Essential characteristics of noise

Sunday, May 10, 2009

Camera Article
Introduction | Noise in shadows | Noise in mid-tones | Noise in highlights | Summary | Annex

Why does photonic noise variance have to be proportional to the signal?

It is worth noting that photonic noise is due to the light signal itself and is independent of the camera. It is mathematically modeled by a Poisson process, and consequently, the mean signal is equal to its variance. (This is a mathematical property of a Poisson process.) It is possible to prove this property without any assumptions; however:

Assume that a pixel receives photons and has a noise standard deviation . Let’snow cut this pixel into four smaller pixels of equal size. Each small pixel receives an average number of photons and has a noise standard deviation . Since the variance is additive, the variance of the large pixel value is the sum of the variances of the small pixel values. Thus:

From this, it is not very difficult to see that has to be proportional to .

Photonic noise is the main source of noise in the midtones, and follows the rule of 3dB per EV:

  • An object reflecting light twice as much as another one has a better SNR (+3dB).
  • Doubling the exposure time improves the SNR by 3dB.
  • A camera with the same field of view and twice as many pixels as another camera has a lower SNR (-3dB). Indeed, each pixel receives two times less light in the high-resolution camera as in the low-resolution camera. However, the high resolution camera contains more detail, and can still be converted into a low-resolution camera by carefully-performed sub-sampling. In this case, the noise level is the same (see “Noise Normalization”).