# Reflecting telescope

Construction of the ELT , the main mirror of which has a diameter of 39 m, completion planned for 2025

Mirror telescopes are telescopes that have a concave mirror as an objective . In addition to this main mirror , most designs also use other optical elements such as lenses , deflecting or secondary mirrors .

Reflector telescopes are used in observational astronomy - both visually and photographically or for spectroscopy . In addition to observations in the visible light range , they are suitable for a wide range of the electromagnetic spectrum , from the ultraviolet to the far infrared .

In large observatories , reflector telescopes with diameters of around 2 to 10 meters are used, on research satellites from 0.5 to 3 meters. A 40-meter telescope from ESO ( ELT ) and space telescopes up to 6 meters are planned . Among the school and amateur telescopes , mirror telescopes are the most common type because they are lighter and cheaper than lens telescopes. They usually have a mirror diameter of 10 to 30 cm, sometimes even larger when you sharpen your own mirror .

## History of the reflecting telescope

The magnifying effect of concave mirrors was known as early as the 13th century and in 1512 Leonardo da Vinci described their use for observing the starry sky. But it wasn't until 1616 , eight years after the invention of the lens telescope , that the Jesuit priest Nicolaus Zucchius built the first reflector telescope. It consisted of a slightly tilted concave mirror and a diverging lens, which formed the eyepiece and was arranged on the side so that the observer would not obscure the light entering the concave mirror. Because of the tilting of the mirror, however, the telescope had severe imaging errors .

The mirrors, which were initially cut from glass, were soon switched to metal mirrors as their diameters increased , and James Short and Wilhelm Herschel in particular achieved mastery in their cutting technique . They dominated until around 1900, when better methods of glass casting were developed.

### Gregory, Cassegrain and Newton telescopes

Beam path in the Cassegrain telescope

In the following years, the Bolognese Cesare Caravaggi and the mathematicians Bonaventura Cavalieri (1632), Marin Mersenne (1636) and James Gregory (1663) dealt with various designs for the construction of a reflector telescope. The best solution came from the French priest Laurent Cassegrain in 1672 , which is still used today as a Cassegrain telescope .

Replica of Isaac Newton's telescope, 1672; the mirror had a diameter of 5 cm.
Illustration from the review in the Construction d'un telescope par reflexion, de mr. Newton, ayant seize pouces de longueur ... ( Acta eruditorum , 1741)

In the years 1668–1672 Isaac Newton developed a telescope that avoided the disadvantage of the tilted main mirror by means of an auxiliary mirror, and demonstrated it to the public. In the optical axis of the main mirror, he attached a flat deflecting mirror through which the observer could look into the instrument from the side. Because of its simple construction, this type of construction formed the prototype of many of the following telescopes, whereby a Europe-wide discussion about the advantages and disadvantages of the various systems took place among the scholars.

“Leviathan” mirror telescope from 1860; the metal mirror was 1.83 m in diameter.

In contrast to spherically shaped main mirrors, parabolic primary mirrors produce a flawless image, as Gregory already postulated. In 1721 the brothers John, Henry and George Hadley succeeded in producing the parabolic primary mirror , which was much more difficult to manufacture . On this basis, larger and larger telescopes were built in the following 150 years, up to the Leviathan with a diameter of 183 cm .

### Mirror material, cut and corrective optics

The main mirrors were made of mirror metal until the middle of the 19th century . In addition to an initial reflectivity of approx. 60%, this had the disadvantage that the metal corroded over time , which made regular polishing necessary, as a result of which the parabolic shape suffered and had to be laboriously restored. Using a method by Justus Liebig to deposit a thin silver film on glass, Léon Foucault and Carl August von Steinheil developed mirrors made of glass with a reflective layer made of silver , which had a significantly higher reflectivity and was easy to renew. Foucault also developed a simplified method for checking the shape of the mirror , which made the production of the mirror much easier.

In 1905 Karl Schwarzschild published his work on higher-order imaging errors in multi- mirror systems and thus laid the basis for coma-free , so-called aplanatic multi - mirror optics . These were implemented by George Willis Ritchey and Henri Chrétien in the Ritchey-Chrétien telescope named after them in a Cassegrain arrangement, which enables not only sharp images in the center, but also observations with a larger field of view . Further constructions were found, some of which allowed a very large angle of view: For example, the Schmidt camera developed by Bernhard Schmidt around 1930 , in which a large corrective lens was located in front of the mirror. The late 1930s designed Frank E. Ross for the 2.5-m Hooker telescope a corrective optics near the focus, which was therefore built significantly less compared to the primary mirror and thus suitable for larger diameter mirror. This construction was further improved by Charles G. Wynne and can also be found, partly in a modified form, in many modern telescopes.

