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We study the universe almost entirely by studying the "light" (ie electro-magnetic radiation) that is produced by objects and events. In principle, therefore, astronomy is simple:
Choose an object; collect all the light emitted by it; split it up into a giant spectrum; use our knowledge of physics and chemistry to explain all the features; move on to the next type of object.
Of course, there are a number of problems with this approach!
Faintness
Light travels in straight lines. Therefore a "pulse" of light emitted by an object will be spread out over an expanding sphere as it travels outwards making the object appear fainter and fainter.
A telescope collects energy at a certain rate (measured in Watts) by intercepting a flux density (often shortened to flux and measured in W m-2) with its area in m2.
If a source radiates light with a luminosity L measured in
Watts then at a distance R the flux density is given by:
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Particularly for very distant or very faint sources, we need to intercept as much of this light as possible so we build as big a telescope as possible and use very sensitive detectors.
Atmospheric Absorbtion
Having got all the way to the Earth certain wavelengths of
light are strongly absorbed by the atmosphere
(this has its advantages
as well!). So, certainly wavelengths can only be observed from balloon
or satellite telescopes.
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| Atmospheric absorbtion as a function of wavelength |
Different Wavelengths
Unfortunately different wavelengths of light interact with matter in different ways i.e. we can't use the same sort of detector nor even telescope for the whole EM spectrum. For example, X-rays don't bounce off glass mirrors, radio waves are not detectable using photographic film and you can't take a photograph with your car radio. We therefore use:
Of course, everything would be in space if we could afford it and operate it effectively and reliably.
Resolution
Resolution is a measure of how "blurred" an image is. There are two main causes of "blurring" in an observation:
These are discussed in more detail below, but in general for large professional telescopes, Seeing is the dominant effect.
A star is such a distant source that light from it can be treated as a parallel beam, so we have a plane wave incident on the circular aperture of the telescope. The plane wave is diffracted at the edges of the aperture and so a point source does not produce a point image in the focal plane but a circular diffraction pattern.
The smaller the aperture the greater the amount of
diffraction. This pattern was studied by Airy in the last century and
the central bright spot containing 84% of the light is named the
Airy disc. This central bright spot is surrounded by
concentric rings of decreasing brightness.
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| On the left is a diffraction pattern for a circular aperture and on the right a graph showing a slice through the pattern. The Airy Disc can be seen with at least two diffraction rings. |
The Rayleigh criterion for resolving two point sources of
equal brightness is when the peak of one diffraction pattern lies upon
the first minimum of the other. This yields a theoretical maximum
angular resolution referred to as diffraction-limited
resolution given by:
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where Δθ is in radians, D is the diameter of the
aperture (i.e. the telescope mirror or lens) in the same units as the
wavelength λ of the light.
Note the spikes often seen in images
of point sources are the diffraction pattern from the secondary mirror
support structure.
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| These pictures show the effect on the diffraction-limited images of a binary star system of increasing the diameter of the aperture. |
For large telescopes the resolution is dominated by atmospheric effects
rather than the optics of the telescope. This is because the
atmosphere is in constant motion on many spatial and
time-scales. These changes cause scintillation ('twinkling' of stars)
due to: variations in air mass along the line of sight causing changes
in the brightness of an object; and variations in refractive index
causing apparent changes in the position of an object.
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| Two very short exposure images of a star showing how the atmospheric scintillation has produced many blurred "images" of the star. |
Thus the image of a star appears to dance about rapidly and is therefore smeared over an area that can be much larger than the Airy disc - this is usually referred to as the seeing disc.
Since planets are much bigger in angular terms their images tend to be less affected unless turbulence is particularly strong. This is why stars "twinkle" and planets tend not to.
Rapid scintillation reduces both resolution and the ability to detect faint objects. The effects are largest near the horizon. Optical telescopes are usually seeing-limited, radio telescopes are diffraction-limited.
Light collecting power
The human eye has a collecting area of only a few mm diameter whereas the largest optical telescope (the Keck I/II telescopes on Hawaii) has a circular aperture of diameter 10m i.e. an area of almost 80 square metres.
Integration
Our eyes cannot store light - they are real-time devices. A telescope can be equipped with detectors which can sit and collect photons before an image is read out e.g. photographic plates.
Resolving power
Since telescopes are much larger than the pupil of an eye, they have a far better resolving power (remember the Rayleigh criterion).
For the human eye, D ~ 5 mm, at l ~ 550 nm, therefore q ~ 30 arcsec. With a 10 m telescope this can be improved by a factor of ~ 1000, although atmospheric seeing limits the resolution to typically 1 arcsec.
