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Three dimensionality or 'contour definition', the CZ term, are both much more accurate descriptions of the phenomena than the ambiguous and misleading term 'plasticity', which is a term perhaps best used to describe the skin of female models shot with 'pro zooms' used by 'pros', that is: a 'plastic look'. It is to be hoped it does not catch on, therefore. '3D' has a neat ring to it as well.
3D is best judged in images that, to a large extent, lack the post-processing tricks, happy or designed circumstances of light and most of all, thin DOF. These are all manipulations of photographer and nature that conspire to fool the viewer's visual system.
For example, in viewing an image, our eyes move: from light to dark, from sharp to less sharp, from in focus to out of focus, from colourful to less colourful, from a main subject to subjects of peripheral interest, from clear to less clear, from looming foregrounds to de-emphasised backgrounds.
All these manipulations are easily observable in the linked image provided by AhamB...
...in which the eye is led to ascertain the image within tight constraints - it cannot wander around looking for secondary objects of interest because there are none. [For many photographers and viewers alike, the art is all about keeping the message simple...not a particularly noble goal, arguably.]
Thin DOF, focus fade, and objects that imply three dimensionality (such as Rustybug's bell on the last page) beg the question: what if the photographer had used aperture f16 - would this image then have any '3D'? Generally the answer is no.
Lenses that exhibit high levels of 3D can do so in less than optimal light conditions and in the absence of overtly obvious visual cues. What it really depends upon is the accuracy of the shaping of objects in image space, both longitudinally (away from the camera) and tangentially (perpendicular to the axis, or 'across the frame' in image space). You can observe it even in quasi-planar subject matter - an example is Anden's fine image of 'Fall colours' in this thread:
To get the best in 3D one needs clarity and excellent resolution, not necessarily of the highest order (Leica output is not noted for high 3D performance) but a certain level of contrast is needed, and it should be consistent in both directions - away from the camera and across the frame.
Since we are talking about human perceptions here, quite far removed from the more verifiable technical issues that seem to obsess us to a great degree, the kind of feelings to look for include: 'Do I feel like I can perceive depth in the image, the feeling I simply can walk into the scene?' (for non-close up compositions), 'Do I feel I can reach out and feel the shape of that object, having observed it depicted so accurately in (seemingly) three dimensional space? (for close ups), and 'Would I feel that way if the image lacked the assistance of the factors listed in para 2 above - the sometimes hidden persuaders?'
Of recent images in this thread, the two by adamdewilde on May 28 exemplify the points made above. Lighting is unhelpful, as it is backlighting in a longitudinal direction, there is no central object that forces eye compliance, light is quite even on all table top objects, sharpness is there for the two nearest objects and is close for the other objects - even the window is drawn quite well, strong colour is present in all objects, as is contrast, and all objects are clear and well lit - crucially there are no deliberate or fortuitous manipulations that attempt to force 3D on the eyes.
Perceptually, however, one feels like s/he could just 'reach out and place an open palm around the vase'...
Now to the lenses adamdewilde used. Zeiss have, as a design goal, the depiction of objects in image space with high levels of countour definition. The MTF charts for these two lenses are shown here:
Zeiss maintain that faithful contour definition is indicated by MTF lines (all six of them) that are close to horizontal across the image space represented by the MTF chart's horizontal axis. You may wish to take a look at the f5.6 charts for each lens. Much, much more here:
Click the Binocular icon at the top left of the PDF and enter: 'contour definition' for references.