Why use glass at all, if we can blow up a perfectly spherical balloon? Just put a thin metallic coating on the balloon itself and use that as the mirror. You’d be looking through the film on the other side, but if the film is thin and uniform enough, it shouldn’t matter. Also, if it’s a flexible balloon, we can probably come up with a way to actively maintain its shape. Perhaps a wire mesh behind the mirror generating an electrostatic field.
Spherical mirrors are already used on some telescope designs such as Maksutov and Schmidt-Cassegrain.
Also methods for active correction of the optics against sagging or other perturbing physical forces is well known:
Note this must be maintained within about 1/8th wave, or about 60 nanometers for green light. Optics are incredibly unforgiving, and just getting it “pretty close” severely damages the image, as was seen in the initial Hubble Space Telescope.
The problem is to resolve an extra-solar planet, an effective mirror diameter of 43 miles (69.2 km) is required. We do not have the ability to maintain a surface 62 km in diameter (3066 square km) within 1/8th of a light wave.
It is conceivable that eventually a free-flying optical interferometer composed of several smaller telescopes could be synchronized in formation with sufficient accuracy to act as a single large mirror for resolution purposes.
Both of which use full-aperture corrective lenses. But yes, there are telescope designs that use a spherical mirror and smaller corrective optics.
Not necessarily. A large, imperfect mirror combined with corrective optics can come close to diffraction limited performance, if only for a small field of view. The mirror needs to be pretty close to perfect, but it doesn’t need to be diffraction-limited on its own. Same way adaptive optics can compensate for atmospheric distortion.
Yes, but don’t you think a 100-kilometer monolithic telescope would be awesome?