Quote:
Originally Posted by Stonius
Can anyone explain why, in simple terms, the noise is always the square root of the signal?
Surely all signals can have varying amounts of noise? Why is there a constant relationship there?
Markus
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Always is always a big ask, but if we're talking about
shot noise ...
In taking the
shot we are measuring (sampling) the light intensity from the DSO at each pixel location. Photons from the DSO travel in to the camera, strike the sensor and are converted in to electrons in accordance with the Quantum Efficiency of the sensor. These are "counted" and digitised in to a light intensity at each pixel location in the image at a bit depth according to the type of image JPEG, RAW, etc... by the camera electronics. At each pixel location in the image
we are counting the number of events that occur in a given time.
<<< That is the classic applicability criterion for the Poisson Distribution - (The probability distribution for a variable that counts the number of events that occur in a given time). When Poisson originally developed it was a distribution of the number of soldiers kicked by horses on a given day (Love the French). Here we measure photons/electrons over a fixed time period.
The Poisson distribution can be modeled as a Normal distribution under certain special conditions, BUT to cut to the chase, your answer lies in the definition of the Standard Deviation (a measure of spread)
for the Poisson distribution. It is quite simply equal to the square root of the mean.
So if we take a series of shots and the mean signal intensity = x, then the standard deviation of the signal intensity (which you could think of as variability or noise) will be sqrt(x). That is simply the math for the Poisson Distribution (perhaps see Poisson Distribution for this derivation)
Puting the standard deviation in more usual Normal Distribution terms:
~ 68% of the intensity would be expected to be in a band 1 standard deviation either side of the mean
~95% of the intensity would be expected to be in a band 2 standard deviation either side of the mean
~99.7% of the intensity would be expected to be in a band 3 standard deviation either side of the mean
That variability is what makes all those disgusting dots we don't like.
Best
JA