SENSITIVITY OF THE EYE 



43 



100 



1.5 



2.0 2.5 1.5 2.0 2.5 1.5 2.0 



Logarithm of average number of photons per flash 



Fig. 19. This figure presents the experimental findings on three different sub- 

 jects. The lines are the theoretical curves given in the previous figure. As may 

 be appreciated by studying the theoretical curves, the choice of a curve with n 

 greater or smaller by unity would give an appreciably poorer fit to the experi- 

 mental points. (From Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819, 

 1942; courtesy the authors and J. Gen. Physiol., Rockefeller Institute Press, New 

 York.) 



The theoretical analysis utilizes the Poisson formula. For any average 

 number of incident photons, we can figure out the fraction of times 

 there will be a minimum of, say, 1 photon hitting the retina. This curve 

 is plotted in Fig. 18 with a 1 beside it. Similarly, we can figure out 

 the fraction of times there will be at least 2 photons hitting the retina 

 for any average intensity. And a similar calculation can be carried out 

 for any threshold number of photons. Figure 18 shows these curves for 

 various values of this threshold number. Next w 7 e try to fit the calculated 

 curves of Fig. 18 to the actual data obtained. Since the shape of the 

 curve depends strongly on the value of the threshold number, it is possible 

 to distinguish quite well between possible curves. In this way, by trying 

 successively 3, 4, 5, 6, 7, etc. photons for the threshold, it is possible to 

 show that the best number is about 6 photons. This means that at low 

 intensities there were few times that the flash was seen because there 

 w r ere few flashes which chanced to contain 6 photons, since the average 

 number of photons was less than 6. When an intensity w T as reached such 

 that an average of 6 photons reached the retinal absorbers, not all the 

 flashes were seen because some of the flashes contained 0, 1, 2, 3, 4, and 

 5 photons, none of which could be seen. When very high intensities were 

 used, all flashes had at least 6 photons, and so all were seen. In fact, as 

 shown in Fig. 19, the data for three different subjects gave 5, 6, and 7 

 photons as the number which best fitted the data. Note that this experi- 

 ment could have been done simply by fitting the curves to the data — it 



