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An optical telescope is a
telescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
that gathers and
focuses light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
mainly from the
visible
Visibility, in meteorology, is a measure of the distance at which an object or light can be seen.
Visibility may also refer to:
* A measure of turbidity in water quality control
* Interferometric visibility, which quantifies interference contrast ...
part of the
electromagnetic spectrum
The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.
The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
, to create a
magnified image for direct visual inspection, to make a
photograph
A photograph (also known as a photo, image, or picture) is an image created by light falling on a photosensitive surface, usually photographic film or an electronic image sensor, such as a CCD or a CMOS chip. Most photographs are now create ...
, or to collect data through electronic
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 ...
s.
There are three primary types of optical telescope:
*
Refracting telescope
A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens (optics), lens as its objective (optics), objective to form an image (also referred to a dioptrics, dioptric telescope). The refracting telescope d ...
s, which use
lenses
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
and less commonly also
prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
s (
dioptrics
Dioptrics is the branch of optics dealing with refraction, similarly the branch dealing with mirrors is known as catoptrics. Dioptrics is the study of the refraction of light, especially by lenses. Telescopes that create their image with an obj ...
)
*
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 ...
s, which use
mirror
A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the ...
s (
catoptrics
Catoptrics (from grc-gre, κατοπτρικός ''katoptrikós'', "specular", from grc-gre, κάτοπτρον ''katoptron'' "mirror") deals with the phenomena of reflected light and image-forming optical systems using mirrors. A catoptric s ...
)
*
Catadioptric telescopes, which combine lenses and mirrors
An optical telescope's ability to resolve small details is directly related to the diameter (or
aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An opt ...
) of its
objective
Objective may refer to:
* Objective (optics), an element in a camera or microscope
* ''The Objective'', a 2008 science fiction horror film
* Objective pronoun, a personal pronoun that is used as a grammatical object
* Objective Productions, a Brit ...
(the primary lens or mirror that collects and focuses the light), and its light-gathering power is related to the area of the objective. The larger the objective, the more light the telescope collects and the finer detail it resolves.
People use optical telescopes (including
monocular
A monocular is a compact refracting telescope used to magnify images of distant objects, typically using an optical prism to ensure an erect image, instead of using relay lenses like most telescopic sights. The volume and weight of a monocul ...
s and
binoculars) for
outdoor activities
Outdoor recreation or outdoor activity refers to recreation done outside, most commonly in natural settings. The activities that encompass outdoor recreation vary depending on the physical environment they are being carried out in. These activiti ...
such as
observational astronomy
Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical ...
,
ornithology
Ornithology is a branch of zoology that concerns the "methodological study and consequent knowledge of birds with all that relates to them." Several aspects of ornithology differ from related disciplines, due partly to the high visibility and th ...
,
pilotage
Piloting or pilotage is the process of navigating on water or in the air using fixed points of reference on the sea or on land, usually with reference to a nautical chart or aeronautical chart to obtain a fix of the position of the vessel or air ...
,
hunting
Hunting is the human activity, human practice of seeking, pursuing, capturing, or killing wildlife or feral animals. The most common reasons for humans to hunt are to harvest food (i.e. meat) and useful animal products (fur/hide (skin), hide, ...
and
reconnaissance
In military operations, reconnaissance or scouting is the exploration of an area by military forces to obtain information about enemy forces, terrain, and other activities.
Examples of reconnaissance include patrolling by troops (skirmisher ...
, as well as indoor/semi-outdoor activities such as
watching performance art
Performance art is an artwork or art exhibition created through actions executed by the artist or other participants. It may be witnessed live or through documentation, spontaneously developed or written, and is traditionally presented to a pu ...
s and
spectator sport
A spectator sport is a sport that is characterized by the presence of spectators, or watchers, at its competitions. Spectator sports may be professional sports or amateur sports. They often are distinguished from participant sports, which are m ...
s.
History
The telescope is more a discovery of optical craftsmen than an invention of a scientist.
