## Optical Telescopes

The telescope fulfills three major tasks in astronomical observations:

1. It collects light from a large area, making it possible to study very faint sources.

2. It increases the apparent angular diameter of the object and thus improves resolution.

### 3. It is used to measure the positions of objects.

The light-collecting surface in a telescope is either a lens or a mirror. Thus, optical telescopes are divided into two types, lens telescopes or refractors and mirror telescopes or reflectors (Fig. 3.4).

Geometrical Optics. Refractors have two lenses, the objective which collects the incoming light and forms an image in the focal plane, and the eyepiece which is a small magnifying glass for looking at the image (Fig. 3.5). The lenses are at the opposite ends of a tube which can be directed towards any desired point. The distance between the eyepiece and the focal plane can be adjusted to get the image into focus. The image formed

Objective Focal plane Eyepiece

Objective Focal plane Eyepiece

Fig. 3.4. A lens telescope or refractor and a mirror telescope or reflector

Fig. 3.4. A lens telescope or refractor and a mirror telescope or reflector

Fig. 3.5. The scale and magnification of a refractor. The object subtends an angle u. The objective forms an image of the object in the focal plane. When the image is viewed through the eyepiece, it is seen at an angle u'

by the objective lens can also be registered, e.g. on a photographic film, as in an ordinary camera.

The diameter of the objective, D, is called the aperture of the telescope. The ratio of the aperture D to the focal length f, F = D/ f, is called the aperture ratio. This quantity is used to characterize the light-gathering power of the telescope. If the aperture ratio is large, near unity, one has a powerful, "fast" telescope; this means that one can take photographs using short exposures, since the image is bright. A small aperture ratio (the focal length much greater than the aperture) means a "slow" telescope.

In astronomy, as in photography, the aperture ratio is often denoted by f/n (e. g. f/8), where n is the focal length divided by the aperture. For fast telescopes this ratio can be f/1... f/3, but usually it is smaller, f/8 ... f/15.

The scale of the image formed in the focal plane of a refractor can be geometrically determined from Fig. 3.5. When the object is seen at the angle u, it forms an image of height s, s = f tan u ~ fu , (3.1)

since u is a very small angle. If the telescope has a focal length of, for instance, 343 cm, one arc minute corresponds to s = 343 cm x 1' = 343 cm x (1/60) x (n/180) = 1 mm.

The magnification a is (from Fig. 3.5)

where we have used the equation s = fu. Here, f is the focal length of the objective and f' that of the eyepiece. For example, if f = 100 cm and we use an eyepiece with f = 2 cm, the magnification is 50-fold. The magnification is not an essential feature of a telescope, since it can be changed simply by changing the eyepiece.

A more important characteristic, which depends on the aperture of the telescope, is the resolving power, which determines, for example, the minimum angular separation of the components of a binary star that can be seen as two separate stars. The theoretical limit for the resolution is set by the diffraction of light: The telescope does not form a point image of a star, but rather a small disc, since light "bends around the corner" like all radiation (Fig. 3.6).

The theoretical resolution of a telescope is often given in the form introduced by Rayleigh (see *Diffraction by a Circular Aperture, p. 81)

As a practical rule, we can say that two objects are seen as separate if the angular distance between them is

This formula can be applied to optical as well as radio telescopes. For example, if one makes observations at a typical yellow wavelength (X = 550 nm), the resolving power of a reflector with an aperture of 1 m is about 0.2''. However, seeing spreads out the image to a diameter of typically one arc second. Thus, the theoretical diffraction limit cannot usually be reached on the surface of the Earth.

In photography the image is further spread in the photographic plate, decreasing the resolution as compared with visual observations. The grain size of photographic emulsions is about 0.01-0.03 mm, which is also the minimum size of the image. For a focal length of 1 m, the scale is 1 mm = 206'', and thus 0.01 mm corresponds to about 2 arc seconds. This is similar to the theoretical resolution of a telescope with an aperture of 7 cm in visual observations.

In practice, the resolution of visual observations is determined by the ability of the eye to see details.

