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Telescopes that use adaptive optics now use flexible mirrors to adjust for distortions in the atmosphere. The mirrors are flexed in real time to account for the distortions. I am wondering if it would be feasible to instead use fixed mirrors and use software to make the needed corrections to the image?

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Short answer: no.

Why not? because the mirror is placed at a position in the optical train such that it controls the wavefront phase and tilt of each subsection, "subaperture" of the incoming beam. Once an optical system has formed an image, all phase information is lost. There are some software methods which can correct for simple aberrations such as astigmatism or coma, but those require a near-constant type of error across the input field. The problem with atmospheric turbulence is that the errors are essentially of a localized and random nature.

Note that even a plenoptic camera which, by tricky use of sublenses at the focal plane, record enough information to change focus, cannot correct for general phase aberrations.

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  • $\begingroup$ ...is on its way to being lost at least. Once you go ahead and record the image with film or a CCD, or otherwise intercept the image with something that converts the electric field irreparably to intensity, then it's completely lost. In some imaging applications (mostly outside of astronomy) people play with various tricks, like white-light interferometry, or the cool Lytro camera that didn't really sell but attracted a lot of venture capital so they could make this stuff. $\endgroup$
    – uhoh
    Apr 5, 2017 at 5:13
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    $\begingroup$ @uhoh, Lytro is a plenoptic camera :-) . And, yes, you're right - even some astronomy observation involves local interferometry tricks. You should see the spatial filters used, too: there's one which removes the bright center of stars (zero-order) so we can look at coronas, planets, etc. (at least in theory) $\endgroup$
    – Carl Witthoft
    Apr 5, 2017 at 12:02
  • $\begingroup$ Do you think this particular demonstration coronograph will work, or will the technology need more time to mature? This reminds me I have a follow-up question in the oven as well. $\endgroup$
    – uhoh
    Apr 5, 2017 at 13:04
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    $\begingroup$ The reverse of this answer also holds: You can do software adaptive optics if you can capture the phase of incoming light. And according to this answer that is regularly done for radio telescopes. Unfortunately phase information cannot be captured for infrared and shorter wavelengths (in practice at least. No idea if the latest experimental tech can do better). $\endgroup$
    – JanKanis
    Sep 1, 2017 at 21:01

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