The
lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
and the properties of refracting and reflecting light had been known since
antiquity, and theory on how they worked was developed by ancient
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
philosophers, preserved and expanded on in the
medieval Islamic world, and had reached a significantly advanced state by the time of the telescope's invention in
early modern Europe
Early modern Europe, also referred to as the post-medieval period, is the period of European history between the end of the Middle Ages and the beginning of the Industrial Revolution, roughly the late 15th century to the late 18th century. Histori ...
. But the most significant step cited in the invention of the telescope was the development of lens manufacture for
spectacles
Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples o ...
,
first in Venice and Florence in the thirteenth century, and later in the spectacle making centers in both the
Netherlands
)
, anthem = ( en, "William of Nassau")
, image_map =
, map_caption =
, subdivision_type = Sovereign state
, subdivision_name = Kingdom of the Netherlands
, established_title = Before independence
, established_date = Spanish Netherl ...
and Germany. It is in the Netherlands in 1608 where the first documents describing a
refracting optical telescope surfaced in the form of a patent filed by spectacle maker
Hans Lippershey
Hans Lipperhey (circa 1570 – buried 29 September 1619), also known as Johann Lippershey or Lippershey, was a German- Dutch spectacle-maker. He is commonly associated with the invention of the telescope, because he was the first one who tried to ...
, followed a few weeks later by claims by
Jacob Metius Jacob (Jacobus; sometimes James) Metius (after 1571–1628) was a Dutch instrument-maker and a specialist in grinding lenses. He is primarily known for the patent application he made for an optical telescope in October 1608, a few weeks after ...
, and a third unknown applicant, that they also knew of this "art".
Word of the invention spread fast and
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, on hearing of the device, was making his own improved designs within a year and was the first to publish astronomical results using a telescope. Galileo's telescope used a convex
objective lens
In optical engineering, the objective is the optical element that gathers light from the object being observed and focuses the light rays to produce a real image. Objectives can be a single lens or mirror, or combinations of several optical elem ...
and a concave
eye lens
The lens, or crystalline lens, is a transparent biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina. By changing shape, it functions to change the focal length of the eye so that it can ...
, a design is now called a
Galilean 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 ...
.
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
proposed an improvement on the design that used a convex
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 ...
, often called the
Keplerian 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 as ...
.
The next big step in the development of refractors was the advent of the
Achromatic lens
An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane.
The most comm ...
in the early 18th century, which corrected the
chromatic aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...
in Keplerian telescopes up to that time—allowing for much shorter instruments with much larger objectives.
For
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 ...
s, which use a
curved mirror
A curved mirror is a mirror with a curved reflecting surface. The surface may be either ''convex'' (bulging outward) or ''concave'' (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are ...
in place of the objective lens, theory preceded practice. The theoretical basis for
curved mirrors
A curved mirror is a mirror with a curved reflecting surface. The surface may be either ''convex'' (bulging outward) or ''concave'' (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are ...
behaving similar to lenses was probably established by
Alhazen
Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
, whose theories had been widely disseminated in Latin translations of his work. Soon after the invention of the refracting telescope, Galileo,
Giovanni Francesco Sagredo
Giovanni Francesco Sagredo (1571– 5 March 1620) was a Venetian mathematician and close friend of Galileo. He was also a friend and correspondent of English scientist William Gilbert.S. P. Thompson (1903) ''The Geographical Journal'' vol 2 ...
, and others, spurred on by their knowledge that curved mirrors had similar properties to lenses, discussed the idea of building a telescope using a mirror as the image forming objective. The potential advantages of using
parabolic mirrors (primarily a reduction of
spherical aberration with elimination of
chromatic aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...
) led to several proposed designs for reflecting telescopes, the most notable of which was published in 1663 by
James Gregory and came to be called the
Gregorian telescope, but no working models were built.
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
has been generally credited with constructing the first practical reflecting telescopes, the
Newtonian 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. Newto ...
, in 1668
although due to their difficulty of construction and the poor performance of the
speculum metal
Speculum metal is a mixture of around two-thirds copper and one-third tin, making a white brittle alloy that can be polished to make a highly reflective surface. It was used historically to make different kinds of mirrors from personal grooming ...
mirrors used it took over 100 years for reflectors to become popular. Many of the advances in reflecting telescopes included the perfection of
parabolic mirror
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a Mirror, 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 ge ...
fabrication in the 18th century, silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century,
segmented mirror
A segmented mirror is an array of smaller mirrors designed to act as segments of a single large curved mirror. The segments can be either spherical or asymmetric (if they are part of a larger parabolic reflector). They are used as objectives for ...
s to allow larger diameters, and
active optics to compensate for gravitational deformation. A mid-20th century innovation was
catadioptric
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, ...
telescopes such as the
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 ...
