What is photon shot noise?

THIS GUIDE IS FOR:

Persons whose physics is a little rusty

THIS GUIDE OFFERS:

A quick and visual explanation of photon shot noise

Photons (and photoelectrons) are quantum particles—this means that they can only come in whole numbers and the camera can never collect fractions of photons. Because of this and random statistical fluctuations, when collecting photons from an unvarying source over a set amount of time—say ten random 30 seconds intervals over the course of twenty minutes—it is highly unlikely that you will collect 20 photons every single time. Just like if you were to flip a coin ten times, it is highly unlikely that you would get five heads every single set of 10 flips.

Instead, the first interval may give you 20 photons, the next interval 23 photons, the next interval 18 photons, and so on. And if you were to plot the distribution of photons, the curve would follow a Poisson distribution. The variability from one of these thirty-second intervals to the next is the shot noise.

The combination of high sensitivity and low noise ensures high signal-to-noise ratio during low-light imaging

Why should you care about the randomness of photons? Or really, when should you care? When signal is limited. The amount of shot noise inherent in the signal is a function of the amount of signal—the more signal you have, the smaller the fraction of the signal comes from shot noise (see graphs below):

$Shot\ noise=\sqrt{\mathstrut signal}$

So you need to care about shot noise when signal is low. And if you’re doing quantitative studies, you’ll typically use a Poisson distribution to model the shot noise.

(A) At low light levels, the variance introduced by photon shot noise contributes to a large proportion of the signal. (B, C) At higher light ranges, the variance introduced by photon shot noise is a smaller percentage of the overall signal.