Reflecting telescope

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Stratospheric Observatory for Infrared Astronomy SOFIA 2.5M Primary Mirror.jpg
Stratospheric Observatory for Infrared Astronomy
24 inch convertible Newtonian/Cassegrain reflecting telescope on display at the Franklin Institute Franklin reflector 24.jpg
24 inch convertible Newtonian/Cassegrain reflecting telescope on display at the Franklin Institute

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 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. Reflecting telescopes come in many design variations and may 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.

Contents

From the time of Newton to the 1800s, the mirror itself was made of metal  usually speculum metal. This type included Newton's first designs and even the largest telescopes of the 19th century, the Leviathan of Parsonstown with a 1.8 meter wide metal mirror. In the 19th century a new method using a block of glass coated with very thin layer of silver began to become more popular by the turn of the century. A major turning point in reflecting telescopes was the Paris Observatory 1.2 m of 1878, A.A. Common telescopes which led to the Crossley and Harvard reflecting telescopes, which helped establish a better reputation for reflecting telescopes as the metal mirror designs were noted for their drawbacks. Chiefly the metal mirrors only reflected about 2/3 of the light and the metal would tarnish. After multiple polishings and tarnishings the mirror could lose its precise figuring needed.

Reflecting telescopes became extraordinarily popular for astronomy and many famous telescopes such as the Hubble Space Telescope and popular amateur models use this design. In addition, the reflection telescope principle was applied to other wavelengths of light, and for example, X-Ray telescopes also use the reflection principle to make image forming optics.

History

A replica of Newton's second reflecting telescope that he presented to the Royal Society in 1672 NewtonsTelescopeReplica.jpg
A replica of Newton's second reflecting telescope that he presented to the Royal Society in 1672
The great telescope of Birr, the Leviathan of Parsonstown. Modern day remnants of the mirror and support structure. Great Telescope, Birr, Offaly 1.jpg
The great telescope of Birr, the Leviathan of Parsonstown. Modern day remnants of the mirror and support structure.

The idea that curved mirrors behave like lenses dates back at least to Alhazen's 11th century treatise on optics, works that had been widely disseminated in Latin translations in early modern Europe. [1] Soon after the invention of the refracting telescope, Galileo, Giovanni Francesco Sagredo, and others, spurred on by their knowledge of the principles of curved mirrors, discussed the idea of building a telescope using a mirror as the image forming objective. [2] There were reports that the Bolognese Cesare Caravaggi had constructed one around 1626 and the Italian professor Niccolò Zucchi, in a later work, wrote that he had experimented with a concave bronze mirror in 1616, but said it did not produce a satisfactory image. [2] The potential advantages of using parabolic mirrors, primarily reduction of spherical aberration with no chromatic aberration, led to many proposed designs for reflecting telescopes. [3] The most notable being James Gregory, who published an innovative design for a ‘reflecting’ telescope in 1663. It would be ten years (1673), before the experimental scientist Robert Hooke was able to build this type of telescope, which became known as the Gregorian telescope. [4] [5] [6]

Isaac Newton has been generally credited with building the first reflecting telescope in 1668. [7] It used a spherically ground metal primary mirror and a small diagonal mirror in an optical configuration that has come to be known as the Newtonian telescope.

Despite the theoretical advantages of the reflector design, the difficulty of construction and the poor performance of the speculum metal mirrors being used at the time meant it took over 100 years for them to become popular. Many of the advances in reflecting telescopes included the perfection of parabolic mirror fabrication in the 18th century, [8] silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century, [9] segmented mirrors to allow larger diameters, and active optics to compensate for gravitational deformation. A mid-20th century innovation was catadioptric telescopes such as the Schmidt camera, which use both a spherical mirror and a lens (called a corrector plate) as primary optical elements, mainly used for wide-field imaging without spherical aberration.

The late 20th century has seen the development of adaptive optics and lucky imaging to overcome the problems of seeing, and reflecting telescopes are ubiquitous on space telescopes and many types of spacecraft imaging devices.