, which uses both a lens (corrector plate) and mirror as primary optical elements, mainly used for wide field imaging without spherical aberration.
The late 20th century has seen the development of
adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
and
space telescope
A space telescope or space observatory is a telescope in outer space used to observe astronomical objects. Suggested by Lyman Spitzer in 1946, the first operational telescopes were the American Orbiting Astronomical Observatory, OAO-2 launch ...
s to overcome the problems of
astronomical seeing
In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing var ...
.
The electronics revolution of the early 21st century led to the development of computer-connected telescopes in the 2010s that allow non-professional skywatchers to observe stars and satellites using relatively low-cost equipment by taking advantage of
digital astrophotographic techniques developed by professional astronomers over previous decades. An electronic connection to a computer (
smartphone
A smartphone is a portable computer device that combines mobile telephone and computing functions into one unit. They are distinguished from feature phones by their stronger hardware capabilities and extensive mobile operating systems, whic ...
,
pad, or laptop) is
required to make astronomical observations from the telescopes. The digital technology allows
multiple images to be stacked while subtracting the noise component of the observation producing images of
Messier objects
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters'').
Because Messier was only in ...
and
faint stars as dim as an
apparent magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...
of 15 with consumer-grade equipment.
Principles
The basic scheme is that the primary light-gathering element, the
objective
Objective may refer to:
* Objective (optics), an element in a camera or microscope
* ''The Objective'', a 2008 science fiction horror film
* Objective pronoun, a personal pronoun that is used as a grammatical object
* Objective Productions, a Brit ...
(1) (the
convex lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...
or
concave mirror used to gather the incoming light), focuses that light from the distant object (4) to a focal plane where it forms a
real image (5). This image may be recorded or viewed through 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 ...
(2), which acts like a
magnifying glass. The eye (3) then sees an inverted,
magnified virtual image
In optics, an ''image'' is defined as the collection of focus points of light rays coming from an object. A '' real image'' is the collection of focus points made by converging rays, while a virtual image is the collection of focus points ma ...
(6) of the object.
Inverted images
Most telescope designs produce an inverted image at the focal plane; these are referred to as ''inverting telescopes''. In fact, the image is both turned upside down and reversed left to right, so that altogether it is rotated by 180 degrees from the object orientation. In astronomical telescopes the rotated view is normally not corrected, since it does not affect how the telescope is used. However, a mirror diagonal is often used to place the eyepiece in a more convenient viewing location, and in that case the image is erect, but still reversed left to right. In terrestrial telescopes such as
spotting scope
A spotting scope is a compact high-power telescope optimized for detailed observation of distant objects. They are used as portable optical enhancement devices for various outdoor activities such as birdwatching, skygazing and other naturali ...
s,
monocular
A monocular is a compact refracting telescope used to magnify images of distant objects, typically using an optical prism to ensure an erect image, instead of using relay lenses like most telescopic sights. The volume and weight of a monocul ...
s and
binoculars, prisms (e.g.,
Porro prism
In optics, a Porro prism, named for its inventor Ignazio Porro, is a type of ''reflection prism'' used in optical instruments to alter the orientation of an image.
Description
It consists of a block of material shaped like a right geometric ...
s) or a relay lens between objective and eyepiece are used to correct the image orientation. There are telescope designs that do not present an inverted image such as the
Galilean refractor and the
Gregorian reflector. These are referred to as ''erecting telescopes''.
Design variants
Many types of telescope fold or divert the optical path with secondary or tertiary mirrors. These may be integral part of the optical design (
Newtonian 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. Newto ...
,
Cassegrain reflector or similar types), or may simply be used to place the eyepiece or detector at a more convenient position. Telescope designs may also use specially designed additional lenses or mirrors to improve image quality over a larger field of view.
