(I am indebted to my colleague – and son – Alexander whose programming skills led to the geometric understanding reported herein – GCH)
(WE WILL PRESENT FOR THE TIME BEING PRELIMINARY THOUGHTS WITHOUT QUANTITATIVE PROJECTIONS THOSE TO BE ADDED SHORTLY)
We have proposed elsewhere (“A New Model…..”) that the basic light detection “devices” of the retina comprise the dimensionality formed between the quantum confined electron spaces characteristic of the retinal/rhodopsin complexes contained within thylakoid disks. The stack of these disks within each receptor then form what we have termed lengthy quantum confined electron “nanowires.”
The light signal detected is therefore a wave commensurate with “antenna dimensionality.” This corresponds roughly to the center-to-center distances between the receptors (which, in turn, is determined by the diameter of receptor inner segments). This approach differs fundamentally from two traditional retinal light interaction models , i.e., either considering that light as photons interacts with pigment molecules contained within individual receptors, or alternatively, that light interaction is as a wave that is guided (fiberoptically) within individual receptors to eventually one guesses interacts with pigments.
We have proposed further that each of two adjacent receptors is configured as an “electric dipole” that generates a polarization signal proportional to where light energy is deposited along it’s length. A comparator function between receptors (which the hypothesis predicts will be found to exist) will then generate a composite signal which corresponds to the angle of incidence of light entering the device.
We have noted elsewhere the imprecision of defining “optical antenna” dimensions other than projecting that they will correspond roughly to light wavelength divided by twice the index of refraction of the absorbing medium. We had many discussions about antenna dimensionality in this sub-optical wavelength region with our colleague Felix Gutmann but ended up feeling that the overall picture was so compelling that we would simply define the two “endpoints” of the hypothesis as the extremes of the visible spectrum – 700 and 400 nm. – and leave detailed calculations until later. The well known dimensions of the retinal receptors are certainly in the ballpark for these considerations. We have referred generally to “center-to-center” distances between receptors although more precisely the lateral distances between rhodopsin complexes scattered within thylakoid disks of adjacent receptors may be considerably less than this. This will bring actual dimensions closer to correspondence with calculated values.
There is one quantitative statement that we feel can be made – and it is an important one – that the “eight rods around each cone” octagonal motif that exists at 7 – 8 degrees of retinal eccentricity represents the a fixed reference where mid-band wavelengths (~ 550 nm) of the visible spectrum are detected. This provides a spatial, geometrically defined wavelength reference point on the retinal surface that no other vision model provides and which is an inherent requirement of Edwin Land’s color vision concept. This is the basis for the color constancy of vision.
In our model there are, therefore, three types of such light detection devices that we will analyze. These are:
- The “cone/cone” type formed by cone/cone appositions of the fovea centralis that we have proposed are sensitive solely to the longest wavelengths – and form the long wavelength end of the visible band.
- The “cone/rod” antennas formed by cone/rod appositions that begin to form outside of the fovea as the density of rods increases reaching a peak density at ~ 7 -8 degrees.
- The “rod/rod” antennas formed by rod/rod appositions that constitute the bulk of the peripheral retina and that we have proposed are sensitive solely to short wavelengths and form the short wavelength end of the visible band.
In this initial exercise we will use only approximate figures for receptor dimensions – exact numbers can be added later. We do not believe that this detracts from the broad outline of the findings.
Assumptions used in device simulations are:
- The aspect ratio for the light interactive outer segment of rods is assumed to be 40:1, i.e., for example, corresponding to 40 microns in length and 1 micron in diameter.
- Similar dimensions for cone receptors will be 25 microns in length and 2 microns in diameter.
- We will calculate the “viewing angle” for each device and the proportionality of energy deposited in each adjacent receptor as a function of light incidence angle.
PRELIMINARY RESULTS:
a.) The rod/rod device geometry with 40:1 aspect ratio rather obviously possesses a very narrow “viewing angle” of only ~ 1.14 degrees. Energy deposited in each receptor changes linearly with light entrance angle but, rather surprisingly, completely switches the polarity of each receptor across this narrow viewing angle! It seems almost a “digital” situation. This is illustrated in Figure 1.
b.) A diagrammatic representation of the cone/cone device geometry is shown in Figure 2. The cone/cone device exhibits a wider viewing angle of ~4.58 degrees. Energy deposition in adjacent receptors is again linear (as it should be) but the conical shape produces a steeper curve of rate of change than a geometry where adjacent receptors are rectangularly shaped (as rods ). We speculate that this may be the reason for the conical shape of these receptors rate of change must be related to angular sensitivity. Does the fovea with the “outline detection” function that we propose require greater angular sensitivity? Again, we will present these quantitative results shortly.
Incidentally, an explanation for the directional Stiles Crawford effect may follow from this result. Any light entering from outside of the 5 degree viewing angle of the device results in drastically diminished energy absorption and thus output signal. We will simulate this shortly showing quantitatively how energy is apportioned between receptors at large angles of incidence.
c.) The cone/rod device geometry is the most surprising with a pronounced angular asymmetry (which upon simple reflection should be the case). Angular response is not linear with an abrupt polarization signal from the rod component. This asymmetry may have the purpose (as we have proposed elsewhere) of “directing” a signal into a channel related to the logic of image formation. To go to the singular “eight rods surrounding each cone” motif that exists at the 7 -8 degree retinal angle, energy might be directed into eight separate channels..for what reason?
