Tag Archives: planck

illuminant, Information Science, Quantization, Sensors, SPD, variation

Photons, Shot Noise and Poisson Processes

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Every digital photographer soon discovers that there are three main sources of visible random noise that affect pictures taken in normal conditions: Shot, pixel response non-uniformities (PRNU) and Read noise.[1]

Shot noise (sometimes referred to as Photon Shot Noise or Photon Noise) we learn is ‘inherent in light’; PRNU is per pixel gain variation proportional to light, mainly affecting the brighter portions of our pictures; Read Noise is instead independent of light, introduced by the electronics and visible in the darker shadows.  You can read in this earlier post a little more detail on how they interact.

Read Noise Shot Photon PRNU Photo Resonse Non Uniformity

However, shot noise is omnipresent and arguably the dominant source of visible noise in typical captures.  This article’s objective is to  dig deeper into the sources of Shot Noise that we see in our photographs: is it really ‘inherent in the incoming light’?  What about if the incoming light went through clouds or was reflected by some object at the scene?  And what happens to the character of the noise as light goes through the lens and is turned into photoelectrons by a pixel’s photodiode?

Fish, dear reader, fish and more fish.

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Exposure, Radiometry

Photons Emitted by Light Source

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How many photons are emitted by a light source? To answer this question we need to evaluate the following simple formula at every wavelength in the spectral range of interest and add the values up:

(1)   \begin{equation*} \frac{\text{Power of Light in }W/m^2}{\text{Energy of Average Photon in }J/photon} \end{equation*}

The Power of Light emitted in W/m^2 is called Spectral Exitance, with the symbol M_e(\lambda) when referred to  units of energy.  The energy of one photon at a given wavelength is

(2)   \begin{equation*} e_{ph}(\lambda) = \frac{hc}{\lambda}\text{ joules/photon} \end{equation*}

with \lambda the wavelength of light in meters and h and c Planck’s constant and the speed of light in the chosen medium respectively.  Since Watts are joules per second the units of (1) are therefore photons/m^2/s.  Writing it more formally:

(3)   \begin{equation*} M_{ph} = \int\limits_{\lambda_1}^{\lambda_2} \frac{M_e(\lambda)\cdot \lambda \cdot d\lambda}{hc} \text{ $\frac{photons}{m^2\cdot s}$} \end{equation*}

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