Selentschuk : 6 m primary mirror (bottom right) in an open, azimuthal mount

### Modern large telescopes

The principle of the Ritchey-Chrétien-Cassegrain telescope, built from solid glass mirrors, was successfully retained up to a mirror diameter of 5 m ( Mount Palomar 1948) (see also Hale telescope ). However , the six-meter BTA-6 mirror installed at the Zelenchuk Observatory in 1975 showed the limits. The 42-ton glass mirror bent under its own weight and no longer provided sharp images. In order to exceed this limitation, concepts were first implemented to assemble the main mirror from several smaller mirror segments. In the 1980s, processes were developed how one could manufacture large, thin glass mirrors by centrifugal casting or with supporting hollow structures, mostly in honeycomb form . Precondition for this are extremely precise mountings of the mirrors, which align the segments to one another to a fraction of the light wavelength or prevent the deformation of the thin mirrors with the same accuracy. Because of the necessary active elements in the holder, such systems are also referred to as active optics . With these techniques it is possible to manufacture telescopes up to about ten meters in diameter, see Keck Observatory .

In another respect, however, the BTA-6 was trend-setting. Because of the high weight, an equatorial mount of the telescope was no longer useful, instead a mechanically simpler azimuthal mount was chosen. The synchronous control over several axes required for aligning and tracking the telescope to the observed sky region was made possible by advances in computer technology. This concept was adopted in the following for all telescopes of a similar size and simplified for smaller amateur telescopes for GoTo control.

In addition to these frequently used construction methods, other constructions have been developed for special purposes, for example:

• the Schmidt camera and the Baker-Nunn camera , in order to be able to observe the largest possible area of ​​the sky;
• the Hubble Space Telescope , for observations undisturbed by the atmosphere.
• For spectrometry , large telescopes ( Hobby Eberly Telescope , Southern African Large Telescope ) are once again equipped with a spherical main mirror, which can only be rotated around one axis and is segmented. This allows a very cost-effective construction or, with a given budget, a larger mirror surface to be achieved. The imaging errors are compensated for by additional, but significantly smaller and cheaper mirrors.

## Components

### Optical elements

The segmented primary mirror of the Southern African Large Telescope
Liquid mirror made of mercury ( Large Zenith Telescope with 6 m diameter)

A reflector telescope essentially consists of a main mirror and a secondary mirror mounted in the same tube (exception: Schiefspiegler ), which are also called primary and secondary mirrors . In contrast to the objective of a telescope, the incident light is not refracted , but reflected by the main mirror , thus avoiding color errors. Since, in contrast to a lens, the light does not penetrate the mirror, the main mirror can be supported with suitable mechanisms and can therefore be made in almost any size. In scientific astronomy, the current primary mirror diameters are now approaching the ten-meter mark. With glass lenses, there is an upper limit of 1.2 meters due to the weight ratio and the resulting deflection of the lens.

Instead of a conventional mirror, a liquid mirror made of mercury can also be used. Such a mirror is very inexpensive compared to fixed mirrors and diameters of up to 6 meters can be achieved (see Large Zenith Telescope ).

The main mirror is mostly shaped approximately parabolically . It bundles the incident light from the celestial body and reflects it back towards the secondary mirror. This directs the light to the side or through a hole in the primary mirror in the direction of the eyepiece or radiation detector . The detector is only the eye of amateur astronomers . In scientific operations, traditional receivers such as photo plates or photo film were replaced by CCD or CMOS sensors. The bundled light to be examined can be filtered through color filters before recording or subjected to a spectral analysis using a spectrograph . In the case of large reflector telescopes, the radiation detectors or instruments for light analysis often weigh up to over 1000 kg. Particularly massive devices are sometimes no longer placed directly behind the telescope, but separately from it and connected to the telescope via special optical fiber optics .

### Support elements

The honeycomb support structure of the primary mirror from SOFIA before the mirror layer was applied.

In contrast to lens telescopes, with reflector telescopes a bending of the optical elements caused by gravity can be largely prevented by supporting structures, even for very large mirrors.

