Aperture question, re: sharpness

a13

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Just a couple of musings that I'm posing to myself..

1. Is the absolute sharpest a lens can and will ever be, when it is stopped all the way down to its smallest aperture?

Follow-on from above,

2. If so, is that because it's using the very centre of the lens when it's stopped all the way down like this? Meaning that 1) will be true for each and every lens, without exception (well, except maybe ones designed to be sharper on the edges than in the centre...)?

Leading question in relation to above,

3. If a FF lens is stopped down to f/22, what is the f-stop on an m43 that would match the same exact PHYSICAL opening diameter of the FF lens @ f/22?
 
Solution
The sharpest aperture on a lens is most likely 2 or 3 stops down from the maximum. Or, on a lens with an maximum aperture of f 1.4, that might mean that f 2 is actually sharper. Some lenses are made to be used wide open and will exhibit their best sharpness at that point. Closing any lens down as far as possible will not deliver best quality.
Not exactly. This all depends on what the sensor format is. For MFT, most will suggest anywhere between F2.8 - F4 will be the sharpest, since this isn't extremely fast yet is likely at the early stages of diffraction. Faster lenses have more glass, so a F1.4 will have more of a FF like profile to the elements, ie more flaws as you move outward from the center. Faster glass is bigger glass...
The sharpest aperture on a lens is most likely 2 or 3 stops down from the maximum. Or, on a lens with an maximum aperture of f 1.4, that might mean that f 2 is actually sharper. Some lenses are made to be used wide open and will exhibit their best sharpness at that point. Closing any lens down as far as possible will not deliver best quality.
Not exactly. This all depends on what the sensor format is. For MFT, most will suggest anywhere between F2.8 - F4 will be the sharpest, since this isn't extremely fast yet is likely at the early stages of diffraction.
Diffraction occurs at any aperture. It just gets worse as you stop down. So there is really no "early stage of diffraction", just less or more of it. The peak will simply occur at the point where the aberration reduction due to stopping down further will be less than the increase in diffraction.

And while you are right that MFT lenses with a max aperture of f/2.8 or better tend to peak at f/2.8 to f/4 (at least in the center), slower lenses tend to peak later than that. I'd say about f/5.6 when the max aperture is about f/4 and about f/8 when the max aperture is about f/5.6.
Faster lenses have more glass, so a F1.4 will have more of a FF like profile to the elements, ie more flaws as you move outward from the center.

Faster glass is bigger glass, which is harder to make as clean as smaller glass. This is why the center is better than the edges, usually.

This all means that the smaller the aperture the cleaner the glass for any particular lens, but there is a sweet spot between the weak wide open and weak diffracted. This is where i got the F2.8 - F4. Since diffraction affects FF less for example (or it affects FF at later apertures), the sweet spot will likely be at smaller apertures, something like F5.6 - F8. The rule of thumb is, the sharpest stop on the lens is the smallest aperture before diffraction begins to override the benefit of stopping down.
While you are right that MFT lenses tend to peak at a wider f-stop than FF lenses, this is not a direct effect of diffraction. To realize this, consider an FF lens that peaks at f/5.6 in the center. If we put that lens on an MFT camera, it will peak in the center at exactly the same aperture. If we consider the edges rather than the center, the f-stop at which the peak occurs may vary a bit depending on the size of the sensor with which the lens is used. This is so since the f-stop at which the peak occurs varies with the distance from the center of the image circle (typically occuring at narrower apertures as we increase the distance from the center) and since the edges will of course be further away from the center of the image circle with the lens on an FF sensor than on an MFT sensor. However, if we compare the same point within the image circle (say extreme corner on MFT versus a point half way between center and extreme corner on FF), the peak will again be exactly the same.
 
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