That's correct on my observations also. I think that the problem here is those weasel words 'all else equal'. To use that condition, you need to know what is included in 'all else', which isn't that simple, because changing the pixel pitch only has many knock-on consequences which unavoidably change performance parameters, not necessarily in the same direction. I've always thought that if one wants an artificial scenario to assess somehow 'inherent' effect of pixel pitch 2-D scaling is more sensible than 'all else equal', and under 2-D scaling reducing pixel size does not affect light collection and improves DR (per unit area in both cases).
The second issue is that sensors simply aren't designed that way. The pixel circuitry and optics will to a large extent be designed for the pixel pitch, and production economics tends to mean that they are processed on lines suitable for the pixel pitch and no finer.
Not my rabbit hole.
Jim's formula is Q = 2 * (lambda * N) / (2 * pitch) = lamda * N / pitch
derived from Q = 2 * Fcsensor / Fclens
Where Fcsensor = 1 / (2 * pitch), which is simply the cut-off frequency of the sensor due to the Nyquist limit, and Fclens = 1 / lambda * N, which is the standard formula for the cut-off frequency due to sampling.
In short there are two cut-off frequencies, one is determined by diffraction, one is determined by sampling frequency.
Or possibly you were thinking of the other '2', in which case this is a miscommunication caused by different interpretations of the word 'factor' which some take to mean specifically 'divisor', and others to mean any term in a multiplication or division.
So the misunderstanding is different use of 'factor'.
Anyhow, the source that Jim quotes gives the Q formula as Q=λ fn/PixelPitch directly. Looks to me like it's an arbitrary scale factor to allow λ fn/PixelPitch to be used as the metric. The only thing that it affects is which values you consider to mean what. They give Q=1.00 for panchromatic imaging, Q=0.25 for multispectral imaging and Q=2.00 for be critically sampled, or 2 samples per resolution element - which is the Nyquist condition. All that changes is the number for each condition. Jim was explaining it in terms of Nyquist and diffraction, but to do that you need the '2' to arrive at the Q formula. I suspect that the Q formula is as it is because the scale of the value doesn't matter, and making it Q=λ fn/PixelPitch just makes it simpler.
At some point Zeiss were showing that with a microscope "Q" up to 3 were showing visible improvements, but above 3 (they went to 5 for the critics to be sure) no visible improvement happened. That was with a monochrome sensor.
thats right from what ive read. my objetives are f 4 X magnifacation 4 x and now we are hitting f16. do the same with another objective 10x and thats = f40. i hope in on the right path.
exactlly. and when your stacking images noise is stacked its not magically disapearing. its been proven also by hi res images form a m43 camera compared to 42meg FF single image. the single image wins hands down every time.
That's why I'm trying to get a Zeiss S Planar 50/1.6 working on my GFX 100S. At 10:1 (the ratio it's designed for), that'll be f/16. Monochromatic, though.
Stacking purely for noise reduction is a thing. It's equivalent to giving a larger exposure. It also works with focus stacking, if the focus stacking software is clever enough.
but we are looking at images made from microscope objectives with extremely fine detail. read the olympus imaging link a poster had provided. you want the best image quality use a larger sensor. but under most curcomstances good enough is good enough.