Are small pixels bad for diffraction, part 2

Started Sep 25, 2009 | Discussions thread
ejmartin Veteran Member • Posts: 6,274
Re: Theory vs. real world..

ljfinger wrote:

Let's say, for sake of argument, that we have a 1x1 pixel grid, and that 900 photons fall on our one pixel. Shot noise = sqrt(900) = 30. SnR = 900/30=30. Total noise power = 30^2=900.

Now, let's say we divide our 1x1 grid into a 3x3 grid and that we still receive the same 900 photons. Shot noise of each pixel is sqrt (900/9)=10 and SnR=100/10=10. For each pixel. Total noise power = 9*(10^2)=900.

So, the total noise power is the same but the SnR of each pixel is lower. Is that right? Is this the source of many misconceptions on this?

A useful way to think about noise is through its power spectrum. Just as resolution is presented in terms of MTF as a function of spatial frequency up to Nyquist, noise has a power spectrum from the coarsest image scales up to Nyquist. Spatially random noise (such as photon noise and much non-pattern forms of read noise) leads to a noise power spectrum that (averaged over orientations) is a linearly rising function of spatial frequency. For instance, here is a plot of noise power for a midtone of the 40D (red) and 50D (blue) at ISO 1600:

On the horizontal axis, 256 is the Nyquist frequency of the 50D; the 40D Nyquist is a bit over 200. In terms of such a plot, the noise std dev per pixel is proportional to the square root of the area under the curve. It is thus higher for the 50D than the 40D. Since the 40D and 50D collect about as many photons per unit area for a given exposure, the noise is higher by the ratio of Nyquist frequencies -- that is, by the ratio of pixel spacings. An ideal resampling of the 50D to the pixel count of the 40D would chop off all frequencies above the 40D Nyquist in the 50D's noise spectrum (and similarly for the resolution), yielding the same image with the same noise at the lower resolution (modulo secondary effects having to do with interpolation errors from demosaic, AA filter effects on resolution, etc).

So, if we triple the Nyquist frequency, and noise is a linearly rising function of frequency, the total noise power has gone up by a factor of three. SNR of each pixel is lower. But SNR, and noise power, at any fixed spatial frequency is the same as long as the same number of photons are collected per unit area (if we are talking about photon noise; adding in read noise leads to a more complicated discussion).

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