Rethinking the Process of Vision

An interesting discussion yesterday with my son. His question: what factors (evolution again!) determined the limits of the visual band, i.e., from the short 400 nanometer (blue) to the 700 namometer (red) wavelength?

The short wavelength (blue) limit seems rather easy to dispose of… ..in the ultraviolet region below 400 nanometers photons possssess sufficient energy to damage biological structures. In my explanation of light interaction with the retina it is the physical diameter of the rod receptors that precisely determines this boundary. I have associated variations in this limit (perhaps due to genetic differences in determination of rod size) as an initial cause for such medical conditions as macular degneration.

Discussion of the long wavelength limit leads to some interesting asociations. At longer wavelengths than red, i.e., into the infrared and betyond, photons possess less energy even transitioning into the “heat” region with intractions being decribed in terms of classical (i.e., not quantized) wavelengths. The lower energies of these interactions would seem to require that interfering noise be commensurately lowered to achieve the same (required?) signal-to-noise level in the image formation process. This would be true even in the very short time domain that I have invoked as being characteristic of the image forming process of vision.

The obvious way to lower noise (and retain vision?) is to reduce temperature and there are a number of instances in vision literature where this seems to correllate. The vision of fish species as I have noted elsewhere lies in the infrared, i.e., beyond 700 nanometers. In consonance with my explanation, the cone diameters of fish retinas are found to be larger than the human variety at ~ 7 microns. Then too, snakes sense (see?) even further into the infrared even to the point where their sensory organs are said to detect “heat”. Both of these species are cold blooded with their lower body body temperatures taking that of their environment.

Is the long wavelength limit of the visual band somehow determined by the signal-to-noise ratio requirements for a visual image thus relating light energy to temperature? (My son points out that the peak of a black body curve for body temperature is ~ 8 microns…but?)

(Always remember that the geometric ratio of the sizes of cones to rods on the human retina is 1.8:1 and that this corresponds to the visible band from 700-400 nanometers.)

NOTE:

Again, please note that I believe that the term “photon” in the context of light interaction with the retina of the eye should properly be termed a “quantized interaction”. The interaction process IS quantized, but it is the absorbing mass (the electron) that is spatially constrained to quantum confinement dimensions. It is obvious that the biological retina of the eye evolved to detect light as a wave.

GCH

NOTING AGAIN: I have proposed substitution of the term ‘quantized interaction’ for the purely quantum term ‘ photon’ reflecting my understanding of visible light interaction with the biological retina of the eye that teaches that visible light is absorbed in finite nanostructural spaces or ‘antennas’  - i.e., as the wave of classical physics -  but necessarily adjacent to quantum-confined electron spaces that constitute the absorbing mass. Thus, neither the quantum or classical view of the interaction is violated.

There really can be no doubt that the eye at low light levels can detect at the photon level (the ‘quantum limit’), i.e., it can discern and discriminate single photons of light in the process of forming an image. What mechanism does it use to accomplish this feat at body temperature (+ 98 F) when our most advanced photonic technology requires cooling to cryogenic temperatures approaching absolute zero (-273 F)?

A few relevant numbers: Albert Rose (reference in an earlier Comment), using the only model available to him that viewed the eye as a camera, writes on p 32:

“The physical storage time of the eye is between 0.1 and 0.2 sec, and is probably closer to the latter. The physical storage time is the equivalent of exposure time in a photographic camera………”

Thus the ‘overall’, or what be termed ‘seemingly biologically possible, ’ time required by the eye to accumulate sufficient data for the eye-brain to acquire and discern that an image is ‘there’ is of this relatively slow magnitude. This is analogous to the ~1/20 sec ‘frame time’ of movies or television – images acquired in this time, when viewed in rapid succession, appears as motion. This is the time frame historically assumed by vision science – and by Rose the engineer. The only way to reconcile this with vision at the quantum limit is, as Rose had to assume, that a gain factor of a million must be present somewhere in the range from light interaction with the retina and registry of the signal in the brain. Such a gain factor is not, and has never been in evidence.

But how to reconcile this with the eye’s ability to detect at the quantum limit?

The answer must lie in distinguishing two separate times differentiating between: 1.) an initial time ‘sufficient to accumulate events on the retina that results in a required information content’, and 2.) a second ‘biologically slow time where information constituting the entire image is transferred in one discrete package forward to the brain’. The latter presents no problem as it refers to the slow time described above and is consistent with, or constitutes, the image formation time discussed by Rose.

What is new, the ‘initial time’ of 1.) above would be defined by light interaction at the ‘front end’ or with the retinal outer segments as defined in this work. More specifically, this time would encompass the interaction event and isomerization of the retinal molecules contained within each receptor. I propose that an ‘electronically viable signal’ would result in this process that wold form one picture element of the acquired image.

WILL BE CONCLUDED SHORTLY

GCH

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).

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!

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