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.