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This Question and Answer got me thinking. If atmospheric seeing at visible wavelengths is the result of refractive index inhomogeneity, would it also be a similar problem for mm to cm wavelengths? From a quick search, the index of refraction of air at STP is about 1.0003 (visible) and 1.0002 (radio).

If it is not, is there a way to understand quantitatively why it is not a problem?

File:Atmos struct imaging.svg File:Atmospheric seeing r0 t0.svg

Images from Wikipedia

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In fact, the techniques of adaptive optics are already being used in radio astronomy. They are implicit in the basic imaging algorithms (e.g., CLEAN) used to produce maps from radio interferometers. In those cases, they are usually being used to correct for the artificial structure introduced by the way the interferometer samples the sky, rather than for structure imposed by the intervening material. But at low frequencies (1 GHz and below, certainly) they are also used to correct for the artificial structure imposed on the incoming radio wavefronts as they pass through the ionosphere. Current large low-frequency instruments (such as the LWA and LOFAR) rely heavily on these methods.

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    $\begingroup$ Thank you for your answer! Indeed - a search for "CLEAN radio astronomy" immediately brings up pdf's with lots of goodies - including discussion of atmospheric seeing. I'll ask a follow-up question in a day or so. $\endgroup$ – uhoh Mar 2 '16 at 17:23
  • $\begingroup$ In the case of the arrays you mention - the adaptive optics is applied in software - phase corrections for individual receivers. In visible light we're most familiar with fast mechanical phase corrections within the aperture of a single receiver, so it seems more "high tech" and catches the eye. Is there any room for within-dish correction, analogous to visible light telescopes? Especially for large reflectors at high frequency (which may or may not be currently operating)? $\endgroup$ – uhoh Mar 2 '16 at 17:37
  • $\begingroup$ Still working on my follow-up question about array data processing, but I've just asked a cluster of radio telescope related questions today - you can click my profile to get a list. (circa 15-6-2016). $\endgroup$ – uhoh Jun 15 '16 at 4:39
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The purpose of adaptive optics is to reach or approach the diffraction limit of the system, which is the maximum resolution achievable due to the wave nature of electromagnetic radiation. The formula for the diffraction limit (in radians) is approximately $\lambda / D$. For a 30-meter radio telescope observing the 21-centimeter line, this works out to 0.007 radians, or about 24 arcminutes. This is much larger than the sub-arcsecond diffraction limit of an optical telescope; no matter what you do with your telescope you can't do better than this, so seeing is simply not a factor for single-dish radio astronomy.

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    $\begingroup$ You need to explain why it is not an issue for interferometers. $\endgroup$ – Rob Jeffries Feb 29 '16 at 17:16
  • $\begingroup$ There are dishes bigger than 30m and arrays far far bigger than that. See for example Why does radio astronomy offer higher resolution images than optical?. $\endgroup$ – uhoh Mar 1 '16 at 1:50
  • $\begingroup$ ...and the question asks "...a similar problem for mm to cm wavelengths?", not 21 cm. $\endgroup$ – uhoh Mar 1 '16 at 5:24

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