Technical considerations

Gran Telescopio Canarias Gran Telescopio Canarias.jpg
Gran Telescopio Canarias

A curved primary mirror is the reflector telescope's basic optical element that creates an image at the focal plane. The distance from the mirror to the focal plane is called the focal length. Film or a digital sensor may be located here to record the image, or a secondary mirror may be added to modify the optical characteristics and/or redirect the light to film, digital sensors, or an eyepiece for visual observation.

The primary mirror in most modern telescopes is composed of a solid glass cylinder whose front surface has been ground to a spherical or parabolic shape. A thin layer of aluminum is vacuum deposited onto the mirror, forming a highly reflective first surface mirror.

Some telescopes use primary mirrors which are made differently. Molten glass is rotated to make its surface paraboloidal, and is kept rotating while it cools and solidifies. (See Rotating furnace.) The resulting mirror shape approximates a desired paraboloid shape that requires minimal grinding and polishing to reach the exact figure needed. [10]

Optical errors

Reflecting telescopes, just like any other optical system, do not produce "perfect" images. The need to image objects at distances up to infinity, view them at different wavelengths of light, along with the requirement to have some way to view the image the primary mirror produces, means there is always some compromise in a reflecting telescope's optical design.

An image of Sirius A and Sirius B by the Hubble Space Telescope, showing diffraction spikes and concentric diffraction rings. Sirius A and B Hubble photo.jpg
An image of Sirius A and Sirius B by the Hubble Space Telescope, showing diffraction spikes and concentric diffraction rings.

Because the primary mirror focuses light to a common point in front of its own reflecting surface almost all reflecting telescope designs have a secondary mirror, film holder, or detector near that focal point partially obstructing the light from reaching the primary mirror. Not only does this cause some reduction in the amount of light the system collects, it also causes a loss in contrast in the image due to diffraction effects of the obstruction as well as diffraction spikes caused by most secondary support structures. [11] [12]

The use of mirrors avoids chromatic aberration but they produce other types of aberrations. A simple spherical mirror cannot bring light from a distant object to a common focus since the reflection of light rays striking the mirror near its edge do not converge with those that reflect from nearer the center of the mirror, a defect called spherical aberration. To avoid this problem most reflecting telescopes use parabolic shaped mirrors, a shape that can focus all the light to a common focus. Parabolic mirrors work well with objects near the center of the image they produce, (light traveling parallel to the mirror's optical axis), but towards the edge of that same field of view they suffer from off axis aberrations: [13] [14]

There are reflecting telescope designs that use modified mirror surfaces (such as the Ritchey–Chrétien telescope) or some form of correcting lens (such as catadioptric telescopes) that correct some of these aberrations.

Use in astronomical research

Main mirror assembled at Goddard Space Flight Center, May 2016. James Webb Space Telescope Revealed (26832090085).jpg
Main mirror assembled at Goddard Space Flight Center, May 2016.

Nearly all large research-grade astronomical telescopes are reflectors. There are several reasons for this:

Reflecting telescope designs

Gregorian

Light path in a Gregorian telescope. Gregorian telescope.svg
Light path in a Gregorian telescope.

The Gregorian telescope , described by Scottish astronomer and mathematician James Gregory in his 1663 book Optica Promota, employs a concave secondary mirror that reflects the image back through a hole in the primary mirror. This produces an upright image, useful for terrestrial observations. Some small spotting scopes are still built this way. There are several large modern telescopes that use a Gregorian configuration such as the Vatican Advanced Technology Telescope, the Magellan telescopes, the Large Binocular Telescope, and the Giant Magellan Telescope.

Newtonian

Light path in a Newtonian telescope. Newtonian telescope2.svg
Light path in a Newtonian telescope.

The Newtonian telescope was the first successful reflecting telescope, completed by Isaac Newton in 1668. It usually has a paraboloid primary mirror but at focal ratios of f/8 or longer a spherical primary mirror can be sufficient for high visual resolution. A flat secondary mirror reflects the light to a focal plane at the side of the top of the telescope tube. It is one of the simplest and least expensive designs for a given size of primary, and is popular with amateur telescope makers as a home-build project.

The Cassegrain design and its variations

Light path in a Cassegrain telescope. Cassegrain Telescope.svg
Light path in a Cassegrain telescope.

