The objects astronomers study such as stars, galaxies, quasars, pulsars, planets, supernovae and more, all emit visible light, as well as radiation that our eyes can't detect such as infrared and ultraviolet radiation. They also emit radio waves which are another part of the same electromagnetic spectrum. Radio waves have much longer wavelengths than the rest of the electromagnetic spectrum and range from several centimeters to several kilometers.

Radio telescopes are used to study radio waves and microwaves between wavelengths of about 10 meters and 1 millimeter emitted by astronomical objects. Radio waves with wavelengths longer than about 10 meters are absorbed and reflected by the Earth's atmosphere and do not reach the ground. Many radio waves shorter than 1 centimeter are also absorbed by the Earth's atmosphere and only a few wavelength bands make it through. Wavelengths between 1 and 20 cm only experience minor distortions while traveling through the atmosphere and signal processing software can be used to correct for these effects.

#### Angular Resolution

Radio telescopes have to be much larger than optical telescopes because the wavelengths of radio waves are so much larger than the wavelengths of visible light. Radio wavelengths are between λ ≈ 3 km to λ 1 cm, while visible light wavelengths are between λ 4 x 10-7m (violet) and λ 7 x 10-7m (red). Angular resolution is a measure of how small details of an area in the sky can be seen. The larger the telescope, the more detail can be observed in a given wavelength.

Angular resolution (θ) of a telescope can be calculated using the wavelength of light or radio waves (λ) the telescope is being used to observe, and the diameter (D) of the telescope.

θ = 2.5 x 105 x λ/D, where θ is in arcseconds and λ and D are in meters

or

θ = 1.22 x λ/D, where θ is in radians and λ and D are in meters

So for example, one of LCOGT's 1-meter telescopes should have an angular resolution of approximately 0.1" when observing violet wavelengths. A 65 meter diameter radio telescope observing radio wavelengths of 5 cm would have an angular resolution of 192".

#### Interferometry

As you can see, the resolution achieved by a typical radio telescope at typical radio wavelengths is not very detailed. To overcome this difficulty, radio astronomers use multiple radio telescopes at the same time, a technique called interferometry. This gives angular resolutions of 0.001" or better by effectively creating a single telescope as large as the distance between the two farthest telescopes. The light gathering power is not increased by this technique, but the angular resolution in greatly improved. The Very Large Array (VLA) in New Mexico consists of 27 radio telescopes each 25 meters in diameter, arranged in a Y shaped configuration. All 27 telescopes are used simultaneously to observe a target, then their observations are added together.

Image courtesy of NRAO/AUI

#### Very Long Baseline Interferometry

The longer the distance between two telescopes, the better the resolution when they are used together. Radio astronomers sometimes use telescopes that are thousands of kilometers apart to improve the resolution of their observations. This is called very long baseline interferometry or VLBI. At such great distances, it takes too long to send information from the observations back and forth, so each telescope has its own atomic clock and records the observations. Then, later, the observations from the various telescopes can be synchronized and combined. In recent years there have been several attempts to make use of high-bandwidth fibre optic connections to allow VLBI to happen in real time. Doing this speeds up how quickly radio astronomers can respond to changes in the objects they are observing.

#### Dr. Stuart Lowe Explains How Astronomers Make Pretty Pictures With Radio Telescopes

Making images of the sky with a single radio telescope is quite difficult. As well as having much lower resolution than a similarly sized optical telescope, radio telescopes usually only have a 1-pixel view of the sky. To make an image with a single radio telescope you have to do a raster-scan; slowly move left/right and up/down making many individual observations to build up an image. This technique is very time consuming particularly at shorter wavelengths because the resolution increases and you need more points to observe the same amount of the sky. As a result, there have been few all-sky images made with radio telescopes. One of the best known is a 408 MHz map of the sky created using observations from 3 radio telescopes in Germany, the UK, and Australia.

Over the past 30 years, radio astronomers have attempted to speed up imaging by putting arrays of receivers at the focus of radio telescopes. These radio "cameras" provide as many as 10s of pixels and are limited by the space available at the focus of the telescope and the smallest size of receiver that can detect a particular wavelength. These cameras speed up how quickly images can be made by roughly the same factor as the increase in pixels.

Interferometers can also create images of the sky but they do so in a very different way to single radio telescopes or optical cameras. Every pair of telescopes in an interferometer is called a baseline. The radio waves from a pair of telescopes are combined in a computer - a correlator - to create the virtual focus of a much larger radio telescope with the diameter equivalent to their separation.

Each baseline gives you information about the sky but only at the resolution determined by the telescope spacing*. A pair close together (a short baseline) can only see with a low resolution whereas a widely separated pair (a long baseline) only see high resolutions. If you only had long baselines you'd only be able to see the compact objects on the sky and large objects would be invisible to you! So, to produce a complete image you need a combination of different length baselines to get information about all the size scales. Using this technique an array of radio telescopes of 217 km in diameter can produce an image with a resolution equivalent to the Hubble Space Telescope.

* Unfortunately, this increased resolution only applies in the direction of the separation of the two telescopes. With two fixed telescopes you'd get an image that had high resolution in one direction but low resolution in the direction at right angles to that i.e. it would look a bit like a barcode. To get around this, radio astronomers cleverly make use of the daily rotation of the Earth. As the day goes on the direction in which you have high-resolution rotates with respect to the astronomical object and you can effectively combine all the highest resolution parts into a single image with the high resolution. This is called Earth-rotation aperture synthesis.