Cassegrain reflector

Last updated March 17, 2024

Light path in a Cassegrain reflecting telescope Cassegrain.en.png — Light path in a Cassegrain reflecting telescope

The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas, 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 and the convex secondary adds a telephoto effect creating a much longer focal length in a mechanically short system.^[1]

In a symmetrical Cassegrain both mirrors are aligned about the optical axis, and the primary mirror usually contains a hole in the center, thus permitting the light to reach an eyepiece, a camera, or an image sensor. 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 as the primary while the secondary mirror is hyperbolic.^[2] 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 design that appeared in the April 25, 1672 Journal des sçavans which has been attributed to Laurent Cassegrain.^[3] Similar designs using convex secondary mirrors have been found in the Bonaventura Cavalieri's 1632 writings describing burning mirrors^[4]^[5] and Marin Mersenne's 1636 writings describing telescope designs.^[6] James Gregory's 1662 attempts to create a reflecting telescope included a Cassegrain configuration, judging by a convex secondary mirror found among his experiments.^[7]

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 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.^[8] 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

R_{1}=-{\frac {2DF}{F-B}}=-{\frac {2F}{M}}

and

R_{2}=-{\frac {2DB}{F-B-D}}=-{\frac {2B}{M-1}}

where

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

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 $D=f_{1}(F-b)/(F+f_{1})$ and $B=D+b$ .

The conic constant of the primary mirror is that of a parabola, $K_{1}=-1$ . 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 $B$ . Thus, the classical Cassegrain has ideal focus for the chief ray (the center spot diagram is one point). We have,

K_{2}=-1-\alpha -{\sqrt {\alpha (\alpha +2)}}

,

where

\alpha ={\frac {1}{2}}\left[{\frac {4DBM}{(F+BM-DM)(F-B-D)}}\right]^{2}

.

Actually, as the conic constants should not depend on scaling, the formulae for both $\alpha$ and $K_{2}$ can be greatly simplified and presented only as functions of the secondary magnification. Finally,

\alpha ={\frac {8M^{2}}{(M^{2}-1)^{2}}}

and

K_{2}=-1-{\frac {4M}{(M-1)^{2}}}=-\left({\frac {M+1}{M-1}}\right)^{2}

.

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 Keck Telescopes, and the Very Large Telescope (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 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 primary mirror and a convex spherical 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 ratios, 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 ^[9]) 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.^[10]

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

Light path in a Schmidt-Cassegrain

Light path in a Maksutov-Cassegrain

Light path in a Klevtsov-Cassegrain telescope

The Schmidt-Cassegrain was developed from the wide-field Schmidt camera, although the Cassegrain configuration gives it a much narrower field of view. The first optical element is a Schmidt corrector plate. 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,^[11] with the film holder placed outside the telescope.

Maksutov-Cassegrain

The Maksutov-Cassegrain is a variation of the Maksutov telescope named after the Soviet/Ukrainian optician and astronomer Dmitri Dmitrievich Maksutov. 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, 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".^[12]

Cassegrain radio antennas

Cassegrain designs are also utilized in satellite telecommunication earth station 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.

Related Research Articles

In telecommunications and radar, a Cassegrain antenna is a parabolic antenna in which the feed antenna is mounted at or behind the surface of the concave main parabolic reflector dish and is aimed at a smaller convex secondary reflector suspended in front of the primary reflector. The beam of radio waves from the feed illuminates the secondary reflector, which reflects it back to the main reflector dish, which reflects it forward again to form the desired beam. The Cassegrain design is widely used in parabolic antennas, particularly in large antennas such as those in satellite ground stations, radio telescopes, and communication satellites.

A parabolicreflector 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 generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave travelling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis.

<span class="mw-page-title-main">Ritchey–Chrétien telescope</span> Specialized Cassegrain telescope

A Ritchey–Chrétien telescope is a specialized variant of the Cassegrain telescope that has a hyperbolic primary mirror and a hyperbolic secondary mirror designed to eliminate off-axis optical errors (coma). The RCT has a wider field of view free of optical errors compared to a more traditional reflecting telescope configuration. Since the mid 20th century, a majority of large professional research telescopes have been Ritchey–Chrétien configurations; some well-known examples are the Hubble Space Telescope, the Keck telescopes and the ESO Very Large Telescope.

A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves. The most common form is shaped like a dish and is popularly called a dish antenna or parabolic dish. The main advantage of a parabolic antenna is that it has high directivity. It functions similarly to a searchlight or flashlight reflector to direct radio waves in a narrow beam, or receive radio waves from one particular direction only. Parabolic antennas have some of the highest gains, meaning that they can produce the narrowest beamwidths, of any antenna type. In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used, so parabolic antennas are used in the high frequency part of the radio spectrum, at UHF and microwave (SHF) frequencies, at which the wavelengths are small enough that conveniently sized reflectors can be used.

In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. The effect of spherical aberration was first identified by Ibn al-Haytham who discussed it in his work Kitāb al-Manāẓir.

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 electronic image sensors.

A reflecting telescope 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 alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.

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.

In geometrical optics, a focus, also called an image point, is a point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's aperture. Aberrations tend to worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures.

