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For background, let's go through a couple of abstractions. If you stand at a given location and look into some direction, a ray tells which color you see. Now, if you have all rays from some location (picture), you can create any image from that viewpoint by associating with each pixel the ray that goes through it. However, we cannot move the viewpoint.
If, on the other hand, we had the full light field function, that is, all the rays starting from any location, we could in theory create any image from any viewpoint.