Every single picture, any part that has a sharp contrast between light subject and dark background (and vice versa). This, for example:
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Or this:
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Which is at least a millennium old technique of "3D pop" image enhancement, but has nothing to do with lenses.
Thanks for your examples; I had a closer look and saw it, too on the swan. By the way, the yellow machine is downsized by almost nine times... that hardly retains the sharpening halos. By the way, do you know how human visual perception works? Our brains do exactly the same - they lay a mask over bright objects in a contrasting scene (and not only luminosity, but color, too) and if you slightly move your eyeball then you will see it. Since the dynamic range of a daytime scene is much greater than whatever the monitor can shine on you, the effect will also be stronger.
Below I provide these images with the sharpening completely turned off in Capture One. Now guess what - no difference to the 3D pop of the image, really. Att 100% it may even look better now unsharpened. The 3D pop dwells in something else - most likely a good degree of preservation of the tonal gradation across the image, not just sharp transitions around contrasty edges.
This is the swan picture with all sharpening turned off (it is now att 100% crop):
A 100% crop from the yellow machine with all sharpening completely turned off - the fine tonal gradations and the 3D pop are still there, especially if you back out of the screen a little:
Now the whole image downsized to 1024 pixels on the long edge by Photoshop's bicubic method optimized for smooth gradations - still "pops" nicely out, at least as far as I can see. Still with all sharpening completely turned off:
I think this rules out that it's sharpening in post that adds the 3D pop. Whatever the pop dwells in; it contributes to the object being recognized by my brain as floating in a pleasant 3D space rather than a flat sterile and boring surface (slightly exaggerated words here).
Do you see the subtle shifts of tonality across the swan or the yellow machine as their different surfaces curve? This is more what I concentrated on rather than pixelpeeping for sharpness, sharpening and halos (all that is about high-frequency intertonal detail; I'm studying the low-frequency one here). That is undoubtedly what promotes my perception of that 2D image as a 3D scene.
Don't forget what the ultimate goal of photography as an art is: Mediate the strongest way of seeing a scene.
If this 3D pop rendering character of a lens (and even if it was 100% postprocessing which it is not, actually to about zero degree) helps me mediate a stronger way of seeing a scene than otherwise, then it is a heck of an asset to my photography. And in such case I can't care less what some dogmatically limited a-priori judging mind might say about it. It simply works and it works beautifully. Above is some evidence for it.
EDIT:
No, it's physically impossible.
It might be for the sharpening halos...
On the other hand, the lens gets in the light through a pretty wide front element - light that at different positions as entering the lens througout the time of the light travel and capture has different spectrum of intensity, wavelength, polarization... you name it. The information input to the lens is far far richer than whatever the sensor can capture, irrespectively of resolution. Why do you think that it is physically imposible to make a lens that would convert part of that information into a part of the information that is captured by the sensor, so as to help our brains reconstruct the captured 2D image into a 3D scene in our perception?
Maybe this is what every lens is supposed to do, but the more optical imperfections of e.g., lesser quality glass; and imperfections introduced by optical corrections from a lens, the more this reproduction suffers - in the same direction as Yannick etc. claim. I say maybe, as I don't have any proof of that nor any clear evidence for that statement.
I actually intend to follow up on these examples with a comparison of the same scene captured by two or three different lenses. Let's see what that yields.