The conceptually simplest method is to make the mirror thick enough so that its mechanical rigidity reduces deflection. For this, the thickness is typically chosen to be one sixth of the diameter. However, this method has its limits with larger mirror diameters, which are complex to manufacture, since the resulting thick cast glass plates require a lot of material and take a very long time to cool down without tension. A further development consists in the production of a lightweight, hollow support structure from the same material, usually in a honeycomb shape or using hollow chambers; this is integrated on the mirror through a corresponding design of the casting mold.

Underside of the primary mirror carrier of the MOA telescope - the Lassell levers, formed from the white compensation weight disks on the black lever structures, are clearly visible.

Alternatively or in addition, gravity can be absorbed by a so-called whiffletree . In this case, the load is supported at many points by mostly multi-level, articulated beams or plates, continuing the principle of table scales . Another support mechanism, developed by William Lassell around 1840 and named after him, uses lever mechanisms at these points, through which a counterforce corresponding to the optical axis is introduced by weights. The component of the weight force acting perpendicular to the optical axis is often absorbed in these designs by a half loop around the mirror.

Other support structures, on the other hand, deform the mirror in a targeted manner, for example in order to convert an easily manufactured spherical surface into a parabolic or hyperbolic surface by introducing forces in a targeted manner by means of springs or negative pressure.

In modern large telescopes, the primary mirrors are built so thin that they would break under their own weight if they were not held in shape by active support elements. On the one hand, the thin construction has the advantage that the mirror is lighter and thus the telescopic construction can be less massive. On the other hand, with such mirrors, the required shape of the paraboloid can be achieved in any orientation of the mirror by means of active optics. The active optics use a computer and adjustable support elements to automatically correct the distortions of the mirror caused by its own weight.

The largest mirror was the 5 m telescope on Mt. Palomar , California from 1947 to 1975 . In the years from 1990 to 2000, mirror diameters over 8 m were realized, such as the Very Large Telescope (VLT) of the European Southern Observatory (ESO) in Chile. Mirror telescopes were also built, such as the Keck telescope in Hawaii with a total of 10 m mirror diameter, the main mirror of which consists of individual hexagonal segments that are placed next to each other like a honeycomb and whose position can be corrected hydraulically. A computer regulates the position of the segments automatically so that an optimal image is always created. Since July 2009, the largest reflector telescope with a 10.4 m mirror diameter is around 2400 meters above sea level on the Roque de los Muchachos , the highest peak on the Canary Island of La Palma .

### Tube

Serruier trellis tube of the 60 cm Zeiss telescope in Ostrowik

The tube of a reflector telescope carries the main and secondary or deflecting mirrors, in many implementations also eyepiece or image recorder and holds them on a common optical axis. It is designed as a tube or lattice tube construction, in which the primary mirror is arranged at one end and the secondary or deflection mirror is arranged at the other end.

In order to avoid decentering the optical components due to their weight, especially the primary mirror, when the telescope is tilted, a Serruier lattice tube, which was developed in 1935 for the 5 m Hale telescope , is usually used for larger mirror telescopes .

The Serruier tube consists of two parts, which are arranged in front of and behind the inclination axis known as the declination pivot. Viewed from the side, both parts each form a parallelogram , consisting of a pivot frame, upper and lower lattice tubes and a front frame or primary mirror holder. The stiffness of the front and rear parts is adjusted by means of lateral struts so that they yield to the same extent with every inclination under the influence of weight and the optical components remain on a common optical axis and only this is shifted parallel.

### Lens hoods

For high-contrast images, lens hoods are required in a telescope, which prevent light from reaching the eyepiece or image recorder through scattering in the tube or from regions of the sky outside the observation field. Different concepts have been developed for this, depending on the mirror arrangement. For the primary mirror, a number of pinhole diaphragms with a diameter decreasing towards the mirror are often used, so that the field of view is not restricted. Venetian blinds are suitable for Cassegrain telescopes and a repeated arrangement for Gregorian telescopes as for simple mirrors.

## Manufacture and maintenance

### From the glass melt to the blank

Opening the rotary furnace after casting the VLT Zerodur mirror
Grinding one of the primary mirrors for the VLT

The precise shaping of large astronomical mirrors is a technically demanding and usually very tedious job in which only a few companies worldwide have specialized; the best known are Zeiss in Oberkochen / Württemberg, Schott in Mainz , both of which are companies of the Carl-Zeiss Foundation , and the Russian manufacturer LZOS . You can also do the mirror grinding yourself up to a diameter of 50 to 60 cm .

