Theoretically, what is the biggest optical telescope that may exist? Recently, I read yet another news about E-ELT. It will have 39.3-metre-diameter segmented primary mirror. And I was interested in the next question:
Theoretically, what size of the primary mirror (single/multiple/segmented) can have a telescope on Earth for observing at optical wavelengths? And why? I mean what are physical limitations exists?

And the same question about space (not on Earth)?

Update:

On the advice of @TildalWave, to make this question answerable let's make a few adjustments:


Primary mirror should be segmented (or it variations) like on E-ELT.
Suppose we have a large (several square kilometers), flat surface high above sea level.
We have to build telescope for observing at optical wavelengths.


I know that, there is concept of OWL with 100 metre-diameter segmented primary mirror.

But what about 500 metre-diameter or 1000? Is it possible in theory?
It's complicated.

Until late-20th century, we've tried to make bigger and bigger monolithic telescopes. That worked pretty well up to the 5 meter parabolic mirror on Mount Palomar in California in the 1940s. It kind of worked, but just barely, for the 6 meter mirror on Caucasus in Russia in the 1970s. It did work, but that was a major achievement, for the twin 8.4 meter mirrors for the LBT in Arizona in the 2000s.

We've learned eventually that the way to go is not by pouring larger and larger slabs of low-expansion glass. It is generally accepted that somewhere just below 10 meters diameter is about as large as possible for monolithic mirrors.

The way to go is by choosing to make smaller mirror segments (1 meter to a few meters in diameter each) and combining those into a tiled mirror. It's somewhat harder to carve the asymmetrical parabolic (or hyperbolic, or elliptic, or spherical) reflecting curved surface in a segment like that, but it's far easier to manage thermal and cooling issues when you have to deal with smaller solid objects.

Each segment is mounted in an active mirror cell, with piezo actuators that very precisely control its position. All segments must combine into a single smooth surface with a precision better than 100 microns (much better than that in reality). So now you have a large array of massive objects, dynamically controlled via computer, each with its own vibration modes, each with its own source of mechanical noise, each with its own thermal expansion motions, all of them "dancing" up and down a few microns on piezo elements.

Is it possible to orchestrate a very large system like that? Yes. The 100 meter OWL was considered feasible technically. From the perspective of keeping the mirrors aligned, an even larger structure should be doable; the computer-controlled actuators should overcome most vibrations and shifts up to quite large distances.

Like you said, the real limits are financial. The complexity of such a system increases with the square of the diameter, and with complexity comes cost.



The entire discussion above was about "filled aperture" telescopes: given a round shape of a certain diameter, it is filled with mirror segments. For a given aperture, this design captures the largest amount of light.

But the aperture does not have to be filled. It can be mostly empty. You could have a few reflecting segments on the periphery, and the center would be mostly void. You'd have the same resolving power (you would see the same small details), it's just that the brightness of the image would decrease, because you're capturing less light total.

This is the principle of the interferometer. The twin 10 meter segmented Keck mirrors in Hawaii can work as an interferometer with a baseline of 85 meters. This is effectively equivalent to a single 85 meter aperture in terms of resolving power, but obviously not in terms of image brightness (amount of light captured).

The US Navy has an interferometer in Arizona with mirrors placed on 3 arms in a Y shape, each arm 250 meters long. That gives the instrument a baseline (equivalent aperture) of several hundreds of meters.

U of Sydney has a 640 meter baseline interferometer in the Australian desert.

Interferometers cannot be used to study very faint objects, because they can't capture enough light. But they can produce very high resolution data from bright objects - e.g. they are used to measure the diameter of stars, such as Betelgeuse.

The baseline of an interferometer can be made extremely large. For terrestrial instruments, a kilometers-wide baseline is very doable now. Larger will be doable in the future.

There are talks about building interferometers in outer space, in orbit around Earth or even bigger. That would provide a baseline at least in the thousands of kilometers. That's not doable now, but seems feasible in the future.