How far away would a 5p coin need to be to have an angular size of 1 arcsec?
These factors allow telescopes to detect point-like objects more than a billion times fainter than can be detected by the naked eye.
The ability of a telescope to enlarge images is the best-known feature of a telescope. Though it is so well known, the magnification power is the least important power of a telescope because it enlarges any distortions due to the telescope and atmosphere. A small, fuzzy blob becomes only a big, fuzzy blob. Also, the light becomes more spread out under higher magnification so the image appears fainter! The magnifying power = (focal length of objective) / (focal length of eyepiece); both focal lengths must, of course, be in the same units.
The very first telescopes used for astronomical purposes (Galileo
1609, Kepler 1610 although others had suggested the possibility
before) used the principle of refraction to form an image. A lens made
of a substance with a different refractive index to air is used to
focus the light. Telescopes using lenses are called refracting
telescopes, see figure below
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| A schematic showing how refraction can be used in a telescope. Note the eyepiece magnifies the image and should match the image of the objective (the exit pupil) to the size of the eye's pupil to gather all the light. |
Refracting telescopes typically have large focal ratios = F/D (sometimes called f-ratios) where F is the focal length and D is the telescope diameter. In fact, the image scale (sometimes referred to as the plate scale) in radians per mm (if the focal length F is measured in mm) is equal to 1/F, or 206265/F in arcsec per mm. Note a small f-ratio means a large image scale which means a large number of arcsec per mm i.e. a given field of view is spread over a larger area in the focal plane. The smaller the focal ratio, the 'slower' the optical system - the light is spread over a larger area in the focal plane so longer integration times are needed.
Refractors have several advantages. They are rugged: after the initial alignment, their optical system is more resistant to misalignment than reflecting telescopes. The glass surface inside the tube is sealed from the atmosphere so it rarely needs cleaning. Since the tube is closed off from the outside, air currents and effects due to changing temperatures are eliminated. This means that the images are steadier and sharper than those from a reflector telescope of the same size. Unfortunately, the images formed by a lens are not perfect, they suffer from several so-called aberrations.
The first two of the above items apply both to mirrors and lenses but chromatic aberration is only found in lens systems. Its effects can be diminished by using so-called achromatic doublets (or even triplets) in which the light passes through a strongly converging lens then a less-strongly diverging lens which removes the dispersion and the light is brought to a focus somewhat farther back down the system. This system is only practical for the small lenses used in eyepieces which magnify the image for eye-ball viewing and in any case is not perfect. The biggest refractor in use is the 40" Yerkes in Wisconsin.
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| The 40" Yerkes Refractor | |
Lenses can only be supported from the edges, are heavy and so can not be manoeuvred around the sky without distorting. The length of the tube must also be longer than the focal length and so a large expensive dome is required.
Newton realised that reflection from a mirror would eliminate chromatic aberration and built the first reflecting telescope in 1670. The mirror was made of a solid disc of beaten copper-tin alloy and polished until it had a reasonable reflecting surface (this is called a speculum, also used on the 'Lassell Telescope', a replica of which can be viewed in the Liverpool Conservation Centre).
However, spherical mirrors suffer from spherical aberration just as lenses do. The solution is to grind them into a paraboloidal shape which does bring all the light to a single focus. This is more difficult to achieve than grinding a spherical mirror - a famous case of not quite getting it right is the HST primary mirror. They also suffer from coma and astigmatism but these are really only a problem for wide-field imaging. These can be reduced by careful optical design or the addition of correcting lenses but even so most normal telescopes have a useful field of view of only 1 degree (note an exception is the Schmidt telescope, see later).
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| The 2 metre mirror of the Liverpool Telescope | |
An advantage of refractors over reflectors is that they are thermally stable, the system remaining undisturbed over many years. Mirrors change shape as their temperature changes and much effort has gone into developing special materials which have low thermal coefficients. They also need regular re-aluminizing (at least every few years) and so the optical system is constantly being disturbed.
All large modern optical telescopes are reflectors. The only problem
is how do you get the light out of the tube and where do you form an
image. There are various possible foci, see figures below.
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| Examples of focal positions (or foci) for reflecting telescopes. |
Prime Focus
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| An astronomer in the Prime-focus cage of the AAT | |
The focus of the main paraboloidal primary mirror. This is in some ways the simplest, has the least light losses and the shortest focal length. The latter point means it is the fastest focus and is most suitable for imaging very faint objects over a wide field. Some older telescopes have a prime-focus cage in which the observer sits. These days instruments take his/her place usually. Typical focal ratios of around f/3.