The cassegrain telescope (sometimes called the "Classic Cassegrain") was first published in a 1672 design attributed to Laurent Cassegrain. It has a parabolic primary mirror, and a hyperbolic secondary mirror that reflects the light back down through a hole in the primary. The folding and diverging effect of the secondary mirror creates a telescope with a long focal length while having a short tube length.

Ritchey–Chrétien

The Ritchey–Chrétien telescope, invented by George Willis Ritchey and Henri Chrétien in the early 1910s, 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 nearly flat focal plane if the primary and secondary curvature are properly figured, making it well suited for wide field and photographic observations. [16] Almost every professional reflector telescope in the world is of the Ritchey–Chrétien design.

Three-mirror anastigmat

Including a third curved mirror allows correction of the remaining distortion, astigmatism, from the Ritchey–Chrétien design. This allows much larger fields of view.

Dall–Kirkham

The Dall–Kirkham Cassegrain telescope's 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 editor at the time. It uses a concave elliptical primary mirror and a convex spherical secondary. While this system is easier to grind than a classic Cassegrain or Ritchey–Chrétien system, it does not correct for off-axis coma. Field curvature is actually less than a classical Cassegrain. Because this is less noticeable at longer focal ratios, Dall–Kirkhams are seldom faster than f/15.

Off-axis designs

There are several designs that try to avoid obstructing the incoming light by eliminating the secondary or moving any secondary element off the primary mirror's optical axis, commonly called off-axis optical systems.

Herschelian

Light paths
Herschel-Lomonosov reflecting telescope.svg
Herschelian telescope
Off-axis optical telescope diagram.svg
Schiefspiegler telescope

The Herschelian reflector is named after William Herschel, who used this design to build very large telescopes including the 40-foot telescope in 1789. In the Herschelian reflector the primary mirror is tilted so the observer's head does not block the incoming light. Although this introduces geometrical aberrations, Herschel employed this design to avoid the use of a Newtonian secondary mirror since the speculum metal mirrors of that time tarnished quickly and could only achieve 60% reflectivity. [17]

Schiefspiegler

A variant of the Cassegrain, the Schiefspiegler telescope ("skewed" or "oblique reflector") uses tilted mirrors to avoid the secondary mirror casting a shadow on the primary. However, while eliminating diffraction patterns this leads to an increase in coma and astigmatism. These defects become manageable at large focal ratios — most Schiefspieglers use f/15 or longer, which tends to restrict useful observation to the Moon and planets. A number of variations are common, with varying numbers of mirrors of different types. The Kutter (named after its inventor Anton Kutter) style uses a single concave primary, a convex secondary and a plano-convex lens between the secondary mirror and the focal plane, when needed (this is the case of the catadioptric Schiefspiegler). One variation of a multi-schiefspiegler uses a concave primary, convex secondary and a parabolic tertiary. One of the interesting aspects of some Schiefspieglers is that one of the mirrors can be involved in the light path twice — each light path reflects along a different meridional path.

Stevick-Paul

Stevick-Paul telescopes [18] are off-axis versions of Paul 3-mirror systems [19] with an added flat diagonal mirror. A convex secondary mirror is placed just to the side of the light entering the telescope, and positioned afocally so as to send parallel light on to the tertiary. The concave tertiary mirror is positioned exactly twice as far to the side of the entering beam as was the convex secondary, and its own radius of curvature distant from the secondary. Because the tertiary mirror receives parallel light from the secondary, it forms an image at its focus. The focal plane lies within the system of mirrors, but is accessible to the eye with the inclusion of a flat diagonal. The Stevick-Paul configuration results in all optical aberrations totaling zero to the third-order, except for the Petzval surface which is gently curved.

Yolo

The Yolo was developed by Arthur S. Leonard in the mid-1960s. [20] Like the Schiefspiegler, it is an unobstructed, tilted reflector telescope. The original Yolo consists of a primary and secondary concave mirror, with the same curvature, and the same tilt to the main axis. Most Yolos use toroidal reflectors. The Yolo design eliminates coma, but leaves significant astigmatism, which is reduced by deformation of the secondary mirror by some form of warping harness, or alternatively, polishing a toroidal figure into the secondary. Like Schiefspieglers, many Yolo variations have been pursued. The needed amount of toroidal shape can be transferred entirely or partially to the primary mirror. In large focal ratios optical assemblies, both primary and secondary mirror can be left spherical and a spectacle correcting lens is added between the secondary mirror and the focal plane (catadioptric Yolo). The addition of a convex, long focus tertiary mirror leads to Leonard's Solano configuration. The Solano telescope doesn't contain any toric surfaces.

