# Shot noise

 related topics {math, energy, light} {system, computer, user} {rate, high, increase} {food, make, wine} {ship, engine, design} {game, team, player}

Shot noise is a type of electronic noise that occurs when the finite number of particles that carry energy (such as electrons in an electronic circuit or photons in an optical device) is small enough to give rise to detectable statistical fluctuations in a measurement. It is important in electronics, telecommunications, and fundamental physics.

It also refers to an analogous noise in particle simulations, where due to the small number of particles, the simulation exhibits detectable statistical fluctuations not observed in the real-world system. Magnitude of this noise increases with the average magnitude of the current or intensity of the light. However, since the magnitude of the average signal increases more rapidly than that of the shot noise (its relative strength decreases with increasing signal), shot noise is often only a problem with small currents or light intensities.

The intensity of a source will yield the average number of photons collected, but knowing the average number of photons which will be collected will not give the actual number collected. The actual number collected will be more than, equal to, or less than the average, and their distribution about that average will be a Poisson distribution.

Since the Poisson distribution approaches a normal distribution for large numbers, the photon noise in a signal will approach a normal distribution for large numbers of photons collected. The standard deviation of the photon noise is equal to the square root of the average number of photons. The signal-to-noise ratio is then

where N is the average number of photons collected. When N is very large, the signal-to-noise ratio is very large as well. It can be seen that photon noise becomes more important when the number of photons collected is small.

## Contents

### Intuitive explanation

It is known to everyone that in a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after a great many throws will differ by only a tiny percentage, while after only few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot. (It can be proved that the relative fluctuations reduce as the square root of the number of throws, a result valid for all statistical fluctuations, including shot noise.)

Shot noise exists because phenomena such as light and electric current consist of the movement of discrete, quantized 'packets'. Consider light—a stream of discrete photons—coming out of a laser pointer and hitting a wall to create a visible spot. The fundamental physical processes that govern light emission are such that these photons are emitted from the laser at random times; but the many billions of photons needed to create a spot are so many that the brightness, the number of photons per unit time, varies only infinitesimally with time. However, if the laser brightness is reduced until only a handful of photons hit the wall every second, the relative fluctuations in number of photons, i.e. brightness, will be significant, just as when tossing a coin a few times. These fluctuations are shot noise.