Fig. 3.6a-e. Diffraction and resolving power. The image of a single star (a) consists of concentric diffraction rings, which can be displayed as a mountain diagram (b). Wide pairs of stars can be easily resolved (c). For resolving close bi naries, different criteria can be used. One is the Rayleigh limit 1.22 X/D (d). In practice, the resolution can be written X/D, which is near the Dawes limit (e). (Photo (a) Sky and Telescope)

Fig. 3.6a-e. Diffraction and resolving power. The image of a single star (a) consists of concentric diffraction rings, which can be displayed as a mountain diagram (b). Wide pairs of stars can be easily resolved (c). For resolving close bi naries, different criteria can be used. One is the Rayleigh limit 1.22 X/D (d). In practice, the resolution can be written X/D, which is near the Dawes limit (e). (Photo (a) Sky and Telescope)

In night vision (when the eye is perfectly adapted to darkness) the resolving capability of the human eye is about 2'.

The maximum magnification «max is the largest magnification that is worth using in telescopic observations. Its value is obtained from the ratio of the resolving capability of the eye, e ~ 2' = 5.8 x 10-4 rad, to the resolving power of the telescope, 0,

the objective goes behind the eyepiece. From Fig. 3.7 we obtain f D

f rn Thus the condition L < d means that m > D/d.

In the night, the diameter of the pupil of the human eye is about 6 mm, and thus the minimum magnification of a 100 mm telescope is about 17.

If we use, for example, an objective with a diameter of 100 mm, the maximum magnification is about 100. The eye has no use for larger magnifications.

The minimum magnification «min is the smallest magnification that is useful in visual observations. Its value is obtained from the condition that the diameter of the exit pupil L of the telescope must be smaller than or equal to the pupil of the eye.

The exit pupil is the image of the objective lens, formed by the eyepiece, through which the light from

Fig. 3.7. The exit pupil L is the image of the objective lens formed by the eyepiece

Fig. 3.7. The exit pupil L is the image of the objective lens formed by the eyepiece

Refractors. In the first refractors, which had a simple objective lens, the observations were hampered by the chromatic aberration. Since glass refracts different colours by different amounts, all colours do not meet at the same focal point (Fig. 3.8), but the focal length increases with increasing wavelength. To remove this aberration, achromatic lenses consisting of two parts were developed in the 18th century. The colour dependence of the focal length is much smaller than in single lenses, and at some wavelength, k0, the focal length has an extremum (usually a minimum). Near this point the change of focal length with wavelength is very small (Fig. 3.9). If the telescope is intended for visual observations, we choose k0 = 550 nm, corresponding to the maximum sensitivity of the eye. Objectives for photographic refractors are usually constructed with k0 « 425 nm, since normal photographic plates are most sensitive to the blue part of the spectrum.

By combining three or even more lenses of different glasses in the objective, the chromatic aberration can be corrected still better (as in apochromatic objectives). Also, special glasses have been developed where the wavelength dependences of the refractive index cancel out so well that two lenses already give a very good correction of the chromatic aberration. They have, however, hardly been used in astronomy so far.

The largest refractors in the world have an aperture of about one metre (102 cm in the Yerkes Observatory telescope (Fig. 3.10), finished in 1897, and 91 cm in the Lick Observatory telescope (1888)). The aperture ratio is typically f/10... f/20.

The use of refractors is limited by their small field of view and awkwardly long structure. Refractors are

Fig. 3.8. Chromatic aberration. Light rays of different colours are refracted to different focal points (left). The aberration can be corrected with an achromatic lens consisting of two parts (right)

1.000

Fig. 3.9. The wavelength dependence of the focal length of a typical achromatic objective for visual observations. The focal length has a minimum near k = 550 nm, where the eye is most sensitive. In bluer light (k = 450 nm) or in redder light (k = 800 nm), the focal length increases by a factor of about 1.002

used, e. g. for visual observations of binary stars and in various meridian telescopes for measuring the positions of stars. In photography they can be used for accurate position measurements, for example, to find parallaxes.