After the glass melt has been produced and the mirror has been cast (the specialist for this is the Schott company in Mainz), the blank must slowly cool down. B. took over a year with the 5 m mirror of Mount Palomar , and with the 6 m mirror of the BTA-6 almost failed. The glass-ceramic materials used today, such as Borofloat , Pyrex , Cervit, Sital, Zerodur, are less sensitive to thermal stresses , but it was only when they were manufactured in rotary furnaces, which already give the melt a parabolic shape, that larger mirrors up to a diameter of 8 were made , 4 m . Even larger mirrors than these are composed of individual hexagonal segments.

After the melt has cooled down, the glass blank is subjected to an initial inspection and checked for its freedom from streaks in the glass. Then it gets its shape by grinding , which mostly corresponds to a spherical segment or a paraboloid .

### Grinding and polishing the main mirror

The art of mirror grinding can be learned for mirrors up to about 60 cm in diameter in courses that are already regularly offered by astro clubs and public observatories . The grinding is carried out with increasingly finer carborundum and grinding powder with increasingly better adaptation to the ideal shape, which is assessed using our own test methods . With larger mirrors, this process is automated and carried out by large programmable robots.

The mirror receives the final refinement of its shape through polishing . Since the beginning of 1990 an alternative process developed by the Kodak company has been available for this purpose, so-called ion beam milling or ion beam figuring. Finally, the mirror is vaporized with one or more reflective layers made of aluminum and covered with a final protective layer, usually made of SiO 2 . This gives the mirror a reflectivity of up to 96%. The final optical tolerance for amateur telescopes is at least λ / 4 ("lambda quarter") of the wavelength used, but is usually set at λ / 8 or even below λ / 10 despite the higher costs . Professional observatories have even higher demands, which in addition to the larger mirror diameters also entails additional effort .

The first real functional test is the so-called first light , the first recording of a well-suited and mostly known celestial body or a galaxy . A successful recording is popularly published and finds great interest in many media - e. B. in October 2005 the Milky Way-like spiral galaxy NGC 891 from the first light of the Large Binocular Telescope . This test is then followed by further, often lengthy, adjustment work on the main and secondary mirrors until the telescope can begin its full function after about a year.

If the optics exceed certain error tolerances , they must be reworked. The one from the Hubble space telescope got through the media, but in addition to the installation of corrective optics, it was also a test of the ability of astronauts to work with demanding repairs.

Alignment laser in the focuser

Smaller amateur telescopes, which are often transported and subject to significant temperature fluctuations, have to be readjusted regularly. This applies in particular to Newtonian telescopes and the easiest way to do this is with a battery-operated laser and a marking in the middle of the main mirror (the mirror must be removed once for this).

The tube of the Newtonian telescope is aligned so that the focuser points upwards. The alignment laser is inserted without clamping into the focuser or the reducing sleeve visible in the photo and then the secondary mirror is adjusted so that the laser beam hits the marking in the center of the main mirror. After loosening the lock nuts (main mirror), the adjusting screws of the main mirror are adjusted so that the laser reflects in itself. For this, the laser has a focusing screen with a small hole in the middle. If the red laser beam falls through the hole again (it can no longer be seen on the screen) the telescope is adjusted. Finally, the main mirror is fixed with the lock nuts.

## Resolving power

The diffraction of light limits the resolving power of a reflecting telescope. A point-shaped observation object (star) is not depicted as a point, but as a diffraction disk . The theoretical resolving power of a mirror telescope, i.e. the minimum angle between two objects that can just be separated, depends on the diameter of the main mirror ( aperture ) and the wavelength of the light received . Two neighboring stars can be resolved if their diffraction disks do not overlap too much. The Dawes criterion (angle in radians ) applies approximately : ${\ displaystyle \ alpha}$${\ displaystyle D}$ ${\ displaystyle \ lambda}$

${\ displaystyle \ alpha = {\ lambda \ over D}}$

In order to reduce image errors, the mirrors must be machined very precisely. The mirror is ground and polished to 1/4 to 1/20 of the light wavelength, i.e. with an accuracy of 150 to 30 nm .

