# more pixels are better!

Started Dec 14, 2008 | Discussions thread
Re: Are those figures for "print" or "screen"? (nt)

Les Olson wrote:

I do not follow what you mean by "pixel noise" in this context.

Std dev of pixel values in a uniform tonality region in an image.

The estimated SNR cannot vary with the number of exposures, or
pixels, you use to estimate it, once you have enough to be confident
that the sample mean and SD are close to the population mean and SD.
The mean and SD of the outputs (ie, SNR) of a suitably large sample
of pixels (or exposures for a single pixel) must have a very low
probability of being different from (ie, for practical purposes must
be the same as) the mean and SD of the outputs (ie, SNR) of all the
pixels (or all the exposures the camera will ever make for a single
pixel).

In summary, unless the Central Limit Theorem has stopped applying
chez vous the idea that you could have an "SNR per sensor area" is
wrong (it is the same as saying that your camera's SNR increases
every time you make an exposure because the total amount of light it
has received increases - which is not to be confused with saying that
SNR increases when you prolong a single exposure because the amount

Noise is properly characterized not by a single number; it has a spectral power distribution as a function of spatial frequency. It is therefore important to take into account when comparing images from cameras with different pixel counts, that one has image data out to higher spatial frequencies than the other.

For instance, in the graph I presented above, the Nyquist frequency of the 40D was at 209 on the horizontal axis, while the Nyquist frequency of the 50D was at 256. The noise power spectra are clearly the same, out to the limit of resolution of the 40D; the 50D noise spectrum then continues out to the limit of its resolution.

The std dev of uniform tonality patches is a particular average over the power distribution -- the square root of the area under the power distribution curve. Because the 50D has more resolution, and only because of that, the std dev of noise in uniform tonality patches is higher for the 50D.

One way to see that the std dev is measuring a scale dependent quantity is to resample the 50D image to the dimensions of the 40D. This throws away all the image information at fine scales, and it also throws away all the noise power at high scales. A good downsampling algorithm (eg Lanczos) quite faithfully reproduces the noise power spectrum of the 40D from the 50D after downsampling, and the std devs are quite close. This is not because downsampling has reduced the noise at any particular spatial frequency -- the noise power at fixed spatial frequency differs very little after downsampling -- rather it is because downsampling has removed some frequencies from the spectrum altogether, and the noise power at those frequencies has been removed along with it.

In any case, there is an alternative: calculate the ratio of the SNR
at 10% reflectance to the SNR at 1% reflectance, which takes account
of anything there is to take account of. The multiple regression
using pixel pitch and camera date as predictors of this ratio is
practically identical to the regression using them as predictors of
the component SNRs.
--

The slope of the SNR of RAW data is a measure of something else entirely, indirectly and imprecisely an indicator of the photon gathering efficiency per pixel. The precise way to measure the latter is actually to plot the noise variance per pixel as a function of mean signal in raw levels; the inverse of the slope is the number of photons gathered per raw level.

Again, to be converted to a meaningful statistic, one should divide by the pixel area to get a sense of the efficiency of the sensor.

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