![Cassegrain](https://upload.wikimedia.org/wikipedia/commons/2/2c/Cassegrain.en.png)
The Cassegrain reflector is a combination of a primary
concave mirror and a secondary
convex mirror, often used in
optical telescope
An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through elect ...
s and
radio antenna
In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an ...
s, the main characteristic being that the optical path folds back onto itself, relative to the optical system's primary mirror entrance aperture. This design puts the
focal point at a convenient location behind the
primary mirror
A primary mirror (or primary) is the principal light-gathering surface (the objective) of a reflecting telescope.
Description
The primary mirror of a reflecting telescope is a spherical or parabolic shaped disks of polished reflective meta ...
and the convex secondary adds a
telephoto
A telephoto lens, in photography and cinematography, is a specific type of a long-focus lens in which the physical length of the lens is shorter than the focal length. This is achieved by incorporating a special lens group known as a ''telephoto ...
effect creating a much longer
focal length in a mechanically short system.
In a symmetrical Cassegrain both mirrors are aligned about the
optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light propaga ...
, and the primary mirror usually contains a hole in the center, thus permitting the light to reach an
eyepiece
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through the device. The ...
, a
camera
A camera is an optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), with a ...
, or an
image sensor
An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves (as they pass through or reflect off objects) into signals, small bursts of c ...
. Alternatively, as in many radio telescopes, the final focus may be in front of the primary. In an asymmetrical Cassegrain, the mirror(s) may be tilted to avoid obscuration of the primary or to avoid the need for a hole in the primary mirror (or both).
The classic Cassegrain configuration uses a
parabolic reflector
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface gener ...
as the primary while the secondary mirror is
hyperbolic
Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.
The following phenomena are described as ''hyperbolic'' because they ...
. Modern variants may have a hyperbolic primary for increased performance (for example, the
Ritchey–Chrétien design); and either or both mirrors may be spherical or elliptical for ease of manufacturing.
The Cassegrain reflector is named after a published
reflecting telescope
A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternati ...
design that appeared in the April 25, 1672 ''
Journal des sçavans'' which has been attributed to
Laurent Cassegrain
Laurent Cassegrain (; – 1 September 1693) was a Catholic priest who is notable as the probable inventor of the Cassegrain reflector, a folded two-mirror reflecting telescope design.
Biography
Laurent Cassegrain was born in the region of Char ...
. Similar designs using convex secondary mirrors have been found in the
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri ( la, Bonaventura Cavalerius; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of in ...
's 1632 writings describing burning mirrors and
Marin Mersenne's 1636 writings describing telescope designs.
James Gregory's 1662 attempts to create a reflecting telescope included a Cassegrain configuration, judging by a convex secondary mirror found among his experiments.
The Cassegrain design is also used in
catadioptric systems.
Cassegrain designs
"Classic" Cassegrain telescopes
The "classic" Cassegrain has a parabolic primary mirror and a hyperbolic secondary mirror that reflects the light back down through a hole in the primary. Folding the optics makes this a compact design. On smaller telescopes, and camera lenses, the secondary is often mounted on an optically flat, optically clear glass plate that closes the telescope tube. This support eliminates the "star-shaped" diffraction effects caused by a straight-vaned support spider. The closed tube stays clean, and the primary is protected, at the cost of some loss of light-gathering power.
It makes use of the special properties of parabolic and hyperbolic reflectors. A concave
parabolic reflector
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface gener ...
will reflect all incoming light rays parallel to its axis of symmetry to a single point, the focus. A convex hyperbolic reflector has two foci and will reflect all light rays directed at one of its two foci towards its other focus. The mirrors in this type of telescope are designed and positioned so that they share one focus and so that the second focus of the hyperbolic mirror will be at the same point at which the image is to be observed, usually just outside the eyepiece. The parabolic mirror reflects parallel light rays entering the telescope to its focus, which is also the focus of the hyperbolic mirror. The hyperbolic mirror then reflects those light rays to its other focus, where the image is observed.
In most Cassegrain systems, the secondary mirror blocks a central portion of the aperture. This ring-shaped entrance aperture significantly reduces a portion of the
modulation transfer function (MTF) over a range of low spatial frequencies, compared to a full-aperture design such as a refractor or an offset Cassegrain. This MTF notch has the effect of lowering image contrast when imaging broad features. In addition, the support for the secondary (the spider) may introduce diffraction spikes in images.
