SENSITIVITY OF THE EYE 41 



and in turn this reaction initiates a sequence of other chemical reactions 

 leading finally to stimulation of a single nerve fiber. It must then be 

 true that the requirement for 5 photons is exerted at the level of the 

 nerves. The nerve excitation resulting from summing the effects of 5 

 individual nerve fibers is what is finally sufficient to trigger the optical 

 nerve into transmitting an impulse to the brain. 



On quite general grounds, a result greater than one photon is to be 

 expected. If one photon were the threshold, then a single firing of a 

 nerve fiber would result in vision. A single nerve fiber can be excited 

 randomly by heat, fluctuations in chemical reactions in the retina, pres- 

 sure, etc., so that we should be seeing flashes all the time. Therefore, we 

 would guess that more than one photon would be needed, so as to reduce 

 the random triggering of vision by these agents when it is irrelevant to 

 the seeing processes. Of course, psychologists might maintain the en- 

 tirely possible position that the triggerings occur but are suppressed by 

 the mind so as to free the eye for purposeful vision. 



A number such as 5 photons is interesting because the fluctuations in 

 this number (from the Poisson Distribution) yield a standard deviation 

 of \/5, which is about 2.3. Two standard deviations (2s) equal about 5. 

 Therefore, in some 5% of the cases where an average of 5 photons was 

 delivered to the retina, the fluctuations should be great enough to result 

 in no photons getting through and therefore the subject would not see 

 the flash that the experimenter thought he was giving. 



This leads us to another way of approaching the visual threshold 

 problem. Consider that, for a subject to detect a flash, a threshold of n 

 photons must be equaled or exceeded on the retina in the area being 

 stimulated. When the number of photons arriving is less than n, the 

 subject will see no flash at all; when it is n or greater, the flash will be 

 seen each time. Thus, if this simple model were correct, the frequency of 

 seeing flashes of increasing intensity would rise abruptly from zero to 

 100% at the threshold value of n. However, there are two sources of 

 variation in such an experiment: biological variability and physical 

 variability. We can't do anything about biological variability, for the 

 term includes factors which we don't understand or cannot control. So 

 we focus attention on physical variability. In this situation it means 

 that when one shines n photons, on the average, on a retina, there will be 

 fluctuations of this number. Indeed, we know that the standard devia- 

 tion of the number is \/ n - That is, in one third of the cases, the number 

 will differ from n by \/n or more. Now, when the average is n, the frac- 

 tion of times there will be n or more is not unity, as in the simple non- 

 fluctuating example first mentioned in the paragraph, but is something 

 less than unity. For any given intensity of light, the flash will contain 



