It isn't projecting a 3D surface (I'm not sure that even makes sense in this context) and it isn't storing volumetric information.
It is just using refraction to make brighter and darker areas in its shadow/caustics to make an image. The paper is 10 years old at this point and linked by this article.
I think once you read the papers you will realize that the only thing 3D is the surface of the lens and that is only so it can get curves and angles for the refraction.