The
radii of curvature of the primary and secondary mirrors, respectively, in the classic configuration are
:
and
:
where
*
is the effective
focal length of the system,
*
is the back focal length (the distance from the secondary to the focus),
*
is the distance between the two mirrors and
*
is the secondary magnification.
If, instead of
and
, the known quantities are the focal length of the primary mirror,
, and the distance to the focus behind the primary mirror,
, then
and
.
The
conic constant of the primary mirror is that of a parabola,
. Thanks to that there is no
spherical aberration introduced by the primary mirror. The secondary mirror, however, is of a hyperbolic shape with one focus coinciding with that of the primary mirror and the other focus being at the back focal length
. Thus, the classical Cassegrain has ideal focus for the chief ray (the center spot diagram is one point). We have,
:
,
where
:
.
Actually, as the conic constants should not depend on scaling, the formulae for both
and
can be greatly simplified and presented only as functions of the secondary magnification. Finally,
:
and
:
.
Ritchey-Chrétien
The Ritchey-Chrétien is a specialized Cassegrain reflector which has two hyperbolic mirrors (instead of a parabolic primary). It is free of
coma and
spherical aberration at a flat focal plane, making it well suited for wide field and photographic observations. It was invented by
George Willis Ritchey and
Henri Chrétien in the early 1910s. This design is very common in large professional research telescopes, including the
Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most vers ...
, the
Keck Telescopes, and the
Very Large Telescope
The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m acro ...
(VLT); it is also found in high-grade amateur telescopes.
Dall-Kirkham
The Dall-Kirkham Cassegrain telescope design was created by Horace Dall in 1928 and took on the name in an article published in ''
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
'' in 1930 following discussion between amateur astronomer Allan Kirkham and Albert G. Ingalls, the magazine's astronomy editor at the time. It uses a concave
elliptical
Elliptical may mean:
* having the shape of an ellipse, or more broadly, any oval shape
** in botany, having an elliptic leaf shape
** of aircraft wings, having an elliptical planform
* characterised by ellipsis (the omission of words), or by conc ...
primary mirror and a convex
spherical
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
secondary. While this system is easier to polish than a classic Cassegrain or Ritchey-Chretien system, the off-axis coma is significantly worse, so the image degrades quickly off-axis. Because this is less noticeable at longer
focal ratio
In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill Pro ...
s, Dall-Kirkhams are seldom faster than f/15.
Off-axis configurations
An unusual variant of the Cassegrain is the ''
Schiefspiegler'' telescope ("skewed" or "oblique reflector"; also known as the "Kutter telescope" after its inventor,
Anton Kutter
Anton Kutter (13 June 1903, in Biberach an der Riß – 1 February 1985, in Biberach) was a German film director and screenwriter. He studied mechanical engineering at Stuttgart Technical University.
In 1926 Kutter went to Cologne and joined ...
) which uses tilted mirrors to avoid the secondary mirror casting a shadow on the primary. However, while eliminating diffraction patterns this leads to several other aberrations that must be corrected.
Several different off-axis configurations are used for radio antennas.
Another off-axis, unobstructed design and variant of the Cassegrain is the '
Yolo' reflector invented by Arthur Leonard. This design uses a spherical or parabolic primary and a mechanically warped spherical secondary to correct for off-axis induced astigmatism. When set up correctly the Yolo can give uncompromising unobstructed views of planetary objects and non-wide field targets, with no lack of contrast or image quality caused by spherical aberration. The lack of obstruction also eliminates the diffraction associated with Cassegrain and Newtonian reflector astrophotography.
Catadioptric Cassegrains
Catadioptric Cassegrains use two mirrors, often with a spherical primary mirror to reduce cost, combined with refractive corrector element(s) to correct the resulting aberrations.
Schmidt-Cassegrain
The Schmidt-Cassegrain was developed from the wide-field
Schmidt camera
A Schmidt camera, also referred to as the Schmidt telescope, is a catadioptric astrophotographic telescope designed to provide wide fields of view with limited aberrations. The design was invented by Bernhard Schmidt in 1930.
Some notable e ...
, although the Cassegrain configuration gives it a much narrower field of view. The first optical element is a
Schmidt corrector plate
A Schmidt camera, also referred to as the Schmidt telescope, is a catadioptric astrophotographic telescope designed to provide wide fields of view with limited aberrations. The design was invented by Bernhard Schmidt in 1930.