$<span class="mw-page-title-main">Catadioptric system</span> Optical system where refraction and reflection are combined$

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric", such as surveillance catadioptric sensors.

The Maksutov 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 lens is usually full diameter and placed at the entrance pupil of the telescope. The design corrects the problems of off-axis aberrations such as coma found in reflecting telescopes while also correcting chromatic aberration. It was patented in 1941 by Soviet optician Dmitri Dmitrievich Maksutov. Maksutov based his design on the idea behind the Schmidt camera of using the spherical errors of a negative lens to correct the opposite errors in a spherical primary mirror. The design is most commonly seen in a Cassegrain variation, with an integrated secondary, that can use all-spherical elements, thereby simplifying fabrication. Maksutov telescopes have been sold on the amateur market since the 1950s.

<span class="mw-page-title-main">Schmidt–Cassegrain telescope</span> Type of catadioptric telescope

The Schmidt–Cassegrain is a catadioptric telescope that combines a Cassegrain reflector's optical path with a Schmidt corrector plate to make a compact astronomical instrument that uses simple spherical surfaces.

Vixen is a Japanese company that makes telescopes, binoculars, spotting scopes and accessories for their products.

<span class="mw-page-title-main">Curved mirror</span> Mirror with a curved reflecting surface

A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex or concave. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical lenses, suffer from spherical aberration. Distorting mirrors are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances.

The Houghton telescope or Lurie–Houghton telescope is a catadioptric telescope. Houghton's original design uses a two-lens corrector at the front of the telescope and a spherical mirror at the back; it was patented in 1944. Instead of the hard to make intricately shaped compound curve Schmidt corrector plate, or the heavy Maksutov-type meniscus corrector lens, the Houghton double-lens corrector is relatively easy to make.

The Klevtsov–Cassegrain telescope is a type of catadioptric Cassegrain telescope that uses a spherical primary mirror and a sub-aperture secondary corrector group composed of a small lens and a Mangin mirror.

A meniscus corrector is a negative meniscus lens that is used to correct spherical aberration in image-forming optical systems such as catadioptric telescopes. It works by having the equal but opposite spherical aberration of the objective it is designed to correct.

<span class="mw-page-title-main">Yebes Observatory RT40m</span>

The Yebes Observatory RT40m, or ARIESXXI, is a radio telescope which is part of the observatory at Yebes, Spain. It is a 40-metre Cassegrain–Nasmyth telescope.

References

↑ Wilson, Raymond N. (2013). Reflecting Telescope Optics I: Basic Design Theory and its Historical Development. Springer Science & Business Media. pp. 43–44. ISBN 978-3-662-30863-9.
↑ "Diccionario de astronomía y geología. Las ciencias de la Tierra y del Espacio al alcance de todos. Cassegrain". AstroMía.
↑ Baranne, André; Launay, Françoise (1997). "Cassegrain: un célèbre inconnu de l'astronomie instrumentale" [Cassegrain: a famous unknown of instrumental astronomy]. Journal of Optics (in French). 28 (4): 158–172. doi:10.1088/0150-536X/28/4/004.
↑ Lo specchio ustorio, overo, Trattato delle settioni coniche
↑ Stargazer, the Life and Times of the Telescope, by Fred Watson, p. 134
↑ Stargazer, p. 115.
↑ Stargazer, pp. 123 and 132
↑ "THE EFFECTS OF APERTURE OBSTRUCTION".
↑ .telescopemaking.org - The Kutter Schiefspiegler Archived February 19, 2009, at the Wayback Machine
↑ Milligan, T.A. (2005). Modern antenna design. Wiley-IEEE Press. ISBN 0-471-45776-0. pp. 424-429
↑ US Patent 2,403,660, Schmidt-Cassegrain camera
↑ New optical systems for small-size telescopes

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[1] Wilson, Raymond N. (2013). Reflecting Telescope Optics I: Basic Design Theory and its Historical Development. Springer Science & Business Media. pp. 43–44. ISBN 978-3-662-30863-9.

[2] "Diccionario de astronomía y geología. Las ciencias de la Tierra y del Espacio al alcance de todos. Cassegrain". AstroMía.

[3] Baranne, André; Launay, Françoise (1997). "Cassegrain: un célèbre inconnu de l'astronomie instrumentale" [Cassegrain: a famous unknown of instrumental astronomy]. Journal of Optics (in French). 28 (4): 158–172. doi:10.1088/0150-536X/28/4/004.

[4] Lo specchio ustorio, overo, Trattato delle settioni coniche

[5] Stargazer, the Life and Times of the Telescope, by Fred Watson, p. 134

[6] Stargazer, p. 115.

[7] Stargazer, pp. 123 and 132

[8] "THE EFFECTS OF APERTURE OBSTRUCTION".

[9] .telescopemaking.org - The Kutter Schiefspiegler Archived February 19, 2009, at the Wayback Machine

[10] Milligan, T.A. (2005). Modern antenna design. Wiley-IEEE Press. ISBN 0-471-45776-0. pp. 424-429

[11] US Patent 2,403,660, Schmidt-Cassegrain camera

[12] New optical systems for small-size telescopes

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