Liquid-mirror telescopes

One design of telescope uses a rotating mirror consisting of a liquid metal in a tray that is spun at constant speed. As the tray spins, the liquid forms a paraboloidal surface of essentially unlimited size. This allows making very big telescope mirrors (over 6 metres), but unfortunately they cannot be steered, as they always point vertically.

Focal planes

Prime focus

A prime focus telescope design. The observer/camera is at the focal point (shown as a red X). Prime focus telescope.svg
A prime focus telescope design. The observer/camera is at the focal point (shown as a red X).

In a prime focus design no secondary optics are used, the image is accessed at the focal point of the primary mirror. At the focal point is some type of structure for holding a film plate or electronic detector. In the past, in very large telescopes, an observer would sit inside the telescope in an "observing cage" to directly view the image or operate a camera. [21] Nowadays CCD cameras allow for remote operation of the telescope from almost anywhere in the world. The space available at prime focus is severely limited by the need to avoid obstructing the incoming light. [22]

Radio telescopes often have a prime focus design. The mirror is replaced by a metal surface for reflecting radio waves, and the observer is an antenna.

Cassegrain focus

Cassegrain design Cassegrain-Teleskop.svg
Cassegrain design

For telescopes built to the Cassegrain design or other related designs, the image is formed behind the primary mirror, at the focal point of the secondary mirror. An observer views through the rear of the telescope, or a camera or other instrument is mounted on the rear. Cassegrain focus is commonly used for amateur telescopes or smaller research telescopes. However, for large telescopes with correspondingly large instruments, an instrument at Cassegrain focus must move with the telescope as it slews; this places additional requirements on the strength of the instrument support structure, and potentially limits the movement of the telescope in order to avoid collision with obstacles such as walls or equipment inside the observatory.

Nasmyth and coudé focus

Nasmyth/coude light path. Nasmyth-Telescope.svg
Nasmyth/coudé light path.

Nasmyth

The Nasmyth design is similar to the Cassegrain except the light is not directed through a hole in the primary mirror; instead, a third mirror reflects the light to the side of the telescope to allow for the mounting of heavy instruments. This is a very common design in large research telescopes. [23]

Coudé

Adding further optics to a Nasmyth-style telescope to deliver the light (usually through the declination axis) to a fixed focus point that does not move as the telescope is reoriented gives a coudé focus (from the French word for elbow). [24] The coudé focus gives a narrower field of view than a Nasmyth focus [24] and is used with very heavy instruments that do not need a wide field of view. One such application is high-resolution spectrographs that have large collimating mirrors (ideally with the same diameter as the telescope's primary mirror) and very long focal lengths. Such instruments could not withstand being moved, and adding mirrors to the light path to form a coudé train, diverting the light to a fixed position to such an instrument housed on or below the observing floor (and usually built as an unmoving integral part of the observatory building) was the only option. The 60-inch Hale telescope (1.5 m), Hooker Telescope, 200-inch Hale Telescope, Shane Telescope, and Harlan J. Smith Telescope all were built with coudé foci instrumentation. The development of echelle spectrometers allowed high-resolution spectroscopy with a much more compact instrument, one which can sometimes be successfully mounted on the Cassegrain focus. Since inexpensive and adequately stable computer-controlled alt-az telescope mounts were developed in the 1980s, the Nasmyth design has generally supplanted the coudé focus for large telescopes.

