in a 2-D Fourier transform is contained in the small central region - the fovea in this case. The fact that red response is associated with this region in this model corresponds well with the phenomenologically observed fact that low intensity red illumination provides the best overall scene viewing in airplane cockpits, submarines, etc. to. The addition of shorter wavelengths to the 2-D transform add details - and in this case color (in accord with Land, we reserve the term “color” for the sensation perceived by the brain computed using intensity compensated ratios ratios of these optical wavelength interactions). The peripheral retinal surface we propose acts as an “overall intensity meter” and provides the intensity compensating signal as proposed by Land. We further see the possibility that each individual, wavelength specific, retinal receptor apposition possesses the capability for performing an inverse frequency transform thus presenting the potential that an actual spatial image is formed on the retina and presented to the brain in this fashion.
END
GCH 4/14/94
It is certainly to be understood that the eye is capable of detecting at the level of a few photons as shown elegantly by Rose(10). That seems to me, however, to be unimportant here and not inconsistent with this new view of retinal action - this fact being merely the “ultimate extension of the beautifully unique dynamic range characteristic of the visual system”. Single photon detection capability is not in fact often used in vision but fixation on it has certainly drawn the field of vision research totally off track!
(10.) 5. A. Rose, “Quantum and Noise Limitations of the Human Visual System”, J. Opt. Soc.Am.,Vol. 43, 715, (1953)
