Chapter 6. Resolution of Telescopes

6.1 Introduction

Angular Resolution

The goals of this module: After completing this exercise, you should be able to:

1. Define angular resolution and diffraction.
2. Explain the limitations of a telescope in terms of its angular resolution.
3. Explain the limitations of a telescope in terms of atmospheric turbulence.
4. Describe how adaptive optics can reduce the effect of atmospheric turbulence.

In this module you will explore:

1. The relationship between angular resolution, wavelength and the size of a telescope.
2. How the Earth's atmosphere can distort observational images.
3. How astronomers can create a fake star to probe and correct for atmospheric turbulence.

Why you are doing it: We can observe only so much with just our eyes. We are limited by how much light they can gather and how quickly our brain processes the data. Astronomers have developed a number of tools that allow us to gather and store more data, and therefore detect fainter objects and determine various properties associated with them.

6.2 Background

The telescope was originally invented by Dutch opticians back during the early 1600's. When Galileo Galilei heard of this invention, he made one for himself and revolutionized our understanding of the world around us based on his observations. Galileo was able to observe mountains on the Moon and sunspots on the Sun. He observed that Saturn had "ears" (which were later determined to be rings), and was the first to see that the Milky Way was composed of "a mass of innumerable stars". Two of his greatest observations, though, were of the moons of Jupiter and the phases of Venus. The fact that Galileo was able to detect moons orbiting around another planet suggested that Earth was not the only planet around which objects could orbit. The fact that Galileo was able to observe Venus undergo a full cycle of phases confirmed that the Sun had to be at the center of our Solar System, with the planets orbiting around it, rather than Earth being at the center of everything. Galileo's observations definitively proved that we live in a heliocentric solar system.

Why was Galileo able to observe all of these things? One property of a telescope is its ability to resolve objects. Angular resolution measures how well a telescope can distinguish between two closely spaced objects rather than observe them as one fuzzy object. A telescope with good angular resolution is able to pick out fine detail and create sharp images. It is because of a telescope's ability to resolve detail better than the human eye (a person with 20/20 vision can resolve two objects about 1 arcminute apart) that Galileo was able to observe all that he did.

6.3 Diffraction and Resolution

Telescopes resolve objects better than the human eye because they are bigger in size. A telescope's ability to resolve objects is limited by a property of waves known as diffraction. Diffraction is the tendency of a wave to bend around corners, or through openings. As light enters a telescope, it treats this as an opening, and the light diffracts around the opening as a result.

The angular resolution of a telescope (the Greek letter theta or θ) depends on two quantities: the wavelength of light (abbreviated as lambda λ) and the diameter of the telescope (D). A formula for the diffraction-limited angular resolution of a telescope is given by:

This equation means that the bigger the diameter of the telescope (D), the smaller the angular separation between objects the telescope can resolve (θ). The angular separation is in arcseconds (1/60^th of an arcminute).

This figure shows two observations of the 51st galaxy in Messier's catalog (called M51 for short), both taken from Kitt Peak National Observatory. See how the observed detail taken with the 4-meter on the left shows much more detail than the image taken with the 0.9-meter.

6.4 The Earth's Atmosphere and Resolution

Have you ever wondered why stars appear to 'twinkle' when we look at them at night? The Earth's atmosphere does not sit still; it moves over time. As the atmospheric particles move, they can scatter the photons slightly, altering their path as they travel towards the telescope. Because the atmosphere is moving, no two photons will be scattered exactly the same, causing them to strike the telescope at slightly different regions. This causes a blurring of the image (as well as the twinkling of stars when we look at them at night.)

The angular size of the imaged star is a common way to quantify the amount of blurring, and is called the seeing disk. In the animation below, use the slide bar to vary the turbulence of the atmosphere, from calm to turbulent. See how the seeing disk changes in response.

6.5 Adaptive Optics

Until relatively recently, the resolution of ground-based telescopes was limited by either their own diameter (diffraction-limited resolution), or by the turbulence-limited resolution of the atmosphere. Astronomers have developed a way to overcome the turbulence problem.

As we saw previously, the effects of Earth's atmosphere is that it causes the photons from an object to be scattered slightly such that they don't all strike the telescope at exactly the same place. If we could correct for this, then we could produce a crisper, cleaner image.

Because stars are so far away from us, it is impossible to resolve all but a few of them through a telescope. Most of them simply should look like a point of light in the sky. Due to the atmosphere, though, that point gets blurred out. If we had a bright star in our view, though, we could monitor the beams of photons from that source and deform the shape of a secondary mirror such that all of the photons hit at exactly the same spot. Unfortunately, a bright star isn't always in view, so astronomers have determined a way to create one. They fire a laser beam up into the atmosphere where it ionizes a layer of sodium high in the ionosphere. This ionized sodium then acts like a bright star. We can then correct for this artificial star, and therefore also correct for our real star. This process is known as adaptive optics.

You might well ask at this point "So why don't astronomers just put all of their telescopes above the atmosphere?" There are many reasons why this can't be done for all telescopes, including the high price of launching and maintaining space telescopes and the fragility of modern electronics.

6.6 Quick Check Quiz

Indepth Activity: Resolution of Telescopes