Ritchey–Chrétien telescope

A Ritchey–Chrétien telescope (or RCT) is a specialized Cassegrain telescope invented in the early 20th century that has a hyperbolic primary mirror and a hyperbolic secondary mirror designed to eliminate optical errors (coma). They have large field of view free of optical errors compared to a more conventional reflecting telescope configuration. Since the mid 20th century most large professional research telescopes have been Ritchey–Chrétien configurations.

1 History
2 Mirror parameters
3 Examples of large Ritchey–Chrétien telescopes
4 Commercial instruments
5 See also
6 References

History

The Ritchey–Chrétien telescope was invented in the early 1910s by American astronomer George Willis Ritchey and French astronomer Henri Chrétien. Ritchey constructed the first successful RCT, which had a diameter aperture of 60 cm (24 in) in 1927 (e.g. Ritchey 24-inch reflector). The second RCT was a 102 cm (40 in) instrument constructed by Ritchey for the United States Naval Observatory; that telescope is still in operation at the Naval Observatory Flagstaff Station.

The Ritchey–Chrétien design is free of third-order coma and spherical aberration,^[1] although it does suffer from fifth-order coma, severe large-angle astigmatism, and comparatively severe field curvature.^[2] When focused midway between the sagittal and tangential focusing planes, stars are imaged as circles, making the RCT well suited for wide field and photographic observations. As with the other Cassegrain-configuration reflectors, the RCT has a very short optical tube assembly and compact design for a given focal length. The RCT offers good off-axis optical performance, but examples are relatively rare due to the high cost of hyperbolic primary mirror fabrication; Ritchey–Chrétien configurations are most commonly found on high-performance professional telescopes.

Mirror parameters

The radii of curvature of the primary and secondary mirrors, respectively, in a two-mirror Cassegrain configuration are

$R_1 = -\frac{2DF}{F - B}$

and

$R_2 = -\frac{2DB}{F - B - D}$

where

$F$ is the effective focal length of the system,
$B$ is the back focal length (the distance from the secondary to the focus), and
$D$ is the distance between the two mirrors.

If, instead of $B$ and $D$ , the known quantities are the focal length of the primary mirror, $f_1$ , and the distance to the focus behind the primary mirror, $b$ , then $D = f_1(F - b)/(F %2B f_1)$ and $B = D %2B b$ .

For a Ritchey–Chrétien system, the conic constants $K_1$ and $K_2$ of the two mirrors are chosen so as to eliminate third-order spherical aberration and coma; the solution is

$K_1 = -1 - \frac{2}{M^3}\cdot\frac{B}{D}$

and

$K_2 = -1 - \frac{2}{(M-1)^3}\left(M(2M-1)%2B\frac{B}{D}\right)$

where $M = F/f_1 = (F-B)/D$ is the secondary magnification.^[3] Note that $K_1$ and $K_2$ are less than $-1$ (since $M>1$ ), so both mirrors are hyperbolic. (The primary mirror is typically quite close to being parabolic, however.)

The hyperbolic curvatures are difficult to test, especially with equipment typically available to amateur telescope makers or laboratory-scale fabricators; thus, older telescope layouts predominate in these applications. However, professional optics fabricators and large research groups test their mirrors with interferometers. A Ritchey–Chrétien then requires minimal additional equipment, typically a small optical device called a null corrector that makes the hyperbolic primary look spherical for the interferometric test. On the Hubble Space Telescope, this device was built incorrectly (a reflection from an un-intended surface leading to an incorrect measurement of lens position) leading to the error in the Hubble primary mirror.^[4] Incorrect null correctors have led to other mirror fabrication errors as well, such as in the New Technology Telescope.

