After watching Dr. Marc Levoy’s talk on light fields and the Stanford camera array I thought I’d investigate for myself the uses for synthetic aperture photography. From the talk:
By changing the amount of shift, you can change the depth of objects that are in focus. And here’s what that looks like. So we’re focusing synthetically on the bushes, across the street through my grad students into the building and there’s a step stool in the building.
This is about the same as matching up the left/right channel on a stereo anaglyph, but with more perspectives as inputs. To get a feel for things I drilled out a camera mount to attach to the end of a macro bellows rail and took a series of horizontally displaced images, shifting and combining them in Octave to focus at different depths.
There are three main depths in this sequence: two bike wheels, with a snowshoe leaning against the wall behind them. The ‘a’ for ‘atlas’ on the snowshoes becomes pretty visible at the end of the sequence, even though it is occluded by the seat stay of the first bike at the beginning of the sequence. Here I was only using a horizontal shift in camera position, so the horizontal elements (e.g. chain stays) and the horizontal components of diagonal elements aren’t much affected as we change depth. Adding vertical shift (such as below) should change that, but of course it all depends on what you are imaging whether that matters or not. 