In practice, however, the ability to resolve is very limited by seeing , which is mainly caused by turbulence and other movements in the earth's atmosphere . Due to seeing, the achievable resolution in visible light is typically around 1 to 2 arc seconds on the European mainland, which corresponds to the theoretical resolution of a 12 cm mirror. Seeing can be considerably cheaper in other regions of the world. The best value ever measured is 0.18 arc seconds in the Atacama Desert on the Paranal in northern Chile . The image quality is also influenced by dust , stray light from cities - so-called light pollution - and the amount of water vapor in the air; In the near infrared , water vapor in the atmosphere in particular interferes with the observation, since it attenuates the corresponding wavelengths of light very strongly. Large telescopes are therefore usually set up far away from human settlements in dry regions on high mountains in order to obtain the best possible resolution.

With adaptive optics , new devices are increasingly able to use the higher resolution of large optics. Either a known point-like object such as a bright star is used as a reference or a laser is used to stimulate sodium , which comes from micrometeorites that burn up in the earth's atmosphere, to glow in the upper earth's atmosphere at an altitude of about 90 km and thus a artificial guiding star with known shape created. Computer programs then evaluate the image of this guiding star generated by the telescope many times per second (sometimes more than 1000 times per second) and bend an additional correction mirror with adjustable control elements so that the distortions caused by the air are compensated as far as possible. As a result, the objects to be observed in the same region are also sharply imaged up to the theoretical limit of resolution.

## Designs

A large number of different designs have been developed which differ in the number and configuration of the optical elements. You optimize the structure with regard to different, partly contradicting criteria:

• large aperture ,
• large angle of view ,
• small overall dimension,
• easy to manufacture optical surfaces,
• easy assembly and operation.

No suitable reflective material is known for the short wavelengths of X-rays . Instead, Wolter telescopes use total reflection at a small angle of incidence, which results in a different structural design. For sound waves, however, the same arrangement can be used as for light, which is implemented in concave mirror microphones . Radio telescopes are also designed according to the same principles as a reflector telescope.

Known types of reflector telescopes with their beam paths are listed in the following table.

designation property Schematic representation
Newton telescope Parabolic or spherical primary mirror, planar deflecting mirror,
simple structure
Nasmyth telescope flat tertiary mirror, can be used in Cassegrain or other designs, typically to connect external measuring equipment
Herschel telescope Free of obstruction (the entrance opening is not covered by the secondary mirror)
Cassegrain telescope Concave main mirror / convex secondary mirror:
1. parabolic / hyperbolic
2. Ellipsoid / spherical
3. spherical / ellipsoid
4. hyperbolic / hyperbolic
Gregory telescope Parabolic primary mirror / concave ellipsoidal secondary mirror
Schmidt telescope
also Schmidt camera
aspherical corrective lens ,
spherical primary mirror,
very large field of view, but aperture of <1.35 m limited by the corrective lens.
Only suitable as a camera with internal focus (Schmidt camera); In the case of instruments with a long focal length, the convergent beam can also be guided out through a hole in the main mirror for visual observation (see Schmidt-Cassegrain telescope.)
Baker-Nunn camera Similar to the Schmidt camera, apochromatic corrector made of three aspherical lenses,
spherical main mirror,
extremely large field of view of 30 °, focal
ratio of 1: 1 at 50 cm aperture,
only suitable as a camera due to the internal focus
Schmidt-Cassegrain telescope aspherical correction lens, spherical primary mirror, spherical secondary mirror
Schwarzschild telescope ,
Couder telescope
Aplanat , flat picture
Anastigmat , but convex picture
Maksutov Telescope
or Maksutov-Cassegrain Telescope
Spherical, meniscus-shaped correction lens ,
spherical main mirror,
aperture of <1 m limited by the correction lens
Lurie Houghton Telescope Concave and convex spherical correction lens,
spherical main mirror
, aperture of <1 m limited by the correction lens
Klevtsov telescope spherical primary mirror,
spherical subaperture corrective lens
and spherical Mangin secondary mirror
Cutter-Schiefspiegler
Yolo-Schiefspiegler
small aperture ratio with a comparatively compact design,
obstruction-free

When building very large telescopes, e.g. B. ESO's Very Large Telescope or the Hubble Space Telescope (HST), the Ritchey-Chrétien-Cassegrain system has established itself . In the case of telescopes with diameters of more than 10 m, spherical primary mirrors are increasingly used again due to the lower production costs, but more complex secondary optics. Examples are the Hobby Eberly Telescope , the Southern African Large Telescope and the Overwhelmingly Large Telescope, which was followed until 2005 . The use of Nasmyth tertiary mirrors is also common in order to switch the beam path between different measuring platforms.

