Vision at Low Light - An experimental case study

1. The problem.

2. Anatomy and physiology of the human eye.

  • Basic anatomy - the fovea, "blind spot" (optic nerve), retina. (Eckert, Fig. 7-37)
  • The retina consists of layers of interconnected cells, with the sensory receptor cells, the rods and cones, at the back of the retina and the nerve cells going to the brain coming out of the front of the retina (towards the light) and then back through the retina at the "blind spot".
  • Receptor cells in the retina are of two types: 1) Rods, that contain the visual pigment rhodopsin, and are used for peripheral, low light vision. These cells are found on outside the fovea. 1) Cones, that contain visual pigments very similar to rhodopsin, and are used for detailed color vision. (The cones are of three types. Each type absorbs either red, green, or blue light preferentially.) These cells are found densely packed in the fovea. Rhodopsin and the pigment molecules in the cones consist of a protein that sits in the folded membranes of the receptors. This protein contains a non-protein component, retinal, that actually absorbs the light. Retinal changes shape when light is absorbed and that shape change is transmitted to the opsin protein. This change starts a G-protein (transducin) mediated signal cascade. (Eckert, Fig. 7-44a)

3. The experiment of Hecht, Schlaer and Pirenne (1942).

  • Maximum sensitivity of the rod cells is at 20 degrees of angle from the fovea. This is where we want to make test flashes appear. Note the blind spot is located about 15 degrees on the nasal side of the fovea, which corresponds to an image point 15 degrees on the temporal side of the person's view. We want to stay away from the blind spot so, let's make the flashes appear 20 degrees off the temporal side of the fovea on the retina
  • To orient a person's vision, have them stare at a constant point of light, then make the low light test flashes appear at 20 degrees off that point.
  • Test flashes should be at a wavelength of 510 nm (yellow-green), at the peak of the sensitivity of the scotopic (rod) vision. (Rhodopsin is most sensitive to yellow-green light. Note that glasses for dim light are often yellow in color!)
  • Flash should be short - less than 1/10 second in duration. Note that longer or more rapidly occuring flashes temporally integrate - the sum of the response of the eye over a longer time than 1/10 sec. is less than the sum of the responses to the individual, very brief, flashes. (Flicker fusion frequency - television, movies.)
  • Flash area must small. If the flash covers too many receptor cells in the retina, then the response will be less than expected. This is the result of lateral inhibition, which causes sharpening of edges on images. The flash must cover one "receptive field" or less. A receptive field is a region on the retina of about 49 microns in diameter. A circular area of 49 microns includes about 270 rod cells and corresponds to a angle of view of about 10 minutes of arc (1/6 of a degree, or in your lecture hall, a spot 3.5 cm in diameter on the screen, viewed as viewed by somone in a center middle seat.)

  • The subject must be dark adapted for at least 40 minutes so all the rhodopsin is fully regenerated.
  • Now, we have our dark adapted subject, sitting in the dark room for a good part of an hour. We turn on the red light and ask the subject to stare at it. We have covered one eye, say the left one, with a patch. Now, we flash the yellow-green flash at random intervals. The subject is asked to tell us when she sees a flash. We vary the intensity of the flash from very dim to brighter.
  • We can tell how many photons of light are, on the average, in a given flash from the energy. We measure energy of a light flash. The following gives the energy of a single photon of a given wavelength (510 nm, in this case): E = h c / wavelength. (h is Planck's constant, c is the speed of light). So, dividing the total energy of the flash by E gives the number of photons.

3. Results and Interpretation.

  • If the flash is really dim, it is almost never detected by the subject. If the flash is fairly bright, it is ALMOST always detected. If the flash contains approximately 50 - 150 photons, then the subject will detect the flash about 60% of the time.
  • This 50 - 150 photons translates into about 5 - 15 photons being absorbed by rhodopsin. About 50% of light entering the eye is scattered and lost before it reaches the retina. Then, only one in 5 photons (20%) of those that reach the retina is actually absorbed by the rhodopsin. So, we have 5 - 15 photons (approximately 10% of those entering the eye) reaching 270 or so cells. Chances are cells excited by a photon are capturing only one photon - AN AMAZING CONCLUSION - ONE RECEPTOR CELL CAN DETECT A SINGLE PHOTON!!!!!
  • This is a very rough calculation. Hecht and colleagues went a bit further. They concluded that the detection of light was a random process. After all, when they flashed 100 photons, this was seen only 60% of the time by the average subject. Sometimes the person saw the flash and sometimes not. The "frequency of seeing" was zero at low light levels, rose to 60% for flashes of 100 photons, and then rose to 100% for very intense flashes. But, probability is working here!
  • So, they plotted the frequency of seeing a flash (a frequency of 1 = 100%) vs. the intensity of the flash in photons. And, then, they constructed a mathematical model which predicted the experimental results for various threshold values. This is what they saw:

  • The black curves are the theoretical predictions for frequency of seeing. Each curve is calculated for a different value of threshold (minimum number of photons absorbed by cells in one receptive field so that an an average observer will see the flash at least 60% of the time). The red points are experimental observations based on number of flashes entering the eye.
  • When we correct for the absorption of light by the eye we get the following:
  • The theoretical curves are for 2, 3, 4 ..., 12 minimum number of photons required. Notice that the points seem to best fit the model for 7 or 8 minumum photons. The second most AMAZING thing is that we really don't need to know anything about how much light is lost on the way to being absorbed by the rod cells. We simply guess the absorption and slide the corrected data points over the theoretical curves. When we correctly guess the light absorption, then the data will fit one of the curves well but not the others, because they are different shapes. The results shown above are for transmission of 8% of light from the flash (92% absorption), in good agreement with other types of measurements. (We predicted about 10% transmission from some very rough measurements on the optical properties of the eye.) If we chose 5%, say, the red data points would all be pushed over to the left and wouldn't fit any single theoretical curve. If we chose 15% transmission, the data points would be stretched out to the right and again wouldn't fit any single theoretical curve.

4. Randomness and ability to see small differences in light intensity - Some things to discuss, as time permits.

  • We can't ever do better than to detect 5 - 8 photons per receptive field because of noise.
  • Experiments on cooled frogs confirm the relationship of noise (random events) to the detection of light at low light levels.
  • Detection of differences in light intensity is closely related to the problem of detection of light at low levels.
  • The Weber-Fechner Law is a result of noise theory.

All text and images, not attributed to others, including course examinations and sample questions, are Copyright, 2008, Thomas J. Herbert and may not be used for any commercial purpose without the express written permission of Thomas J. Herbert.