Why does photonic noise variance have to be proportional to the signal?
It is worth noting that photonic noise is due to the light signal itself and is independent of the camera. It is mathematically modeled by a Poisson process, and consequently, the mean signal is equal to its variance. (This is a mathematical property of a Poisson process.) It is possible to prove this property without any assumptions; however:
Assume that a pixel receives photons and has a noise standard deviation . Let’snow cut this pixel into four smaller pixels of equal size. Each small pixel receives an average number of photons and has a noise standard deviation . Since the variance is additive, the variance of the large pixel value is the sum of the variances of the small pixel values. Thus:
From this, it is not very difficult to see that has to be proportional to .
Photonic noise is the main source of noise in the midtones, and follows the rule of 3dB per EV: