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This article makes the claim that the Giant Magellan Telescope (GMT, number 4 in the list) will have resolution 10 times better than that of Hubble, while the Thirty Meter Telescope (TMT, number 3 in the list) will have resolution 12 times better than that of Hubble. These are claims I find impossible to believe.

A simple application of, for instance, the Raleigh Criterion ($\theta = 1.22~\lambda/D$), where $\theta$ is the angular resolution of the telescope, $\lambda$ is the wavelength of the light in question, and $D$ is the diameter of the telescope, would show that a comparison between angular resolutions is as simple as comparing the diameters of the telescope apertures. Hubble's mirror is 2.4 m; comparing with the 24.5 m GMT and the 30 m TMT we see that the GMT will have 10.2 times the angular resolution of Hubble, while the TMT will have 12.5 times the angular resolution of Hubble. I think a calculation similar to the one I have described is how the article linked above came up with the numbers they did about the angular resolution of these telescopes compared to Hubble.

However, the Raleigh criterion only applies to telescopes working at their diffraction limit. Space telescopes (if they're designed well and built correctly) can work close to the diffraction limit (maybe even at the diffraction limit). Ground-based telescopes, however, are limited in angular resolution by the atmosphere, which at best will limit resolution to about an arc-second at the best sites on Earth. Thus the GMT and TMT by themselves will not have better image resolution than Hubble.

My question, then, is whether this article is correct (possibly because of one of the reasons I list below) or whether it seems this article naively applied the Raleigh Criterion for angular resolution with no thought about how the atmosphere will affect the resolving capabilities of these large ground-based telescopes.

Possible reasons the article may still be correct:

  • Adaptive optics, a developing technology which can allow telescopes to correct for distortions to the image produced by the atmosphere. Perhaps GMT and TMT will have very fancy adaptive optics systems.
  • Another technique, such as speckle imaging or lucky imaging.
  • Article could be referring to spectral resolution, rather than angular resolution (or image resolution). However, obtaining good spectral resolution is as much the job of the spectral instrument as it is of the telescope so I don't consider "spectral resolution" to be an inherent property of a telescope.
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    $\begingroup$ Yes, it is because diffraction limited imaging using adaptive optics is becoming possible. This is currently very difficult in the visible, so possibly like is not being compared with like. $\endgroup$
    – ProfRob
    May 10, 2015 at 20:10
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    $\begingroup$ Lucky imaging is of course always possible, but I think doesn't work so well for a very large aperture. $\endgroup$
    – ProfRob
    May 10, 2015 at 20:11

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Adaptive optics, as it says on the GMT website:

One of the most sophisticated engineering aspects of the telescope is what is known as “adaptive optics.” The telescope’s secondary mirrors are actually flexible. Under each secondary mirror surface, there are hundreds of actuators that will constantly adjust the mirrors to counteract atmospheric turbulence. These actuators, controlled by advanced computers, will transform twinkling stars into clear steady points of light. It is in this way that the GMT will offer images that are 10 times sharper than the Hubble Space Telescope.

and on the TMT web site:

In addition to providing nine times the collecting area of the current largest optical/infrared telescopes (the 10-meter Keck Telescopes), TMT will be used with adaptive optics systems to allow diffraction-limited performance, i.e., the best that the optics of the system can theoretically provide. This will provide unparalleled high-sensitivity spatial resolution more than 12 times sharper than what is achieved by the Hubble Space Telescope. For many applications, diffraction-limited observations give gains in sensitivity that scale like the diameter of the mirror to the fourth power, so this increase in size has major implications.

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  • $\begingroup$ And are they comparing like with like - ie the performance at UV/optical wavelengths?? $\endgroup$
    – ProfRob
    May 11, 2015 at 11:29
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    $\begingroup$ At least one of the sites says from UV to IR IIRC, why not go look and see what they say yourself. $\endgroup$ May 11, 2015 at 12:33
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    $\begingroup$ Obviously, a ground based telescope can not see where the atmosphere is nearly opaque. So it can not see invisible to the eye UV, that is below ~310 nm and in the near IR, it can only see in the atmospheric windows at J, H, and K. Hubble works down to 200 nm and has filters and a near IR spectrometer from 0.8 to 2.4 nm. $\endgroup$
    – eshaya
    Jul 4, 2015 at 17:19
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The latest adaptive optics systems now allows diffraction limited images from the 8 meter Very Large Telescope in the visible spectrum. So it seems reasonable that with continued improvements this will be feasible with larger telescopes in the future, including the 24-39 meter huge telescopes currently planned:

https://www.eso.org/public/usa/news/eso1824/

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  • $\begingroup$ The link is dead. $\endgroup$
    – ProfRob
    Feb 12, 2023 at 12:33
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The claims that you have seen refer to the possibility of attaining near diffraction-limited images using adaptive optics.

Both telescopes will feature wavefront sensors that can apply corrections to the telescope optics using either natural guide stars or laser guide stars and aim to provide diffraction-limited imaging.

However, the comparison is not quite what it seems. The AO systems on both telescopes will operate in the near infrared only (see Bouchez et al. 2014 and here ). The HST of course operates over a broader wavelength range, from the UV to the near infrared. So, in the near infrared then indeed these new telescopes will provide images with a sharpness that should greatly exceed the NIR images from HST or JWST. However, it appears that at visible wavelengths that will not be the case, although systems are now starting to be developed that will work in the red part of the optical spectrum. So possibly the comparison will be more apt in a few years time. See for example Why aren't ground-based observatories using adaptive optics for visible wavelengths? and How did VLT's adaptive optics obtain this resolution for Neptune? Is it really working in visible wavelengths?

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  • $\begingroup$ Are there any indications that current or developing AO systems will actually allow these telescopes to work near the diffraction limit? $\endgroup$ May 11, 2015 at 22:49
  • $\begingroup$ @Joshua the technology works well on 8m telescopes. I have no reason to doubt the claims that it will on larger telescopes. $\endgroup$
    – ProfRob
    May 11, 2015 at 22:53
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Yes , the 6.5m Magellan telescopes for one had limited abilities to, under the favorable conditions with the better instruments attached, exceed HST’s image resolution of ~0.05” (instrument-dependent).

If I spent enough time, I could find instances of telescope X and Y and so forth exceeding Hubble resolution. Given apertures of so-and-so meters, a telescope will exceed 0.05” under such-and-such observations these days. We’ve learned a thing or two, including speckle work (which Labeyrie published in 1970) and intensity interferometry, which an Australian group did in the Sixties . The difference is that HST reaches 0.05” consistently, without stipulations or scheduling limits (except those specific to HST of course, which any observatory would have in some form). And there’s the issue of background noise, which is apples-to-oranges with angular resolution.

Not only will a ~30m telescope exceed HST image resolution in certain modes, but the NPOI interferometer was handily beating HST- in the same wavelengths- by, oh, 2002 or so. And NPOI uses ~30cm sub-apertures, four to five of them.

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