Synthetic aperture for visible light camera It seems to me a camera array for visible light could be constructed to synthesize a large effective aperture to achieve high angular resolution just as a synthetic aperture radar does. This could be used for example on a satellite with several small cameras mounted on extended poles. However, I was told the present engineering cannot accomplish this. Is this true and if so, why?
 A: The major difference is that the antennas in RF domain capture amplitude and phase of the incident EM wave but the photodetectors in optical domain are only square law detectors, i.e. they detect power and not phase of the EM wave.
However, the information on EM wave phase is crucial for synthetic aperture methods.
What you would need is holography.
So, in principle, yes, the SAR principle can also be applied to optical domain, but this is inherently more difficult than in RF domain. Measuring phase in optical domain not only requires higher mechanical stability (due to lower wavelength) but also a way more complex and expensive apparatus than a simple camera (as in  holography).
Edit: actually in microscopy there seems to be methods that precisely do this, i.e. use of holographic methods to emulate a higher numerical aperture to ultimately achieve higher resolution.
A: Short answer: Yes... and also no...
Longer answer as to why "yes" and how to turn it into a "no" below:
For wavelengths of visible light our sensors can only collect intensity (amplitude) but the phase information is lost. So just attching several cameras spread out is not an option with current technology.
But there is a way to keep the phase information: we just don't convert to electrical signals before we do the interference. There is a name for that: Interferometry .
We're doing it on earth already for example with ESAs VLT which consists of 4 telescopes with 8.2m mirrors and 4 movable 1.8m mirrors. They have a incredibly precise system of mirrors to combine the images from the 8 telescopes optically to form basically a single large telescope.

In the foreground you can see the tracks on which the auxilary telescopes can move. The auxilary telescopes are the small pods with the round heads in front to the big ones (Image credit ESO/Y.Beletsky )
If we're picky, every telescope with a segmented mirror (like JWST but also many earth bound large telescopes) is some kind of interferometer. But that's another discussion.
