Radio astronomy has revealed the existence of pulsars, quasars and the microwave background radiation that provides the strongest evidence for the big bang theory. It has also been used to look at the distribution and composition of the vast clouds of material between the stars. None of those things are possible with optical astronomy. But radio astronomy can also be frustrating because the images it produces are much less detailed than images from optical telescopes. This isn't due to flaws in radio telescopes; it's a consequence of the physical nature of the imaging process.
Every schoolchild learns that light travels in straight lines, and that's true -- up to a point. But if you block half a light beam with a knife then look very carefully at the shadow it produces on a screen, you'll see something unusual. If light only travels in straight lines you would expect the half of the screen above the knife edge to be uniformly bright and the half below the edge to be uniformly dark. Instead, a little light creeps into the dark half and a little darkness makes its way into the light half. Light -- and other forms of electromagnetic radiation, including radio waves -- bends a little bit when it hits an edge. That bending effect is called diffraction.
Diffraction and Resolution
Diffraction is always there. Normally you can't see it because there's so much light around that different diffraction patterns average out, but when you focus light the diffraction is revealed. A point of light will not focus down to a perfect point, but to a blurry spot surrounded by fading rings. That's called the diffraction spot or sometimes the "Airy disk."
Two factors determine how big that disk is: the diameter of the mirror or lens and the wavelength of the electromagnetic radiation. The larger that diffraction spot, the less detailed the image. Large diffraction spots overlap each other so you can't make out small features. Astronomers usually quantify blurring in terms of the angular resolution of a telescope. A telescope cannot distinguish two spots that are closer than its angular resolution. The angular resolution of a telescope is proportional to the wavelength divided by its diameter. Other factors can make the angular resolution worse, but never better.
Light and Radio
Light and radio waves are both forms of electromagnetic radiation; the only difference is in the wavelength and frequency. So they both behave exactly the same way. A typical wavelength of light is about 500 nanometers, or 500 billionths of a meter. The largest optical telescopes are around 10 meters in diameter, so they have an angular resolution of about 5 x 10^(-8) radians, or about .01 arcseconds.
Radio waves have a much larger wavelength range. For the purposes of radio astronomy, the range is from about 10 meters to about 1 centimeter. The largest radio telescope is about 300 meters in diameter, so its angular resolution is anywhere from .03 radians to .00003 radians, or about 6000 to 6 arc seconds. The larger the angular resolution, the blurrier the image; images from the largest radio telescope are at least 600 times fuzzier than images from the largest optical telescopes.
As you can tell from the angular resolution equation, the only way to get better resolution is to make the telescope bigger. Large radio telescopes are very difficult to build, so that's really not an option. Instead, radio astronomers combine the measurements from different radio telescopes together in a technique called interferometry. If you perfectly combine the output from two telescopes 500 meters apart, they act like one telescope 500 meters in diameter. The further apart the telescopes, the better the resolution. Unfortunately, the further apart the telescopes, the harder it is to combine their images -- but today's radio astronomers do this all the time.
Even so, the resolution is still limited. If you're looking at 10-meter radio waves and you combine the output of two radio telescopes completely across the Earth from each other you only get a resolution of about .2 arcseconds -- about 20 times worse than the best optical telescopes.
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