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What I'm looking for is a graphic that shows in a general way the best available telescope resolution vs wavelength throughout the entire wavelength spectrum. So for example, there might be two very high resolution peaks aroud

  1. millimeter wavelengths (ALMA)
  2. visible wavelengths (HST and many ground telescopes with Adaptive Optics)

The beautiful image below from this great answer got me thinking. I have reposted it from there.

enter image description here
Image courtesy of Wikipedia user Hunster under the Creative Commons Attribution-Share Alike 3.0 Unported license.

The infrared, ultraviolet, and x-ray images come from the Spitzer Space Telescope, the SWIFT observatory, and the Chandra observatory, respectively.

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After a bit of searching, I found this blog page, which has several charts about various observatories, including this one:

enter image description here
Image courtesy of Olaf Frohn under the Creative Commons Attribution-Share Alike 4.0 License.

The majority are space-based, although the radio telescopes are largely land-based. They cover existing and future telescopes, at energies from the gamma-ray spectrum to radio waves. You are correct, too, in assuming that adaptive optics can cause dramatic increases in angular resolution; CHARA and the European Extremely Large Telescope both use adaptive optics, and actually can have better angular resolutions than some space-based telescopes.

I annotated the graph to cover in green the smallest angular resolution at various wavelengths:

enter image description here

Notice that most of the lines in the radio, microwave, and infrared part of the spectrum are diagonal, with roughly the same slope. This is because they are limited by diffraction. In the case of radio waves, this is because the atmosphere has little impact. In the case of infrared- and visible- wavelength telescopes in space - and in space-based telescopes in general, the main thing that stops them is the diffraction limit.

The diffraction limit is $$d=\frac{\lambda}{2n\sin\theta}$$ where $\lambda$ is wavelength and $n\sin\theta$ is the numerical aperture. On a log-log plot, such as the one above, we have $$\log d=\log\lambda-\log(2n\sin\theta)$$ and $$\frac{\mathrm{d}\log d}{\mathrm{d}\log\lambda}=1$$ for all telescopes limited by the equation. Thus, telescopes restricted by this limit should be described by a diagonal line with a slope of 1 (-1 on this graph).

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  • $\begingroup$ This is an amazing graphic! I don't recognize most of them, but thanks to the internet this can be a great springboard to learn a lot. I'm guessing the X-ray resolution is limited by geometrical optics so it's not wavelength dependent, and the highest energy gamma ray resolution is limited by counting statistics of secondary photons or photoelectrons so it's roughly $\propto 1/\sqrt{E}$? $\endgroup$ – uhoh Oct 31 '16 at 2:20

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