# Would Adaptive Optics be Useful in Radio Astronomy?

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?

Sources: 1, 2

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.