Characteristics
Design specifications relate to the characteristics of the telescope and how it performs optically. Several properties of the specifications may change with the equipment or accessories used with the telescope; such as
Barlow lens
The Barlow lens, named after Peter Barlow, is a diverging lens which, used in series with other optics in an optical system, increases the effective focal length of an optical system as perceived by all components that are after it in the system. ...
es,
star diagonals and
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 ...
s. These interchangeable accessories don't alter the specifications of the telescope, however they alter the way the telescope's properties function, typically
magnification, apparent
field of view
The field of view (FoV) is the extent of the observable world that is seen at any given moment. In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation.
Human ...
(FOV) and actual field of view.
Surface resolvability
The smallest resolvable surface area of an object, as seen through an optical telescope, is the limited physical area that can be resolved. It is analogous to
angular resolution, but differs in definition: instead of separation ability between point-light sources it refers to the physical area that can be resolved. A familiar way to express the characteristic is the resolvable ability of features such as
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
craters or
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
spots. Expression using the formula is given by twice the resolving power
over aperture diameter
multiplied by the objects diameter
multiplied by the constant
all divided by the objects
apparent diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
.
''Resolving power
is derived from the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
using the same unit as aperture; where 550
nm to mm is given by:
.''
''The constant
is derived from
radians
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
to the same unit as the object's
apparent diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
; where the Moon's
apparent diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
of
radians
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
to
arcsecs is given by:
.''
An example using a telescope with an aperture of 130 mm observing the Moon in a 550
nm wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, is given by:
The unit used in the object diameter results in the smallest resolvable features at that unit. In the above example they are approximated in kilometers resulting in the smallest resolvable Moon craters being 3.22 km in diameter. 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 ...
has a primary mirror aperture of 2400 mm that provides a surface resolvability of Moon craters being 174.9 meters in diameter, or
sunspots of 7365.2 km in diameter.
Angular resolution
Ignoring blurring of the image by turbulence in the atmosphere (
atmospheric seeing
In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing var ...
) and optical imperfections of the telescope, the
angular resolution of an optical telescope is determined by the diameter of 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 ...
or lens gathering the light (also termed its "aperture").
The
Rayleigh criterion
Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. ...
for the resolution limit
(in
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
s) is given by
:
where
is the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
and
is the aperture. For
visible light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
(
= 550 nm) in the
small-angle approximation
The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians:
:
\begin
\sin \theta &\approx \theta \\
\cos \theta &\approx 1 - \ ...
, this equation can be rewritten:
:
Here,
denotes the resolution limit in
arcseconds and
is in millimeters.
In the ideal case, the two components of a
double star system can be discerned even if separated by slightly less than
. This is taken into account by the
Dawes limit
:
The equation shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is not given by the maximum
magnification (or "power") of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images.
For large ground-based telescopes, the resolution is limited by
atmospheric seeing
In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing var ...
. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloons and high-flying airplanes, or
in space
''In Space'' is the fourth and final studio album by American rock group Big Star, released in 2005. It was the first new studio recording by the band since '' Third/Sister Lovers'', which was recorded in 1974.
The album featured original Big ...
. Resolution limits can also be overcome by
adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
,
speckle imaging
Speckle imaging describes a range of high-resolution astronomical imaging techniques based on the analysis of large numbers of short exposures that freeze the variation of atmospheric turbulence. They can be divided into the shift-and-add ("'' ...
or
lucky imaging
Lucky imaging (also called lucky exposures) is one form of speckle imaging used for astrophotography. Speckle imaging techniques use a high-speed camera with exposure times short enough (100 ms or less) so that the changes in the Earth's a ...
for ground-based telescopes.
Recently, it has become practical to perform
aperture synthesis
Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection. At each separation and ...
with arrays of optical telescopes. Very high resolution images can be obtained with groups of widely spaced smaller telescopes, linked together by carefully controlled optical paths, but
these interferometers can only be used for imaging bright objects such as stars or measuring the bright cores of
active galaxies
An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not pr ...
.