Some notable e ...
. The plate is
figured by placing a vacuum on one side, and grinding the exact correction required to correct the
spherical aberration caused by the spherical primary mirror. Schmidt-Cassegrains are popular with amateur astronomers. An early Schmidt-Cassegrain camera was patented in 1946 by artist/architect/physicist
Roger Hayward
Roger Hayward (1899 – October 11, 1979) was an American artist, architect, optical designer and astronomer. He is the inventor of an early Schmidt-Cassegrain camera that was patented in 1945. He was born on January 7, 1899, to mother, artist I ...
, with the film holder placed outside the telescope.
Maksutov-Cassegrain
The Maksutov-Cassegrain is a variation of the
Maksutov telescope
The Maksutov (also called a "Mak") is a catadioptric telescope design that combines a spherical mirror with a weakly negative meniscus lens in a design that takes advantage of all the surfaces being nearly "spherically symmetrical". The negative ...
named after the
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...
/
Russia
Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eig ...
n
optician and
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
Dmitri Dmitrievich Maksutov
Dmitry Dmitrievich Maksutov (russian: Дми́трий Дми́триевич Максу́тов) ( – 12 August 1964) was a Russian / Soviet optical engineer and amateur astronomer. He is best known as the inventor of the Maksutov telescope. ...
. It starts with an optically transparent corrector lens that is a section of a hollow sphere. It has a spherical primary mirror, and a spherical secondary that is usually a mirrored section of the corrector lens.
Argunov-Cassegrain
In the Argunov-Cassegrain telescope all optics are spherical, and the classical Cassegrain secondary mirror is replaced by a
sub-aperture corrector consisting of three air spaced lens elements. The element farthest from the primary mirror is a
Mangin mirror
In optics, a Mangin mirror is a negative meniscus lens with the reflective surface on the rear side of the glass forming a curved mirror that reflects light without spherical aberration if certain conditions are met. This reflector was invented i ...
, which acts as a secondary mirror.
Klevtsov-Cassegrain
The Klevtsov-Cassegrain, like the Argunov-Cassegrain, uses a sub-aperture corrector consisting of a small meniscus lens and a Mangin mirror as its "secondary mirror".
New optical systems for small-size telescopes
/ref>
Cassegrain radio antennas
Cassegrain designs are also utilized in satellite telecommunication earth station
A ground station, Earth station, or Earth terminal is a terrestrial radio station designed for extraplanetary telecommunication with spacecraft (constituting part of the ground segment of the spacecraft system), or reception of radio waves fr ...
antennas and radio telescopes, ranging in size from 2.4 metres to 70 metres. The centrally located sub-reflector serves to focus radio frequency signals in a similar fashion to optical telescopes.
An example of a cassegrain radio antenna is the 70-meter dish at JPL's Goldstone antenna complex. For this antenna, the final focus is in front of the primary, at the top of the pedestal protruding from the mirror.
See also
* Catadioptric system
* Celestron
Celestron is an American company based in Torrance, California, United States, that manufactures telescopes and distributes telescopes, binoculars, spotting scopes, microscopes, and accessories manufactured by its parent company, the Synta Technol ...
(Schmidt–Cassegrains, Maksutov Cassegrains)
* List of telescope types
The following are lists of devices categorized as types of telescopes or devices associated with telescopes. They are broken into major classifications with many variations due to professional, amateur, and commercial sub-types. Telescopes can be ...
* Meade Instruments
The Meade Instruments (also shortened to Meade) is an American multinational company headquartered in Watsonville, California, that manufactures, imports, and distributes telescopes, binoculars, spotting scopes, microscopes, CCD cameras, and te ...
(Schmidt–Cassegrains, Maksutov Cassegrains)
* Questar (Maksutov Cassegrains)
* Refracting telescope
A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spyglasses and a ...
* Vixen
Foxes are small to medium-sized, omnivorous mammals belonging to several genera of the family Canidae. They have a flattened skull, upright, triangular ears, a pointed, slightly upturned snout, and a long bushy tail (or ''brush'').
Twelve sp ...
(Cassegrains, Klevtsov–Cassegrain)
References
External links
* {{Commons category inline
Antennas (radio)
Radio frequency propagation
Radio frequency antenna types
Telescope types