For future space exploration, I'd like to see telescopes whose images can be digitally filtered in real time by very fast computers. You could do a lot of neat things with them. Yes, most of today's telescopes are already computer controlled. But this control is usually limited to pointing the scope and doing some optical and digital filtering.
What I'd like to see is a telescope for example, whose attached computer could analyze all points of light in an image, compute each object's Red Shift (which is related to its distance), and then let the observer "dial in" a distance range over which they want to observe. All objects closer or farther than this range would be digitally removed from view, while all objects within the selected range would remain. This could also reduce the optical interference from objects closer to the observer, and might be a useful tool for studying specific eras of the universe's past.
Other useful real-time capabilities might include:
* Filtering objects to display only those that emit certain wavelengths or move at specific speeds.
* Using the distance filter mentioned above to black out brighter nearby objects...and then boosting the signal gain, to help pull faint distant objects more clearly into view.
* An advanced version of Photoshop "upscaling," to digitally zoom in on objects. This would probably involve combining multiple shots of the same area (to counteract atmospheric distortion) and applying an upscaling/contrast-enhancement algorithm that's optimized for astronomical images.
A cool project for this telescope would be to capture changes at the universe's "visible horizon." This is the farthest point that we can theoretically see, because light from objects beyond it can't have reached us yet. And new objects probably come into view across this horizon every decade or century. By setting the telescope to display only the objects just inside this horizon...and then doing the same thing a year, decade, or century from now...the two images might make it easier to spot the objects that have most recently crossed into our view across the edge of the visible universe.
This visible horizon is currently just under 13.5 billion light years away...while the estimated size of the universe itself (due to its expansion over the last 13.5 billion years) has been pegged at not less than 46.5 billion light years. So there's actually a lot of stuff out there beyond our view...and this telescope might make it possible to catch it entering our cosmic view.
And yes, this kind of telescopic research would require extremely fast computers doing millions of high-precision computations in real time. But it's a nice thing to dream about for the future!