Fibre-fed spectrographs

For instruments requiring very high stability, or that are very large and cumbersome, it is desirable to mount the instrument on a rigid structure, rather than moving it with the telescope. Whilst transmission of the full field of view would require a standard coudé focus, spectroscopy typically involves the measurement of only a few discrete objects, such as stars or galaxies. It is therefore feasible to collect light from these objects with optical fibers at the telescope, placing the instrument at an arbitrary distance from the telescope. Examples of fiber-fed spectrographs include the planet-hunting spectrographs HARPS [25] or ESPRESSO. [26]

Additionally, the flexibility of optical fibers allow light to be collected from any focal plane; for example, the HARPS spectrograph utilises the Cassegrain focus of the ESO 3.6 m Telescope, [25] whilst the Prime Focus Spectrograph is connected to the prime focus of the Subaru telescope. [27]

See also

Related Research Articles

Ritchey–Chrétien 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.

History of the telescope Aspect of history

The history of the telescope can be traced to before the invention of the earliest known telescope, which appeared in 1608 in the Netherlands, when a patent was submitted by Hans Lippershey, an eyeglass maker. Although Lippershey did not receive his patent, news of the invention soon spread across Europe. The design of these early refracting telescopes consisted of a convex objective lens and a concave eyepiece. Galileo improved on this design the following year and applied it to astronomy. In 1611, Johannes Kepler described how a far more useful telescope could be made with a convex objective lens and a convex eyepiece lens. By 1655, astronomers such as Christiaan Huygens were building powerful but unwieldy Keplerian telescopes with compound eyepieces.

Spherical aberration Optical aberration

Spherical aberration (SA) is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non-spherical curved surfaces. 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.

Optical telescope Telescope for observations with visible light

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 view, or to make a photograph, or to collect data through electronic image sensors.

Schmidt corrector plate

A Schmidt corrector plate is an aspheric lens which corrects the spherical aberration introduced by the spherical primary mirror of the Schmidt or Schmidt-Cassegrain telescope designs. It was invented by Bernhard Schmidt in 1931, although it may have been independently invented by Finnish astronomer Yrjö Väisälä in 1924. Schmidt originally introduced it as part of a wide-field photographic catadioptric telescope, the Schmidt camera. It is now used in several other telescope designs, camera lenses and image projection systems that utilise a spherical primary mirror.

Newtonian telescope

The Newtonian telescope, also called the Newtonian reflector or just the Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton (1642–1727), 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.

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.

Focus (optics) A point in an optical system where light rays originating from a point on the object converge

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 worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures.

Catadioptric system 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.

Maksutov telescope

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 Russian 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.

Schmidt–Cassegrain 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.

Cassegrain reflector

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.

Schmidt–Newtonian telescope

A Schmidt–Newtonian telescope or Schmidt–Newton telescope is a catadioptric telescope that combines elements from both the Schmidt camera and the Newtonian telescope. In this telescope design, a spherical primary mirror is combined with a Schmidt corrector plate, which corrects the spherical aberration and holds the secondary mirror. The resulting system has less coma and diffraction effects than a Newtonian telescope with a parabolic mirror and a "spider" secondary mirror support. The design uses a 45° flat secondary mirror to view the image, as in a standard Newtonian telescope.

The Gregorian telescope is a type of reflecting telescope designed by Scottish mathematician and astronomer James Gregory in the 17th century, and first built in 1673 by Robert Hooke. James Gregory was a contemporary of Isaac Newton. Both often worked simultaneously on similar projects. Gregory's design was published in 1663 and pre-dates the first practical reflecting telescope, the Newtonian telescope, built by Sir Isaac Newton in 1668. However, Gregory's design was only a theoretical description, and he never actually constructed the telescope. It was not successfully built until five years after Newton's first reflecting telescope.

Telescope Optical instrument that makes distant objects appear magnified

A telescope is an optical instrument using lenses, curved mirrors, or a combination of both to observe distant objects, or various devices used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. The first known practical telescopes were refracting telescopes invented in the Netherlands at the beginning of the 17th century, by using glass lenses. They were used for both terrestrial applications and astronomy.

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. This reflector was invented in 1876 by a French officer Alphonse Mangin as an improved catadioptric reflector for search lights and is also used in other optical devices.

Klevtsov–Cassegrain telescope

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.

Meniscus corrector

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.

References

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  20. Arthur S. Leonard THE YOLO REFLECTOR
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  25. 1 2 "HARPS Instrument Description".
  26. "ESPRESSO Instrument Description".
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