A wider field of view is obtained by using more complex lens systems, and telescopes of this kind are called astrographs. Astrographs have an objective made up of typically 3-5 lenses and an aperture of less than 60 cm. The aperture ratio is f/5... f/7 and the field of view about 5°. Astrographs are used to photograph large areas of the sky, e. g. for proper motion studies and for statistical brightness studies of the stars.

Reflectors. The most common telescope type in astro-physical research is the mirror telescope or reflector. As a light-collecting surface, it employs a mirror coated with a thin layer of aluminium. The form of the mirror is usually parabolic. A parabolic mirror reflects all light rays entering the telescope parallel to the main axis into the same focal point. The image formed at this point can be observed through an eyepiece or registered with a detector. One of the advantages of reflectors is the absence of chromatic aberration, since all wavelengths are reflected to the same point.

In the very largest telescopes, the observer can sit with his instruments in a special cage at the primary

 3.2 Optical Telescopes 53
Fig. 3.10. The largest refractor in the world is at the Yerkes Observatory, University of Chicago. It has an objective lens with a diameter of 102 cm. (Photo by Yerkes Observatory)

Fig. 3.11. Different locations of the focus in reflectors: pri- observations near the celestial pole. More complex coude sys-mary focus, Newton focus, Cassegrain focus and coude tems usually have three flat mirrors after the primary and focus. The coude system in this figure cannot be used for secondary mirrors

Fig. 3.11. Different locations of the focus in reflectors: pri- observations near the celestial pole. More complex coude sys-mary focus, Newton focus, Cassegrain focus and coude tems usually have three flat mirrors after the primary and focus. The coude system in this figure cannot be used for secondary mirrors focus (Fig. 3.11) without eclipsing too much of the incoming light. In smaller telescopes, this is not possible, and the image must be inspected from outside the telescope. In modern telescopes instruments are remotely controlled, and the observer must stay away from the telescope to reduce thermal turbulence.

In 1663 James Gregory (1638-1675) described a reflector. The first practical reflector, however, was built by Isaac Newton. He guided the light perpendicularly out from the telescope with a small flat mirror. Therefore the focus of the image in such a system is called the Newton focus. A typical aperture ratio of a Newtonian telescope is f/3 ... f/10. Another possibility is to bore a hole at the centre of the primary mirror and reflect the rays through it with a small hyperbolic secondary mirror in the front end of the telescope. In such a design, the rays meet in the Cassegrain focus. Cassegrain systems have aperture ratios of f/8... f/15.

The effective focal length ( fe) of a Cassegrain telescope is determined by the position and convexity of the secondary mirror. Using the notations of Fig. 3.12, we get

If we choose a ^ b, we have fe ^ fp. In this way one can construct short telescopes with long focal lengths. Cassegrain systems are especially well suited for spectrographs, photometric and other instruments, which can be mounted in the secondary focus, easily accessible to the observers.

Fig. 3.12. The principle of a Cassegrain reflector. A concave (paraboloid) primary mirror M\ reflects the light rays parallel to the main axis towards the primary focus S1. A convex secondary mirror M2 (hyperboloid) reflects the rays back through a small hole at the centre of the main mirror to the secondary focus S2 outside the telescope s2

Fig. 3.12. The principle of a Cassegrain reflector. A concave (paraboloid) primary mirror M\ reflects the light rays parallel to the main axis towards the primary focus S1. A convex secondary mirror M2 (hyperboloid) reflects the rays back through a small hole at the centre of the main mirror to the secondary focus S2 outside the telescope

More complicated arrangements use several mirrors to guide the light through the declination axis of the telescope to a fixed coudé focus (from the French word couder, to bend), which can even be situated in a separate room near the telescope (Fig. 3.13). The focal length is thus very long and the aperture ratio f/30 ■ ■ ■ f/40. The coude focus is used mainly for accurate spec-troscopy, since the large spectrographs can be stationary and their temperature can be held accurately constant. A drawback is that much light is lost in the reflections in the several mirrors of the coude system. An aluminized mirror reflects about 80% of the light falling on it, and thus in a coude system of, e.g. five mirrors (including the primary and secondary mirrors), only 0.85 ~ 30% of the light reaches the detector.

