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Idea: Mount aluminized mylar or equivalent sheets like the skin of a drum. Then evacuate the inside of the drum slightly. The skin will form a catenoid, so close to parabaloid as to not make much difference. Focusable, light, easily replaceable, cheap, no grinding/polishing. Air pressure against the
surface would dampen vibrations. Good for large radio telescopes,solar collectors and satellite dishs. For optical telescopes, I propose a slightly different approach, fill the "drum" with resin with hollow glass spheres (to reduce weight), then pump some of the mixture out to have the skin take its shape. When it sets, you have a light, cheap mirror as large as you need.
Halfbakery: Blow-Up Solar Collectors
Alternatively, have the mirror on the inside of a half-transparent balloon. [jutta, Oct 04 2004]
As a diy project, not a commercial product or a serious scientific thing [notexactly, Apr 22 2018]
||Don't think you can get the neccasary accuracy. Typically optical mirrors have an RMS accuracy of 1/8th of a wavelength that's an average deviation from a perfect shape of about 50nm that's not much when you think an atom is between 0.1 and 0.5nm