Information in Holograms I was reading about Holograms, and I read something to the effect of the following statement -
"In a hologram, any part of the hologram with sufficient size contains the whole of the stored information"
What exactly is the mathematics behind this? Does it have to do with the frequency domain representation of the object? Also, if someone could point me to a good source for reading about the math behind this stuff, i'd appreciate it very much. Thank you.
 A: This doesn't really answer your question but it might be interesting. Here is an image from Gabor's 1949 "Microscopy by Reconstructed Wavefronts" (which I think was basically the first paper on holography):



Clearly there is some pretty strong spatial corellation between the image and the hologram. So while it might be true that each bit of the hologram has some information about the whole image, it seems likely that different pieces of the hologram would display different parts of the image with different resolution. Maybe modern methods are different?
Mainly posting this because the question reminded me of this cool picture. Someone who actually knows about holograms please correct me.
A: It is not necessarily correct to say that every piece of a hologram contains information about every part of the image.  A great example is a hologram of a scene in which a large object is in front of a smaller object, thereby obscuring the smaller object as seen from some angles.  Peeking through some parts of the hologram, you will see only the large object.  
It is correct, though, if the scene is two-dimensional and every part of the object can be seen from every part of the hologram plane.