Fig. 3.13. The coude system of the Kitt Peak 2.1 m reflector. (Drawing National Optical Astronomy Observatories, Kitt Peak National Observatory)

The reflector has its own aberration, coma. It affects images displaced from the optical axis. Light rays do not converge at one point, but form a figure like a comet. Due to the coma, the classical reflector with a paraboloid mirror has a very small correct field of view. The coma limits the diameter of the useful field to 2-20 minutes of arc, depending on the aperture ratio of the telescope. The 5 m Palomar telescope, for instance, has a useful field of view of about 4', corresponding to about one-eighth of the diameter of the Moon. In practice, the small field of view can be enlarged by various correcting lenses.

If the primary mirror were spherical, there would be no coma. However, this kind of mirror has its own error, spherical aberration: light rays from the centre and edges converge at different points. To remove the spherical aberration, the Estonian astronomer Bernhard Schmidt developed a thin correcting lens that is placed in the way of the incoming light. Schmidt cameras (Figs. 3.14 and 3.15) have a very wide (about 7°), nearly faultless field of view, and the correcting lens is

 Corrector lens at the centre of curvature of the main mirror Curved focal surface

Fig. 3.14. The principle of the Schmidt camera. A correcting glass at the centre of curvature of a concave spherical mirror deviates parallel rays of light and compensates for the spherical aberration of the spherical mirror. (In the figure, the form of the correcting glass and the change of direction of the light rays have been greatly exaggerated.) Since the correcting glass lies at the centre of curvature, the image is practically independent of the incoming angle of the light rays. Thus there is no coma or astigmatism, and the images of stars are points on a spherical surface at a distance of R/2, where R is the radius of curvature of the spherical mirror. In photography, the plate must be bent into the form of the focal surface, or the field rectified with a corrector lens

Fig. 3.14. The principle of the Schmidt camera. A correcting glass at the centre of curvature of a concave spherical mirror deviates parallel rays of light and compensates for the spherical aberration of the spherical mirror. (In the figure, the form of the correcting glass and the change of direction of the light rays have been greatly exaggerated.) Since the correcting glass lies at the centre of curvature, the image is practically independent of the incoming angle of the light rays. Thus there is no coma or astigmatism, and the images of stars are points on a spherical surface at a distance of R/2, where R is the radius of curvature of the spherical mirror. In photography, the plate must be bent into the form of the focal surface, or the field rectified with a corrector lens

so thin that it absorbs very little light. The images of the stars are very sharp.

In Schmidt telescopes the diaphragm with the correcting lens is positioned at the centre of the radius of curvature of the mirror (this radius equals twice the focal length). To collect all the light from the edges of the field of view, the diameter of the mirror must be larger than that of the correcting glass. The Palomar Schmidt camera, for example, has an aperture of 122 cm (correcting lens)/183 cm (mirror) and a focal length of 300 cm. The largest Schmidt telescope in the world is in Tautenburg, Germany, and its corresponding values are 134/203/400 cm.

A disadvantage of the Schmidt telescope is the curved focal plane, consisting of a part of a sphere. When the telescope is used for photography, the plate must be bent along the curved focal plane. Another possibility of correcting the curvature of the field of view is to use an extra correcting lens near the focal plane. Such a solution was developed by the Finnish astronomer Yrjo Vaisala in the 1930's, independently of Schmidt. Schmidt cameras have proved to be very effective in mapping the sky. They have been used to photograph the Palomar Sky Atlas mentioned in the previous chapter and its continuation, the ESO/SRC Southern Sky Atlas.

The Schmidt camera is an example of a catadiop-tric telescope, which has both lenses and mirrors. Schmidt-Cassegrain telescopes used by many amateurs are modifications of the Schmidt camera. They have a secondary mirror mounted at the centre of the correcting lens; the mirror reflects the image through a hole in the primary mirror. Thus the effective focal length can be rather long, although the telescope itself is very short. Another common catadioptric telescope is the Maksu-tov telescope. Both surfaces of the correcting lens as well as the primary mirror of a Maksutov telescope are concentric spheres.

