To my knowledge the signal to noise ratio when talking about shot noise, is defined as the mean signal divided by the standard deviation. In the Poisson distribution, which can be used to model shot noise, the mean and the variance are equal and thus giving us the equation N/N^(1/2).
I have a couple questions regarding this:
The first one being that, since N/N^(1/2) is equal to N^(1/2) we can see that the rate at which the SNR improves with increasing exposure/signal diminishes. I understand that graphically this is quite obvious. However, I cannot seem to wrap my head around it, since the shot noise has a y = N^(1/2) function, meaning that the increase in noise is diminishing as the signal increases and the mean signal has a function of y=N , so the signal is linearly increasing with increasing signal. So why does the rate of increase in SNR decrease?
How do other noise elements factor into this, such as dark current noise (read noise) and is it fair to assume that in most cases (other than very low exposure) shot noise is the most dominant (visibly dominant) form of noise in cinematography/photography.
As the mean signal value increases the Poisson distribution begins to look more and more like a Gaussian distribution and as we know the SNR continuously improves. However, when I look at the graphs, the more and more the signal increases the more the spread of the curve seems to increase, which to me visually would suggest more noise? (graph below from wikipedia)