By Joshua N. Winn, Princeton University
The diameter of the largest optical telescope in the world, over the centuries, ranges, starting from Galileo’s telescopes, from only 10 centimeters across, to today’s largest telescopes which use mirrors 10 meters across. Telescopes have been doubling in size every 40 years, or so. Why? How do we explain this constant drive to build bigger telescopes? Read on to find out.
Improving Angular Resolution
If we compare a series of images of a galaxy with the same field of view but changing the average number of photons that contribute to each pixel, the image with the lowest photon count would be grainy with only the bright center of the galaxy being visible. The fluctuations in the light level swamp everything else. But if we increase the number of photons the fainter spiral structure of the galaxy would definitely come into view, because the fractional level of the fluctuations is smaller.
This helps to explain our constant drive to build bigger telescopes. Another reason we love big telescopes is that it helps us to improve our angular resolution, our ability to measure the direction from which photons are coming, and make sharper images. For this, one has to keep in mind the diffraction limit: the tightest possible focus we can achieve, given that light is a wave.
A Blurring Effect
The smallest angle we can resolve is about 1.22 lambda over D, where lambda is the wavelength and D is the diameter of the primary mirror or the lens. Visible light has a wavelength of about half a micron, and our eyes have a D of about 5 millimeters. So, the diffraction limit works out to be 1.2 times 10 to the minus 4 radians, or about 25 arcseconds. Amazingly, real eyes come pretty close to this fundamental limit. Mother Nature is a good engineer.
But astronomers can do better by increasing D to 10 meters, an improvement by a factor of 2000. In that case the equation gives Delta-theta-min of only 0.013 arc seconds. There is a catch, though, one that hampers angular resolution. Fluctuations in the temperature and density of air produce a blurring effect of order 1 arcsecond, even on a high mountaintop. So, one can’t take full advantage of the large D to improve the angular resolution. At least, not easily. There are 2 ways around the problem. One is to put our telescope in space, above the air, like the famous Hubble Space Telescope. Or, one can stay on the ground, and use a technique called adaptive optics.
This article comes directly from content in the video series Introduction to Astrophysics. Watch it now, on Wondrium.
Adaptive Optics
Adaptive optics is when one puts a deformable mirror somewhere in the light path of their telescope. Lots of mechanical actuators are mounted on the backside of the mirror, which can apply tiny localized forces under computer control, pulling and pushing by just a fraction of a micron. The goal is to distort the mirror in the just the right way to reverse the distorting effects of the air. Even if one has a separate camera staring at an extremely bright star, which they know should appear as a sharp point in the image, it doesn’t, because of the turbulent air. It looks like a big blotch. The computer then has to measure the shape of that blotch and use an algorithm that tells it how to distort the mirror to turn the blotch back into a point. And all of this has to happen within a few milliseconds, because the atmosphere is constantly changing.
It might not surprise us to learn that some of the earliest adaptive-optics systems were developed by the military. They use it to resolve the details of enemy spy satellites. It became popular among astronomers starting in the 1990s.
Reducing the Poisson Noise
The adaptive-optics systems technology allows us to get close to the diffraction limit even with a 10-meter telescope. If one has ever seen the images that show the stars orbiting Sagittarius A*, the black hole at the center of the Milky Way, those were made with adaptive optics. Without that, all those stars would have blurred together into a big smudge.
Better angular resolution also gives us another way to reduce the Poisson noise. The reason it helps is that it improves our ability to separate the star’s light from the other light sources, it reduces N-sky, in our signal-to-noise equation. So, in situations where the sky noise is the main problem, improving the angular resolution leads to a higher signal-to-noise ratio.
Common Questions about Building Bigger Telescopes
The reason we love big telescopes is that it helps us to improve our angular resolution, our ability to measure the direction from which photons are coming, and make sharper images.
Fluctuations in the temperature and density of air produce a blurring effect of order 1 arcsecond, even on a high mountaintop.
The goal of adaptive optics is to distort the mirror in the just the right way to reverse the distorting effects of the air. Even if one has a separate camera staring at an extremely bright star, which they know should appear as a sharp point in the image, it doesn’t, because of the turbulent air.