Focal length and focal ratio
The
focal length of an
optical
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...
system is a measure of how strongly the system converges or diverges
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
. For an optical system in air, it is the distance over which initially
collimated
A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction p ...
rays are brought to a focus. A system with a shorter focal length has greater
optical power
In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the ...
than one with a long focal length; that is, it bends the
rays more strongly, bringing them to a focus in a shorter distance. In astronomy, the f-number is commonly referred to as the ''focal ratio'' notated as
. The
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 ...
of a telescope is defined as the focal length
of an
objective
Objective may refer to:
* Objective (optics), an element in a camera or microscope
* ''The Objective'', a 2008 science fiction horror film
* Objective pronoun, a personal pronoun that is used as a grammatical object
* Objective Productions, a Brit ...
divided by its diameter
or by the diameter of an aperture stop in the system. The focal length controls the field of view of the instrument and the scale of the image that is presented at the focal plane to 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 ...
, film plate, or
CCD.
An example of a telescope with a focal length of 1200 mm and aperture diameter of 254 mm is given by:
Numerically large
Focal ratios are said to be ''long'' or ''slow''. Small numbers are ''short'' or ''fast''. There are no sharp lines for determining when to use these terms, and an individual may consider their own standards of determination. Among contemporary astronomical telescopes, any telescope with a
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 ...
slower (bigger number) than f/12 is generally considered slow, and any telescope with a focal ratio faster (smaller number) than f/6, is considered fast. Faster systems often have more
optical aberrations
In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with th ...
away from the center of the field of view and are generally more demanding of eyepiece designs than slower ones. A fast system is often desired for practical purposes in
astrophotography
Astrophotography, also known as astronomical imaging, is the photography or imaging of astronomical objects, celestial events, or areas of the night sky. The first photograph of an astronomical object (the Moon) was taken in 1840, but it was no ...
with the purpose of gathering more
photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...
in a given time period than a slower system, allowing time lapsed
photography
Photography is the art, application, and practice of creating durable images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employed ...
to process the result faster.
Wide-field telescopes (such as
astrograph
An astrograph (or astrographic camera) is a telescope designed for the sole purpose of astrophotography. Astrographs are mostly used in wide-field astronomical surveys of the sky and for detection of objects such as asteroids, meteors, a ...
s), are used to track
satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope ...
s and
asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere.
...
s, for
cosmic-ray
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
research, and for
astronomical survey
An astronomical survey is a general map or image of a region of the sky (or of the whole sky) that lacks a specific observational target. Alternatively, an astronomical survey may comprise a set of images, spectra, or other observations of obje ...
s of the sky. It is more difficult to reduce
optical aberrations
In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with th ...
in telescopes with low f-ratio than in telescopes with larger f-ratio.
Light-gathering power
![KeckObservatory20071013](https://upload.wikimedia.org/wikipedia/commons/7/78/KeckObservatory20071013.jpg)
The light-gathering power of an optical telescope, also referred to as light grasp or aperture gain, is the ability of a telescope to collect a lot more light than the human eye. Its light-gathering power is probably its most important feature. The telescope acts as a ''light bucket'', collecting all of the photons that come down on it from a far away object, where a larger bucket catches more
photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...
resulting in more received light in a given time period, effectively brightening the image. This is why the pupils of your eyes enlarge at night so that more light reaches the retinas. The gathering power
compared against a human eye is the squared result of the division of the aperture
over the observer's pupil diameter
,
with an average adult having a
pupil
The pupil is a black hole located in the center of the Iris (anatomy), iris of the Human eye, eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing ...
diameter of 7 mm. Younger persons host larger diameters, typically said to be 9 mm, as the diameter of the pupil decreases with age.
An example gathering power of an aperture with 254 mm compared to an adult pupil diameter being 7 mm is given by:
Light-gathering power can be compared between telescopes by comparing the
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape
A shape or figure is a graphics, graphical representation of an obje ...
s
of the two different apertures.
As an example, the light-gathering power of a 10-meter telescope is 25x that of a 2-meter telescope:
For a survey of a given area, the field of view is just as important as raw light gathering power. Survey telescopes such as the
Large Synoptic Survey Telescope
The Vera C. Rubin Observatory, previously referred to as the Large Synoptic Survey Telescope (LSST), is an astronomical observatory currently under construction in Chile. Its main task will be carrying out a synoptic astronomical survey, the Le ...
try to maximize the product of mirror area and field of view (or
etendue
Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include a ...
