# f-number equivalent between m43 and FF

Started Mar 25, 2014 | Discussions thread
Re: Shot noise in the (spatial, as opposed to the optical) frequency domain

Jack Hogan wrote:

Detail Man wrote:

Jack Hogan wrote:

crames wrote:

Another way to look at it is in the frequency domain .

I wonder if that's not a misleading graph in this context, as I think it applies just to read noise: it shows the amplitude of the signal decreasing with increasing frequency, but the noise being constant with it. I understand this discussion to be mainly about rms shot noise, which I think would also decrease with a decreasing signal.

Your point makes sense to me, Jack - as while noise is spectrally "white", photon shot noise itself (as opposed to readout noise) is (also) scaling with the number of transduced photons.

http://www.dpreview.com/forums/post/3985100

... references this web-page:

http://steveharoz.com/research/natural

... which states:

Plots of the power spectra from the natural images are shown above. These plots have nearly straight lines with slopes of approximately -2, which corresponds to an f^(-2) trend.

... and:

These plots have been observed for tens of thousands of images, and the f ^(-2) trend consistently differentiates natural images.

... but does not differentiate between noise sources varying with signal level and those that do not.

Your Total Recall never ceases to surprise me, DM: you must have either a fantastic archival system or a fantastic memory. Either way, bravo

It's simpler (and less glorious) than that. I had previously published a post that referenced ejmartin's post on that thread (and that web-page) - so I just went out and found my previous post again.

But giving the subject a little more thought, is it indeed possible to separate the signal from its own shot noise in the frequency domain as shown in Cliff's graphs?

I guess one way would be to graph the fourier transform of the mean signal over a reasonable interval and then add to the graph the fourier transform of the variance from it. Wouldn't this be equivalent to plotting the lower frequencies (the 'mean') and the higher frequencies (the 'noise') separately as two curves on the same graph? The reasonable interval in this case would be the number of pixels that fit within the CoC of the image as projected on the retina.

To simplify things, what would happen if we took the fourier transform of a laser as processed above? Would we

1) see a large delta function at the laser's wavelength with much smaller, equal white noise throughout the bottom of the graph? Or
2) would the poisson noise be band limited and/or asymmetrical?

If the former I think Cliff would be right, because we could consider a natural image as the superposition of a large number of lasers, each contributing differing amounts of white noise, which would add in quadrature to produce more white noise - a flattish line at the bottom of the graph.

If the latter then perhaps not, because the larger lower frequencies would contribute more noise than the higher ones, resulting in a sloped noise fourier transform.

So I looked for the answer. At the bottom of slide 5 here it says that for shot noise "The noise spectral density is white (independent of frequency) or flat; The noise spectral density is equal to the average rate", which I think in our case would indicate the probability of a photoelectron being generated in a pixel within the CoC.

So it appears that shot noise from a Signal is indeed a superposition of flat curves in the frequency domain, resulting in another flat curve - and Cliff is correct. Right?

I don't know. Am in over my head (which never collected much in it, despite my humble efforts).

Poked about some on the internet. Stared at some stuff. Seemed to me that the "frequency" in question was spatial frequencies within an image - as opposed to optical frequencies (as in optical wavelengths). Seemed that RMS shot noise (in general) is proportional to current ("I"):

... and that less photons registering at higher spatial frequencies would translate to lower shot noises - whereas (random components of) readout noise would not necessarily have similar characteristics ?

Here are some links that appear to address matters specifically related to optical wavelengths:

http://www.rp-photonics.com/shot_noise.html

http://rleweb.mit.edu/sclaser/6.973%20lecture%20notes/Lecture%2019b.pdf

If I'm here missing something fundamental, please do let me know. I await further enlightenment.

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