Another way of removing the coma of the classical reflectors is to use more complicated mirror surfaces. The Ritchey-Chretien system has hyperboloidal primary and secondary mirrors, providing a fairly wide useful field of view. Ritchey-Chretien optics are used in many large telescopes.

< Fig. 3.15. The large Schmidt telescope of the European Southern Observatory. The diameter of the mirror is 1.62 m and of the free aperture 1 m. (Photo ESO)

Mountings of Telescopes. A telescope has to be mounted on a steady support to prevent its shaking, and it must be smoothly rotated during observations. There are two principal types of mounting, equatorial and azimuthal (Fig. 3.16).

In the equatorial mounting, one of the axes is directed towards the celestial pole. It is called the polar axis or hour axis. The other one, the declination axis, is perpendicular to it. Since the hour axis is parallel to the axis of the Earth, the apparent rotation of the sky can be compensated for by turning the telescope around this axis at a constant rate.

The declination axis is the main technical problem of the equatorial mounting. When the telescope is pointing to the south its weight causes a force perpendicular to the axis. When the telescope is tracking an object and turns westward, the bearings must take an increasing load parallel with the declination axis.

In the azimuthal mounting, one of the axes is vertical, the other one horizontal. This mounting is easier to construct than the equatorial mounting and is more stable for very large telescopes. In order to follow the rotation of the sky, the telescope must be turned around both of the axes with changing velocities. The field of view will also rotate; this rotation must be compensated for when the telescope is used for photography.

If an object goes close to the zenith, its azimuth will change 180° in a very short time. Therefore, around the zenith there is a small region where observations with an azimuthal telescope are not possible.

The largest telescopes in the world were equato-rially mounted until the development of computers made possible the more complicated guidance needed for azimuthal mountings. Most of the recently built large telescopes are already azimuthally mounted. Az-imuthally mounted telescopes have two additional obvious places for foci, the Nasmyth foci at both ends of the horizontal axis.

The Dobson mounting, used in many amateur telescopes, is azimuthal. The magnification of the Newtonian telescope is usually small, and the telescope rests on pieces of teflon, which make it very easy to move. Thus the object can easily be tracked manually.

Another type of mounting is the coelostat, where rotating mirrors guide the light into a stationary telescope. This system is used especially in solar telescopes.

Fig. 3.16. The equatorial mounting (left) and the azimuthal mounting (right)

To measure absolute positions of stars and accurate time, telescopes aligned with the north-south direction are used. They can be rotated around one axis only, the east-west horizontal axis. Meridian circles or transit instruments with this kind of mounting were widely constructed for different observatories during the 19th century. A few are still used for astrometry, but they are now highly automatic like the meridian circle on La Palma funded by the Carlsberg foundation.

New Techniques. Detectors are already approaching the theoretical limit of efficiency, where all incident photons are registered. Ultimately, to detect even fainter objects the only solution is to increase the light gathering area, but also the mirrors are getting close to the practical maximum size. Thus, new technical solutions are needed.

One new feature is active optics, used e. g. in the ESO 3.5 metre NTT telescope (New Technology Telescope) at La Silla, Chile. The mirror is very thin, but its shape is kept exactly correct by a computer controlled support mechanism. The weight and production cost of such a mirror are much smaller compared with a conventional thick mirror. Because of the smaller weight also the supporting structure can be made lighter.

Developing the support mechanism further leads to adaptive optics. A reference star (or an artificial beam) is monitored constantly in order to obtain the shape of the seeing disk. The shape of the main mirror or a smaller auxiliary mirror is adjusted up to hundreds of times a second to keep the image as concentrated as possible. Adaptive optics has been taken into use in the largest telescopes of the world from about the year 2000 on.