Examples of large Ritchey–Chrétien telescopes

The 10.4 m Gran Telescopio Canarias at Roque de los Muchachos Observatory
The two 10.0 m telescopes of the Keck Observatory
The four 8.2 m telescopes comprising the Very Large Telescope in Chile
The 8.2 m Subaru telescope at Mauna Kea Observatory
The two 8.0 m telescopes comprising the Gemini Observatory
The 4.1 m Visible and Infrared Survey Telescope for Astronomy at the Paranal Observatory (Chile)
The 3.9 m Anglo-Australian Telescope at Siding Spring Observatory (Australia)
The 3.58 meter New Technology Telescope at the European Southern Observatory.
The 3.5 m Calar Alto Observatory telescope at mount Calar Alto (Spain)
The 3.5 m Herschel Space Observatory currently operating in orbit at the L2 point 1.5 million km from Earth
The 3.50 m WIYN Observatory at Kitt Peak National Observatory
The 2.56 m effective f/11 Nordic Optical Telescope on La Palma, Canary Islands.
The 2.50 m Sloan Digital Sky Survey telescope (modified design) at Apache Point Observatory, New Mexico, U.S.A.
The 2.4 m Hubble Space Telescope currently in orbit around the Earth
The 2.2 m Calar Alto Observatory telescope at mount Calar Alto (Spain)
The 2.1 m San Pedro Martir Observatory telescope at Baja California (Mexico)
The 2.0 m telescope at Rozhen Observatory
The 2.0 m Himalayan Chandra Telescope of the Indian Astronomical Observatory, Hanle, India
The 1.8 m Pan-STARRS telescopes at Haleakala on Maui, Hawaii
The 1.6 m Mont-Mégantic Observatory telescope on Mont-Mégantic in Quebec, Canada
The 1.3 m telescope at Skinakas Observatory, Crete, Greece
The 1.0 m Ritchey Telescope at the United States Naval Observatory Flagstaff Station (the final telecope made by G. Ritchey before his death).
The 85 cm Spitzer Space Telescope, infrared space telescope currently operating in Earth-trailing orbit
The 56 cm (22 inch) SDAA telescope at Tierra del Sol Observatory

Ritchey intended the 100 inch Hooker telescope and the 200-inch (5 m) Hale Telescope to be RCTs. His designs would have provided sharper images over a larger usable field of view compared to the parabolic designs actually used. However, Ritchey and Hale had a falling out. With the 100 inch project already late and over budget, Hale refused to adopt the new design, with its hard-to-test curvatures, and Ritchey left the project. Both projects were then built with traditional optics. Since then, advances in optical measurement^[5] and fabrication^[6] have allowed the RCT design to take over - the Hale telescope turned out to be the last world-leading telescope to have a parabolic primary mirror.^[7]

Commercial instruments

Examples of manufacturers catering for the advanced amateur astronomer market include Alluna Optics, Astrosib, Deep Sky Instruments, Guan Sheng Optical, Officina Stellare, Optical Guidance Systems, RC Optical Systems and Takahashi. In about 2009, Astro-Tech corporation introduced a line of significantly less expensive Ritchey–Chrétien telescopes Astro-Tech.

References

^ Sacek, Vladimir (14 July 2006). "Classical and aplanatic two-mirror systems". Notes on Amateur Telescope Optics. http://www.telescope-optics.net/classical_and_aplanatic.htm. Retrieved 2010-04-24.
^ Rutten, Harrie; van Venrooij, Martin (2002). Telescope Optics. Willmann-Bell. p. 67. ISBN 0943396182.
^ Smith, Warren J. (2008). Modern Optical Engineering (4th ed.). McGraw-Hill Professional. pp. 508–510. ISBN 978-0071476874.
^ Allen, Lew; et al. (1990). The Hubble Space Telescope Optical Systems Failure Report. NASA. NASA-TM-103443. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19910003124_1991003124.pdf.
^ Burge, J.H. (1993). Advanced Techniques for Measuring Primary Mirrors for Astronomical Telescopes. Ph.D. Thesis, University of Arizona. http://www.optics.arizona.edu/loft/Publications/Dissertations/1993_James_Burge.pdf.
^ Wilson, R.N. (1996). Reflecting Telescope Optics I. Basic Design Theory and its Historical Development. 1. Springer-Verlag: Berlin, Heidelberg, New York. P. 454
^ Zirker, J.B. (2005). An acre of glass: a history and forecast of the telescope. Johns Hopkins Univ Press. , p. 317.