When determining the best industrial camera, one of the first considerations is to determine if your application is shot noise limited. This can help you prioritize the most important camera parameters, such as dynamic range or sensitivity.
In this blog we explain how to determine if your imaging system is light limited or shot noise limited.
Shot noise originates from the discrete nature of electrons.
Consider the following example: imagine standing at an overpass above a highway and counting the amount cars passing by in one minute. The next minute, and the next, and the amount counted is probably not the same. The resulting measurement varies from minute to minute, following a Poisson distribution.
In the electron domain this is similar: the standard deviation of the amount of captured electrons in a pixel is the square root of the mean signal level.
The amount of electrons (signal level) depends on the QE and the amount of light (photons) that hit the sensor.
Where QE is Quantum Efficiency: The probability that a photon that reaches the pixel will be converted into an electron. The QE is the only camera parameter that shot noise SNR depends on.
Say that N is the amount of electrons in the pixel, then sqrt(N) is the shot noise that is on top. For an increasing amount of electrons, the shot noise increases as well.
Noise however should not be considered on its own. In applications, the noise has to be seen relative to the signal. In practice, the Signal to Noise Ratio (SNR) is used. In general the ‘noise’ is referred to as its RMS value.
Neglecting other sources but shot noise, the SNR is than N/sqrt(N) = sqrt(N).
The SNR increases for a larger signal!
SNR-wise it is desired to accumulate as many electrons in the pixel as possible, which requires a large Full Well. However this is not always possible due to the limited amount of light.
The system is said to be light limited when, while not yet reaching saturation, the exposure of the sensor cannot be increased.
Large full well is not of the essence here where Full well is the maximal number of electrons that can be contained in the pixel. Other performance parameters such as read noise and fixed pattern noise behavior are more important.
If more light can be captured (for example by increasing the integration time), the better the SNR becomes according to the equation. It does pay off here to use a sensor with a larger full well.
The system is said to be shot noise limited when there is an abundance of light and a large full well is desired to optimize it.