I understand it is common to combine an array of radio telescopes in to a single instrument using interferometry. This has the photon collecting area of the combined radio telescopes but an aperture (and hence resolving power) dependent on the baseline of the devices. There is a nice explanation at the end of this article.
A recent well known application of radio telescope digital interferometry is Event Horizon Telescope's black hole imaging. It demonstrates the additional resolving power of the technique.
For radio telescopes, this interferometry is commonly (now) performed in software, and preceding this, was computed with analgoue signal processing. Individual radio telescopes capture "images" and the signals are jointly processed to build a combined "image" with superior resolution and signal power.
As an example, the proposed square kilometre array has a total receiving surface area equivalent to a single square kilometre radio telescope, but is spread over Africa and Australia, giving it an enormous aperture.
Interferometry is used in optical telescopes too, such as at the Keck Observatory. However, this is achieved with excruciatingly exacting engineering to bring the optical feeds from the telescopes together and combine them.
I speculate that were it was possible to perform digital interferometry on optical telescope images, then this would be pretty neat. I'd like to know why this seems to not be possible.
An immediate problem is that the sensor in an optical telescope only captures the magnitude of the signal and does not capture its phase. In contrast, a radio telescope does capture both magnitude and phase, which allows digital interferometry (?).
However – I don't understand why it's not possible to capture the phase of light collected by a telescope by some means. For example, if the captured signal were split in to an image pair and mixed with a "local clock" from a laser source, this seems like it would give a quadrature pair. Phase could be measured provided the rate of phase change remains within the frame rate of the detector.
Perhaps this isn't relevant, but consider the total photon count and photon arrival rate in an astronomical image.
A million pixel sensor with 16 bits per pixel is able to capture about 64 billion discrete photons. A big number, but well within the storage capacity of modern commodity computers. If an image is exposed over a minute, then the (average) photon arrival rate would amount to a billion events a second – also processable by modern machines.
Presumably this data estimate is wildly off the mark though, because the source data from the Event Horizon Telescope amounted to 5 petabytes (or half a ton of hard drives in old money). Perhaps sheer data volumes are the reason this approach doesn't work?
Basically, if it were possible, it would transform large telescope construction from a hard and very expensive engineering problem, that only a few people want to solve; in to a demanding computing problem, able to take advantage of the enormous growth in processing power afforded by modern society throwing trillions of dollars in to improving processors.
That would be pretty cool.