) rather than raw light gathering ability alone.
Magnification
The magnification through a telescope makes an object appear larger while limiting the FOV. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world. At higher magnifications the image quality significantly reduces, usage of a
Barlow lens
The Barlow lens, named after Peter Barlow, is a diverging lens which, used in series with other optics in an optical system, increases the effective focal length of an optical system as perceived by all components that are after it in the system. ...
increases the effective focal length of an optical system—multiplies image quality reduction.
Similar minor effects may be present when using
star diagonals, as light travels through a multitude of lenses that increase or decrease effective focal length. The quality of the image generally depends on the quality of the optics (lenses) and viewing conditions—not on magnification.
Magnification itself is limited by optical characteristics. With any telescope or microscope, beyond a practical maximum magnification, the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called ''empty magnification''.
To get the most detail out of a telescope, it is critical to choose the right magnification for the object being observed. Some objects appear best at low power, some at high power, and many at a moderate magnification. There are two values for magnification, a minimum and maximum. A wider field of view
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 ...
may be used to keep the same eyepiece focal length whilst providing the same magnification through the telescope. For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction.
Visual
The visual magnification
of the field of view through a telescope can be determined by the telescope's focal length
divided by the
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 ...
focal length
(or diameter).
The maximum is limited by the focal length of the
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 ...
.
An example of visual
magnification using a telescope with a 1200 mm focal length and 3 mm
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 ...
is given by:
Minimum
There is a lowest usable
magnification on a telescope. The increase in brightness with reduced magnification has a limit related to something called the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
. The
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
is the cylinder of light coming out of the eyepiece, hence the lower the
magnification, the larger the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
. The minimum
can be calculated by dividing the telescope aperture
over the exit pupil diameter
.
Decreasing the magnification past this limit cannot increase brightness, at this limit there is no benefit for decreased magnification. Likewise calculating the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
is a division of the aperture diameter
and the visual magnification
used. The minimum often may not be reachable with some telescopes, a telescope with a very long focal length may require a ''longer-focal-length'' eyepiece than is possible.
An example of the lowest usable magnification using a 254 mm aperture and 7 mm
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
is given by:
, whilst the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
diameter using a 254 mm aperture and 36x
magnification is given by:
Optimum
A useful reference is:
*For small objects with low surface brightness (such as
galaxies), use a moderate magnification.
*For small objects with high surface brightness (such as
planetary nebulae
A planetary nebula (PN, plural PNe) is a type of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from red giant stars late in their lives.
The term "planetary nebula" is a misnomer because they are unrelated t ...
), use a high magnification.
*For large objects regardless of surface brightness (such as
diffuse nebulae
A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming region ...
), use low magnification, often in the range of minimum magnification.
Only personal experience determines the best optimum magnifications for objects, relying on observational skills and seeing conditions.
Field of view
Field of view is the extent of the observable world seen at any given moment, through an instrument (e.g., telescope or
binoculars), or by naked eye. There are various expressions of field of view, being a specification of 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 ...
or a characteristic determined from 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 ...
and telescope combination. A physical limit derives from the combination where the FOV cannot be viewed larger than a defined maximum, due to
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
of the optics.
Apparent
Apparent field of view (commonly referred to as AFOV) is the perceived angular size of the field stop of the
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 ...
, typically measured in
degrees. It is a fixed property of the eyepiece's optical design, with common commercially available eyepieces offering a range of apparent fields from 40° to 120°. The apparent field of view of an eyepiece is limited by a combination of the eyepiece's field stop diameter, and focal length, and is independent of magnification used.
In an eyepiece with a very wide apparent field of view, the observer may perceive that the view through the telescope stretches out to their
peripheral vision
Peripheral vision, or ''indirect vision'', is vision as it occurs outside the point of fixation, i.e. away from the center of gaze or, when viewed at large angles, in (or out of) the "corner of one's eye". The vast majority of the area in the ...
