What happens when holograms get "too big"?

Question

Since a hologram is a 3D object represented on a 2D surface...

3D objects scale like $L^3$ whereas 2D objects scales as $L^2$. Thus the information density scales as $L^3/L^2=L$.

This would mean (according to this logic) that the bigger the hologram the more information has to fit into the same space on the 2D film.

According to this naïve way of looking at things, it would seem to suggest that the bigger the hologram, the resolution would deteriorate.

However, according to a different hypothesis, since the hologram is projected to your eyes back into a 2D image, then there is no more information than a 2D image and holograms can be as big as you like without degredation.

Which argument is correct?

Answer 1

The quick answer is that holograms do not contain information about the interior of the object, only the surface appearance. And that scales as $L^2$.

What is going on in a hologram is that it generates a light field similar to what the object would have generated if it had been present. This can of course include internal structure if the object is translucent, but you still do not get more information than was in the light field at the point of intersection with the photographic plate (which is 2D). If you have a vast and complex object you need a sufficiently big plate to make a sharp hologram: if it is too small, then you miss a lot of the light field and detail is lost in the hologram.