Photon noise

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Photon noise simulation.

In physics, the number of photons collected by an instrument which are emitted from any incoherent source are distributed according to a Poisson distribution, as long as the average intensity is constant over the bandwidth of the instrument. This is because the photons are discrete and the probability of one photon's arrival is independent of any other photon's arrival. In other words, it is a Poisson process.

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.

This process should not be confused with the energy distribution of any photon source, which describes the average intensity or average number of photons collected which lie within some energy interval.

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 variance of the photon noise, which is a measure of the expected difference between the number of photons collected and the average number, is equal to the square root of the average number of photons. The signal to noise ratio is then

$SNR=N/\sqrt{N}=\sqrt{N}$

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.