, giving a sensation that they are no longer looking through an eyepiece, or that they are closer to the subject of interest than they really are. In contrast, an eyepiece with a narrow apparent field of view may give the sensation of looking through a tunnel or small porthole window, with the black field stop of the eyepiece occupying most of the observer's vision.
A wider apparent field of view permits the observer to see more of the subject of interest (that is, a wider true field of view) without reducing magnification to do so. However, the relationship between true field of view, apparent field of view, and magnification is not direct, due to increasing distortion characteristics that correlate with wider apparent fields of view. Instead, both true field of view and apparent field of view are consequences of the eyepiece's field stop diameter.
Apparent field of view differs from true field of view in so far as true field of view varies with magnification, whereas apparent field of view does not. The wider field stop of a wide angle eyepiece permits the viewing of a wider section of the
real image formed at the telescope's focal plane, thus impacting the calculated true field of view.
An eyepiece's apparent field of view can influence total view brightness as perceived by the eye, since the apparent angular size of the field stop will determine how much of the observer's retina is illuminated by the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
formed by the eyepiece. However, apparent field of view has no impact on the apparent
surface brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ...
(that is, brightness per unit area) of objects contained within the field of view.
True
True FOV is the width of what is actually seen through any given eyepiece / telescope combination.
There are two formulae for calculating true field of view:
# Apparent field of view method given by
, where
is the true FOV,
is the apparent field of view of the eyepiece, and
is the magnification being used.
# Eyepiece field stop method given by
, where
is the true FOV,
is the eyepiece field stop diameter in millimeters and
is the focal length of the telescope in millimeters.
The eyepiece field stop method is more accurate than the apparent field of view method,
however not all eyepieces have an easily knowable field stop diameter.
Maximum
Max FOV is the maximum useful true field of view limited by the optics of the telescope. It is a physical limitation where increases beyond the maximum remain at maximum. Max FOV
is the barrel size
over the telescope's focal length
converted from
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
to degrees.
An example of max FOV using a telescope with a barrel size of 31.75 mm (1.25
inches
Measuring tape with inches
The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth") ...
) and focal length of 1200 mm is given by:
Observing through a telescope
There are many properties of optical telescopes and the complexity of observation using one can be a daunting task; experience and experimentation are the major contributors to understanding how to maximize one's observations. In practice, only two main properties of a telescope determine how observation differs: the focal length and aperture. These relate as to how the optical system views an object or range and how much light is gathered through an ocular
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 ...
. Eyepieces further determine how the field of view and
magnification of the observable world change.
Observable world
The observable world is what can be seen using a telescope. When viewing an object or range, the observer may use many different techniques. Understanding what can be viewed and how to view it depends on the field of view. Viewing an object at a size that fits entirely in the field of view is measured using the two telescope properties—focal length and aperture, with the inclusion of an ocular
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 ...
with suitable focal length (or diameter). Comparing the observable world and the
angular diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
of an object shows how much of the object we see. However, the relationship with the optical system may not result in high
surface brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ...
. Celestial objects are often dim because of their vast distance, and detail may be limited by
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
or unsuitable optical properties.
Field of view and magnification relationship
Finding what can be seen through the optical system begins with the
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 ...
providing the field of view and
magnification; the magnification is given by the division of the telescope and eyepiece focal lengths. Using an example of an amateur telescope such as a
Newtonian 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. Newto ...
with an aperture
of 130 mm (5") and focal length
of 650 mm (25.5 inches), one uses an eyepiece with a focal length
of 8 mm and apparent FOV
of 52°. The magnification at which the observable world is viewed is given by:
. The field of view
requires the magnification, which is formulated by its division over the apparent field of view:
. The resulting true field of view is 0.64°, not allowing an object such as the
Orion nebula, which appears elliptical with an
angular diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
of 65 × 60
arcminutes, to be viewable through the telescope in its entirety, where the whole of the
nebula
A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regio ...
is within the observable world. Using methods such as this can greatly increase one's viewing potential ensuring the observable world can contain the entire object, or whether to increase or decrease magnification viewing the object in a different aspect.
