The term signal to noise ratio (SNR) is commonly used as an important figure of merit in measurement systems. The SNR is defined as the ratio of a signal power to the noise power corrupting the signal. The ratio is usually measured in decibels (dB). The figure to the right shows a depiction of a continuous time signal with a SNR of 10 dB, showing the pure signal, the noise and the signal and noise combined.
When considering the SNR of an optical sensor one should be aware of the sources of the noise added to the signal. The figure below outlines the sources of noise added to a signal as it is captured and processed by an image sensor. For more detail on the noise sources in image sensors click here.
Out of the noise contributions shown above, all bar the photon shot noise (which is a property of light) are considered when describing the SNR of the sensor. Photon shot noise is the result of the uncorrelated arrival of photons at the photosensitive area of the pixel, as such the best noise performance an optical measurement device can have is limited by this physical property of light. The noise added to the signal by the sensor can be expressed as a sum of three independent components:
- Shot noise which is random fluctuations of the photocurrent current due to the current is carried by discrete charges, and can be approximated by a Gaussian,
- Reset noise, due to thermal noise within the reset switch causing an uncertainty in the reset level and also has a Gaussian distribution,
- Readout noise, introduced by the pixel buffers and output amplifiers etc. If considering a the SNR of a camera system, contributions from external devices and quantization noise would be considered also. Readout noise has a zero mean variance ,
Therefore the output charge can be expressed as,
and provided the photocurrent is constant over a period of exposure, the SNR is given by,
The above equation shows that the SNR increases by 20dB per decade with both photo-current and exposure time when reset and readout noise dominate, and 10dB per decade when shot noise dominates.