To carry and move large telescopes you need mounts . These must have a load-bearing capacity and stability corresponding to the size of the telescope, in particular also with temperature fluctuations. In order to be able to track the apparent movement of the stars in only one axis, an equatorial mount must be aligned with the celestial pole . The tracking is then carried out manually or by motor. In the case of the larger reflector telescopes, however, the simpler azimuthal mountings have prevailed for reasons of cost, but these require tracking in both axes, resulting in a further disadvantage of image field rotation . Precise control options are required for photographs (long exposures) .

## Precautions in observing the sun

A suitable solar filter must be used when observing the sun through a telescope . Sun filters that are attached to the eyepiece usually do not offer sufficient protection, as they can burst or melt under the great heat load. The solar filter should therefore be attached in front of the opening of the telescope. Alternatively, the sun can also be projected onto a white screen, but this is not advisable for all telescopes (heat load in the eyepiece).

## literature

Commons : reflecting telescopes  - collection of images, videos and audio files
Wiktionary: Reflector telescope  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. cf. GALEX , ALEXIS and STEREO . With ALEXIS and STEREO, observations down to 13 or 17 nm are possible: The sun is recorded at different wavelengths in the EUV .
2. Archived copy ( memento of the original dated February 23, 2007 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
3. L. d. Vinci: Codex Arundul , 1512
4. a b c J. Sant: Reflecting on History (Engl.).
5. Cesare Marsili: Un certo Messer Giovanni il quale pretende, doppo la morte d'in Mess. Cesare Caravaggi Bolognese ... , letter, 1626 (ital.)
6. Bartolomeo Imperiali: Il motivo di Vostra Signoria di non aver voluto accettar la riconciliazione del Padre Oratio Grassi ... , letter, 1626 (Italian).
7. Bonaventura Cavalieri: Lo specchio ustorio ouero trattato delle settioni coniche , 1632 (ital.)
8. Marin Marsenne: Harmonie universelle , S. Cramoisy (Paris), 1636–1637, pp. 59–63 (French) (N. Zucchius constructed a copy in 1652).
9. James Gregory, Optica Promota , Londini, 1663 (lat.) ( Translated into English by Ian Bruce ), built by Robert Hooke 1674, Royal Society.
10. Newton, to Accompt of a New Catadioptrical Telescope Invented by Mr. Newton ... Philosophical Transactions, Royal Society, pp 4004-4010, Vol. 7, 1672.
11. ^ A. Rupert Hall, ADC Simpson, An Account of the Royal Society's Newton Telescope , Notes and Records of the Royal Society of London Vol. 50, Number 1/1996.
12. ^ Henry C. King: The History of the Telescope , 2003 (Eng.)
13. E. Hagen, H. Rubens : The reflectivity of metals and coated glass mirrors , Annalen der Physik, pp. 352-375, Vol. 306, 1900
14. ^ RN Wilson, Karl Schwarzschild and Telescope Optics , Reviews in Modern Astronomy, Vol. 7, p. 1-30, 1994, bibcode : 1994RvMA .... 7 .... 1W
15. New Technology Telescope ( Memento of the original from September 30, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. .
16. A Short History of Armagh Observatory ( Memento of the original from January 25, 2010 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
17. Hans Jürgen Kärcher: The Art of Holding Lenses and Mirrors , Stars and Space, March 2012.
18. Alan Adler: Microflexing (PDF; 558 kB) ( Memento from March 19, 2013 in the Internet Archive ) , Sky & Telescope , November 2000.
19. Transition from spherical to parabolic mirrors, analysis of "Kelly's Method" using FEM ( Memento from October 20, 2001 in the Internet Archive ) (English)
20. GR Lemaitre: A Three Reflection Sky Survey at Dome-C with active optics modified-Rumsey telescope (en; PDF; 1.5 MB).
21. Interactive program for the design of Newtonian telescopes , calculates optimal diaphragm arrangements ( baffles ), eng.
22. James E. Gunn et al .: The 2.5 m Telescope of the Sloan Digital Sky Survey , p. 63 arxiv : astro-ph / 0602326
23. ^ RE Pressman: An Experimental Compound Reflecting Telescope . In: Journal of the British Astronomical Association . 57, 1947, p. 224.
24. J. Texereau: Commission des Instruments: 80e et 81e séances . In: L'Astronomie . 68, 1954, p. 387. bibcode : 1954LAstr..68..387T .