Fig. 3.17a-c. The largest telescopes in the world in 1947- ► 2000. (a) For nearly 30 years, the 5.1 m Hale telescope on Mount Palomar, California, USA, was the largest telescope in the world. (b) The BTA, Big Azimuthal Telescope, is situated in the Caucasus in the southern Soviet Union. Its mirror has a diameter of 6 m. It was set in operation at the end of 1975. (c) The William M. Keck Telescope on the summit of Mauna Kea, Hawaii, was completed in 1992. The 10 m mirror consists of 36 hexagonal segments. (Photos Palomar Observatory, Spetsialnaya Astrofizitsheskaya Observatorya, and Roger Ressmeyer - Starlight for the California Association for Research in Astronomy)

Fig.3.18a-c. Some new large telescopes. (a) The 8.1m Gemini North telescope on Mauna Kea, Hawaii, was set in operation in 1999. Its twin, Gemini South, was dedicated in 2000. (b) The European Southern Observatory (ESO) was founded by Belgium, France, the Netherlands, Sweden and West Germany in 1962. Other European countries have joined them later. The VLT (Very Large Telescope) on Cerro Paranal in Northern Chile, was inaugurated in 1998-2000. (c) The first big Japanese telescope, the 8.3 m Subaru on Mauna Kea, Hawaii, started observations in 1999. (Photos National Optical Astronomy Observatories, European Southern Observatory and Subaru Observatory)

The mirrors of large telescopes need not be monolithic, but can be made of smaller pieces that are, e. g. hexagonal. These mosaic mirrors are very light and can be used to build up mirrors with diameters of several tens of metres (Fig. 3.19). Using active optics, the hexagons can be accurately focussed. The California Association for Research in Astronomy has constructed the William M. Keck telescope with a 10 m mosaic mirror. It is located on Mauna Kea, and the last segment was installed in 1992. A second, similar telescope Keck II was completed in 1996, the pair forming a huge binocular telescope.

The reflecting surface does not have to be continuous, but can consist of several separate mirrors. Such

Fig. 3.19. The mirror of a telescope can be made up of several smaller segments, which are much easier to manufacture, as in the Hobby-Eberle Telescope on Mount Fowlkes, Texas. The effective diameter of the mirror is 9.1 m. A similar telescope is being built in South Africa. (Photo MacDonald Observatory)

Fig. 3.19. The mirror of a telescope can be made up of several smaller segments, which are much easier to manufacture, as in the Hobby-Eberle Telescope on Mount Fowlkes, Texas. The effective diameter of the mirror is 9.1 m. A similar telescope is being built in South Africa. (Photo MacDonald Observatory)

Fig. 3.20. The Hubble Space Telescope after the latest service flight in 2002. The telescope got new solar panels and several other upgrades. (Photo NASA)

a telescope was operating on Mount Hopkins, Arizona, in 1979-1999. It was the Multiple-Mirror Telescope (MMT) with six 1.8 m mirrors together corresponding to a single mirror having a diameter of 4.5 m. In 2000 the six mirrors were replaced by one 6.5 m mirror.

The European Southern Observatory has constructed its own multi-mirror telescope. ESO's Very Large Telescope (VLT) has four closely located mirrors (Fig. 3.18). The diameter of each mirror is eight metres, and the total area corresponds to one telescope with a 16 m mirror. The resolution is even better, since the "aperture", i. e. the maximum distance between the mirrors, is several tens of meters.

An important astronomical instruments of the 20th century is the Hubble Space Telescope, launched in 1990 (Fig. 3.20). It has a mirror with a diameter of 2.4 m. The resolution of the telescope (after the faulty optics was corrected) is near the theoretical diffraction limit, since there is no disturbing atmosphere. A second generation Space Telescope, now called the James Webb Space Telescope, with a mirror of about 6.5 m is planned to be launched in about 2011.

The Hubble Space Telescope was the first large optical telescope in Earth orbit. In the future, satellites will continue to be mainly used for those wavelength regions where the radiation is absorbed by the atmosphere. Due to budgetary reasons, the majority of astronomical ob servations will still be carried out on the Earth, and great attention will be given to improving ground-based observatories and detectors.

## Telescopes Mastery

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