Newtonian
Effectively a bent prime - the light is deflected out the side of the tube without changing the focal length by using a flat mirror. Generally used on small amateur telescopes - access to this focus is not straightforward and attaching instruments there can unbalance the system. Typically f/5.
Cassegrain
The commonest focus on a large modern telescope since it is a convenient place to attach instruments. The hyperbolic secondary mirror reflects light back through a hole in the middle of the primary. The focal length is lengthened because the secondary is convex and so the plate scale is increased and the system is somewhat slower than prime-focus. Note one gets a long focal length without a long tube. Typically f/15.
Coude
The addition of a flat mirror sends the light out the side of the tube along the support axis. This allows heavy or fragile instruments to be sited stationary outside the telescope. In an alt-azimuth telescope (see later) like the William Herschel (WHT) there are two Coude foci which lead to Nasmyth platforms on which special experiments can be conducted. The schematic of the Keck telescope shown here illustrates the use of such a focus.
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| A schematic of the Keck telescope showing the position of the Nasmyth platforms. |
This is a special instrument which is designed to achieve a large
field of view (as much as 6 degrees with f/2.5 or less) with
minimum aberration. Two famous examples are the Palomar Schmidt in the
USA and the UK Schmidt in Australia.
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| Two examples of Schmidt designs plus (on the right) an image of the UK-Schmidt telescope in Australia. |
The primary mirror is spherical and of larger diameter than the effective aperture which is 'stopped' such that off-axis rays and consequent aberrations are reduced e.g. the UK Schmidt has a 1.8 m mirror but an aperture of only 1.2 m, see figure above.
A lens is used to correct for spherical aberration. The focal plane is slightly curved. There are several designs, the standard Schmidt used at prime-focus and the Maksutov-Cassegrain and Schmidt-Cassegrain. Many small telescopes use this latter design.
Telescope mountings essentially split into two types - equatorial and altitude-azimuth (alt-az).
These are set up for a particular latitude so that the telescope can
track the stars by driving in only one axis, see below.
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| Equatorial design and some mounting systems |
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| The Anglo-Australian telescope (AAT) | |
The Anglo-Australian telescope (AAT) uses a horseshoe mount which is probably the best as it has excellent all-sky coverage but is also expensive.
The fork mount is next best but at low latitudes the forks have to lean over at angles of as much as 70 degrees (eg Hawaii) and so must be incredibly strong.
The English mount used on the United Kingdom Infra-Red Telescope (UKIRT) in Hawaii is cost-effective but has limited polar sky access (due to the telescope running into the polar piers).
The German mount tends to be used for smaller telescopes.
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| A diagram of the William Herschel Telescope (WHT) | |
The simplest mount in engineering terms. It is like the fork mount but
with the polar disc horizontal. The telescope has to drive in both
axes at once but this is possible using computer control. Stresses
hardly vary with position. The main problem is field rotation. This
can be taken out with a derotator but several degrees around the
zenith are inaccessible due to infinite (or at least very rapid) field
rotation. This is used for the WHT, Keck, Gemini and most
new telescopes being built.
Given that how we detect light depends to a large extent on its
wavelength, the treatment here is confined to the optical regime. The
figure here is an excellent summary of the efficiency of various
detectors at registering photons (the quantum efficiency or QE) as a
function of wavelength.
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| Quantum Efficiency of various types of detector as a function of wavelength |
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| Light detection and read-out of a CCD. In stage 1, no light has been detected. Stage 2 shows the build-up of electron-hole pairs in each well caused by incident photons. In 3, the first column of pixels is read out and the rest are shifted across by "bucket-chain". And so on for each column as shown in 4. |
Photons incident on a detector create an electron-hole pair which is stored in a potential well. These wells can then be read out via a bucket chain by applying an electric field at the side of the array. They are very efficient, highly linear, have a large dynamic range and a broad spectral response. They are of quite small area however. A typical array circa 2001 might be 4096x2048 15 micron pixels so they are not great for wide-field imaging. Because they are so efficient any stray thermal electrons will also be detected (so-called dark counts) and so the detectors must be cooled, usually to liquid nitrogen temperatures. The picture below shows some modern CCDs inside their cryostats.
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CCD Cameras
On the left, the Liverpool Telescope Camera and on the right, the five chips of the INT Wide-Field Camera. |