Editing Shot noise (section)

=== Signal-to-Noise ===
For large numbers, the Poisson distribution approaches a [[normal distribution]] about its mean, and the elementary events (photons, electrons, etc.) are no longer individually observed, typically making shot noise in actual observations indistinguishable from true [[Gaussian noise]]. Since the [[standard deviation]] of shot noise is equal to the square root of the average number of events ''N'', the [[signal-to-noise ratio]] (SNR) is given by:

:<math>\mathrm{SNR} = \frac{N}{\sqrt{N}}  = {\sqrt {N}}. \, </math>

Thus when ''N'' is very large, the signal-to-noise ratio is very large as well, and any ''relative'' fluctuations in ''N'' due to other sources are more likely to dominate over shot noise. However, when the other noise source is at a fixed level, such as thermal noise, or grows slower than <math>\sqrt{N}</math>, increasing ''N'' (the DC current or light level, etc.) can lead to dominance of shot noise.