Why do telephotos produce a sharper image when used for extreme close ups?

There are review sites to help with this. www.photozone.de has reviews on the technicals of lenses showing MFT graphs, vignetting, and chromatic abberation graphs (it explains on the site what they mean and how they work). Some things to take note of. The Nikon 18-135mm f3.5-5.6 is Sharper (as in resolution power) at it's best than the Micro Nikon 105mm f2.8 even though the latter costs more. It is like everything else in life. Cost and manufacturer claims mean little.
 
The general rule is that lenses are sharpest a couple stops down from their maximum aperture. This is true for almost every lens. I would also argue (and I think few who know their stuff will disagree) that prime lenses are categorically sharper than telephoto lenses.

There is one notable exception to the "faster does not mean sharper" rule, and that's the Noctilux f1.0, which was engineered to be sharpest when shot wide open. Anyone who's seen photos taken with that lens will agree that it's one of the sharpest, if not the sharpest in existence.
 
There are review sites to help with this. www.photozone.de has reviews on the technicals of lenses showing MFT graphs, vignetting, and chromatic abberation graphs (it explains on the site what they mean and how they work). Some things to take note of. The Nikon 18-135mm f3.5-5.6 is Sharper (as in resolution power) at it's best than the Micro Nikon 105mm f2.8 even though the latter costs more. It is like everything else in life. Cost and manufacturer claims mean little.

That's because the 105 is a macro lens. Macro lenses are optimized for close focus and usually don't perform as well as non-macro lenses at infinity focus. The 105 will be sharpest where the zoom can't even go. I would be willing to bet the 105 costs quite a bit more to manufacture than the cheap zoom.
 
The general rule is that lenses are sharpest a couple stops down from their maximum aperture. This is true for almost every lens. I would also argue (and I think few who know their stuff will disagree) that prime lenses are categorically sharper than telephoto lenses.

There is one notable exception to the "faster does not mean sharper" rule, and that's the Noctilux f1.0, which was engineered to be sharpest when shot wide open. Anyone who's seen photos taken with that lens will agree that it's one of the sharpest, if not the sharpest in existence.
You mean zoom lenses - there are prime telephoto lenses.

The Noctilux is anything BUT sharp, at any aperture. I own one, and believe me, "painterly" is how most people describe the resulting images...
 
Perhaps a better illustration would be the fast, long telephotos. Many of them are optimized for shooting wide open. As an example, I used to own a 500mm F4 Nikkor ED and a 300 f2.8 ED. There really was no reason to set the aperture any smaller than wide open on either one of them.

But these are long telephotos without overly curved front elements. I would think the Noctilux, as a normal lens with more curvature, would have to do a little better around the edges a stop or two down from wide open. That certainly is true of the Nikkor 50mm f1.2.
 
That's because the 105 is a macro lens.

I was using this to prove a point. It is not just because it's a macro lens. Look at the measurements on the 18-135mm f3.5-5.6 and you will see at it's best it outperforms other prime lenses costing more too. But what do you get for your money, cheaper construction, consumer goods, it doesn't feel as nice or focus as quickly. The end result you should be looking at is value, do you NEED the extra features?
 
I don't know what features I need. I do know that I would need a faster aperture than f5.6 at the long end of the range. That's for sure. You're still comparing apples and oranges.
 

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