# What is the typical resolving power of the largest optical telescopes?

I'd like to estimate the typical resolving power of the largest optical telescopes.

I've calculated the theoretical resolving power of the VLA for 21 cm light, $$R=\frac{\lambda}{B}=\frac{2.1 \times 10^{-1} m}{2.7 \times 10^4 m}=1.6 ''$$

And I know that the largest optical telescopes on Earth are GTC, Keck 1 & 2, SALT, VLT, etc.

But I don't know how to calculate a typical resolving power in practice. How can I make this estimate taking into account astronomical seeing and other effects?

## 1 Answer

The angular resolving power of a telescope is approximately $1.22 \lambda/D \times 648000/\pi$, where this is the Airy disc diameter in arcseconds, $\lambda$ is the working wavelength in metres and $D$ the diameter of the telescope primary mirror in metres. For an 8-m telescope working at 500 nm, this gives an angular resolution of 0.05 arcseconds.

There is then a separate question about whether this theoretical limit is ever achieved because of detector limitations or degradation by blurring due to atmospheric turbulence (seeing).

In practice, at visible wavelengths, seeing always trumps the intrinsic angular resolution and has a typical value of 0.5-1 arcsecond at the world's best astronomical sites. There is no set number for this. It varies with atmospheric conditions from night-to-night or even hour-to-hour. Most observatories publish statistics on this so that you can see what the mean (or median) seeing is. For instance here are some statistics for the Paranal (VLT) site, where the median is about 0.8 arcsec.

Special techniques can mitigate the seeing degradation. You may have heard of adaptive optics - you can analyse the incoming wavefront and send a correcting signal to a tip-tilt or fully deformable mirror that removes the distortion, based either on an adjacent star or a laser guide star. However, these techniques are most effective in the near infrared and are not usually attempted at visible wavelengths. See http://en.wikipedia.org/wiki/Adaptive_optics

Another method is Lucky Imaging - which can be used by amateur astronomers too. Take many pictures with short exposures. If there is a bright point source in the image somewhere, you can use this to select the best images and to shift and stack the images to produce a cleaner final product. The shorter the exposures the better this works. Very close-to the theoretical maximum resolution can be obtained in this way - but it needs a special high speed, low noise CCD and you end up throwing away more than 90% of the images.