Michael Clark
Does this image(s) represent the Sigma Art entire range rendering character qualities you are referring to?
Overall they render the portrait beautifully, but then you open the pictures and zoom in on them, you'll see the flatness of them if you just consider the face or body parts. The 3D separation is there more through the out-of-focus areas than the tonal transitions.
You'll see a lot of difference if you compare a shot taken using a Zeiss or even a Sony FE lens and a Sigma Art lens as Tony Northrup's example also shows:
The 3D-pop of the Sony is way better than the Sigma Art.
There are two articles on microcontrast (or the lens' ability to render 3D characteristics of a scene):
There are more examples on this out there.
Modern lenses often sacrifice this 3D-rendering to resolution (there are some tradeoffs to be made due to physics and what is technologically possible to make); some of them appear to strike a better balance to my taste (e.g., Zeiss) than others (e.g., Sigma). On the one hand, I wouldn't accept poor resolution to retain top microcontrast (e.g., old prime lenses with very low element count); on the other hand, I wouldn't accept poor microcontrast to agressively optimize for the best possible resolution either (e.g., Sigma Art). Good microcontrast creates the perception of a better resolution; and if you finally view a picture, you seldom view it at 100% magnification (unless you are looking at a bird picture that has been heavily cropped, perhaps, or something similar).
EDIT:
I must confess though that there is a bit of confusion around it; and even I feel slighly confused - there are two lines of using the term microcontrast or 3D-pop. The first is what Yannick Hong describes among other in the above mentioned articles. The second is what Lloyd Chambers describes here:
lenspire.zeiss.com
While Yannick bases the notion of it on the quality/fidelity of tonal gradations; Lloyd seems to mostly base it on resolution, the lens' ability to hold contrast at high frequency of changes, which is actually a lot different from Yannick's definition.
To sort this out in my mind, I think there are two distinct things that contribute to an image rendering a scene with a 3D-look:
(1) The quality of the tonal gradations as the low-frequency intertonal detail (low-frequency MTF) - this is probably the dominant factor;
(2) The high-frequency intertonal detail (high-frequency MTF) that helps separate the interfaces between different objects, or an object from its background.
It would be cool to hear something clear and definitive on this, as there seems to be a lot of confusion around it. (The 3D-pop effect in images and the differences between different lenses' rendering are pretty clear at the same time, though.)
EDIT 2 (follow-up):
I'd actually agree with Lloyd on that the term Microcontrast shall for the sake of intuitiveness refer to the high-frequency MTF;
What Yannick refers to, and what often has a more dramatic impact, especially one that is retained when down-sampling the picture, shall be called something like tonal fidelity or tonal rendition.
Both together make up the 3D-pop of an image. The more of each, the better; but when making a lens, the design optimizations for the one compete with the other to a degree.