Sunday, February 19, 2012

How a Telescope Works - Part Three - Resolving Power

It is physically impossible for any telescope, no matter how big or how perfect its optics have been made, to reveal an infinite amount of detail of the celestial object being looked at. This is because a telescope is limited by atmospheric turbulence and diffraction, in other words the telescope's resolving power.

When light passes through an opening its constituent waves spread out. This effect is diffraction and it shows up in an image of a star as a disk surrounded by rings instead of pin-sharp points of light. The same phenomenon blurs fine detail on images of the planets. However, the larger the telescope the less is the diffraction and consequently more detail can be resolved compared to images produced by smaller telescopes.

Greater resolving power means that some stars that appear to be single stars can in fact be separated into double stars. There are two formulae that are used to determine the resolution of telescopes; these are the Dawes limit and the Rayleigh limit. The Dawes limit is given by the ratio 11.6 arcseconds divided by the telescope's aperture in centimetres. The Rayleigh limit for light of 550 nm wavelength is the ratio 14 arcseconds divided by the telescope's aperture in centimetres.

For example, a 9 cm instrument has a Dawes resolution limit of 11.6 arcseconds divided by 9, which is 1.29 arcseconds, and a Rayleigh resolution limit of 14 arcseconds divided by 9, which is 1.55 arcseconds. The Rayleigh limit is in fact theoretical whilst the Dawes limit is determined by the actual observation of double stars that are equal in brightness. So, a double star with components separated by 1.3 arcseconds will be close to the resolving limit of a 9 cm aperture telescope in perfect, steady seeing conditions. A 15 cm aperture telescope by comparison has a Dawes limit of 0.76 arcseconds, so that instrument will easily resolve the double star.

Now, if diffraction were the only limiting factor then the biggest telescopes in the world would obviously provide astronomers with the best images. But the Earth's atmosphere is constantly moving and jiggling around - what is better known as atmospheric turbulence. This means that ground-based telescopes with apertures larger than 75 cm can not show much more detail on objects such as the planets, especially during average seeing conditions.

These days, however, the technology of adaptive optics has come to the rescue of the big ground-based professional telescopes. Most can now compete with the Hubble Space Telescope in resolving fine detail. But amateur astronomers will still have to put up with the limitations imposed by the Earth's atmosphere when it comes to resolving objects through their telescopes.

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