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No doubt a corrector could be designed for it but my feeling is that the complexity of the corrector may exceed the difficulty of making a conventional large mirror.
I suspect that the flexure of the thin mirror as it is pointed in different directions would almost certainly change the figure significantly as you point it to different parts of the sky.
A disk of liquid will spin up into a perfect parabola Mercury will work but once spun, can only point at the zenith. Telescope mirrors have been made this way out of optical plastics which eventually set hard and can then be aluminized.
Joe
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