All conventional photographs are 2D representations of 3D scenes. Our brain creates the illusion of depth based on cues from the image. This process is easily manipulated, see forced perspective or a famous example the Ames room.

Some images contain a particular blend of contrast, vivid colours, lighting direction, DOF and sharpness at the plane of focus that enhance the sensation of depth generated by the brain, hence such images are described as looking "3D", or are said to "pop" (the foreground objects seem to jump, or pop out of the screen).

One key element is microcontrast and suitable lighting such that textures rendered appear so crisp it's hard to believe you are looking at a flat image. It's a bit like the story of Zeuxis the painter who painted a plate of grapes that was so realistic bird flew down to try and peck at them.

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The terms are commonly associated with Zeiss lenses on particular photography forums (cough fredmiranda.com cough), often described as some sort of feature that is either on or off (e.g. "Which portrait lens with 3D effect?"). In reality all lenses do to a certain extent, it's just some Zeiss lenses produce particularly good microcontrast.

In the end the lens is only one factor it also has a lot to do with the skill of the photographer, post processing and sometimes just luck with the way the light falls.

It's also subjective, some people see the effect differently in different images, which is why it's hard to provide a fully scientific explanation. Here's an example I came across recently that constitutes a very 3D image for me:

image copyright Chris Ozer

be sure to check out the rest of his blog, he pretty much has the "3D look" nailed.

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How do you get the 3D look?

There's no one secret technique to it, buying a Distagon is not going to get you there by itself.

You need a contrasty lens. A very good zoom or decent consumer prime (50 f/1.4, 85 f/1.8) will do. Slight background blur helps but is not absolutely necessary, so be careful with your aperture setting.

Create or wait for a mixture of hard and soft light, such as sunshine through haze, direct sunlight during the magic hour or a large north facing window. But at the same time try to eliminate flare. Nothing kills contrast more than veiling flare (use a lens hood, block the light with your hand, whatever is necessary).

Increase contrast and saturation slightly in post, boost local contrast with a large diameter unsharp mask, use use the high pass sharpening technique. Resize to the exact output dimensions and sharpen again, save with the highest quality JPEG settings you can or use the PNG format.