Brightness factor
The
surface brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ...
at such a magnification significantly reduces, resulting in a far dimmer appearance. A dimmer appearance results in less visual detail of the object. Details such as matter, rings, spiral arms, and gases may be completely hidden from the observer, giving a far less ''complete'' view of the object or range. Physics dictates that at the theoretical minimum magnification of the telescope, the surface brightness is at 100%. Practically, however, various factors prevent 100% brightness; these include telescope limitations (focal length,
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 ...
focal length, etc.) and the age of the observer.
Age plays a role in brightness, as a contributing factor is the observer's
pupil
The pupil is a black hole located in the center of the Iris (anatomy), iris of the Human eye, eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing ...
. With age the pupil naturally shrinks in diameter; generally accepted a young adult may have a 7 mm diameter pupil, an older adult as little as 5 mm, and a younger person larger at 9 mm. The
minimum magnification can be expressed as the division of the aperture
and
pupil
The pupil is a black hole located in the center of the Iris (anatomy), iris of the Human eye, eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing ...
diameter given by:
. A problematic instance may be apparent, achieving a theoretical surface brightness of 100%, as the required effective focal length of the optical system may require 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 ...
with too large a diameter.
Some telescopes cannot achieve the theoretical surface brightness of 100%, while some telescopes can achieve it using a very small-diameter eyepiece. To find what eyepiece is required to get
minimum magnification one can rearrange the magnification formula, where it is now the division of the telescope's focal length over the minimum magnification:
. An eyepiece of 35 mm is a non-standard size and would not be purchasable; in this scenario
to achieve 100% one would require a standard manufactured eyepiece size of 40 mm. As the eyepiece has a larger focal length than the minimum magnification, an abundance of wasted light is not received through the eyes.
Exit pupil
The limit to the increase in
surface brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ...
as one reduces magnification is the
exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compou ...
: a cylinder of light that projects out the eyepiece to the observer. An exit pupil must match or be smaller in diameter than one's
pupil
The pupil is a black hole located in the center of the Iris (anatomy), iris of the Human eye, eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing ...
to receive the full amount of projected light; a larger exit pupil results in the wasted light. The exit pupil
can be derived with from division of the telescope aperture
and the
minimum magnification , derived by:
. The pupil and exit pupil are almost identical in diameter, giving no wasted observable light with the optical system. A 7 mm pupil falls slightly short of 100% brightness, where the
surface brightness
In astronomy, surface brightness (SB) quantifies the apparent brightness or flux density per unit angular area of a spatially extended object such as a galaxy or nebula, or of the night sky background. An object's surface brightness depends on it ...
can be measured from the product of the constant 2, by the square of the pupil
resulting in:
. The limitation here is the pupil diameter; it's an unfortunate result and degrades with age. Some observable light loss is expected and decreasing the magnification cannot increase surface brightness once the system has reached its minimum usable magnification, hence why the term is referred to as ''usable''.
Image Scale
When using a CCD to record observations, the CCD is placed in the focal plane. Image scale (sometimes called ''plate scale'') is how the angular size of the object being observed is related to the physical size of the projected image in the focal plane
where
is the image scale,
is the angular size of the observed object, and
is the physical size of the projected image. In terms of focal length image scale is
where
is measured in radians per meter (rad/m), and
is measured in meters. Normally
is given in units of arcseconds per millimeter ("/mm). So if the focal length is measured in millimeters, the image scale is
The derivation of this equation is fairly straightforward and the result is the same for reflecting or refracting telescopes. However, conceptually it is easier to derive by considering a reflecting telescope. If an extended object with angular size
is observed through a telescope, then due to the
Laws of reflection
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ' ...
and
Trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...
the size of the image projected onto the focal plane will be
The image scale (angular size of object divided by size of projected image) will be
and by using the small angle relation
, when
(N.B. only valid if
is in radians), we obtain
Imperfect images
No telescope can form a perfect image. Even if a reflecting telescope could have a perfect mirror, or a refracting telescope could have a perfect lens, the effects of aperture diffraction are unavoidable. In reality, perfect mirrors and perfect lenses do not exist, so image
aberrations in addition to aperture diffraction must be taken into account. Image aberrations can be broken down into two main classes, monochromatic, and polychromatic. In 1857,
Philipp Ludwig von Seidel
Philipp Ludwig von Seidel (; 24 October 1821 in Zweibrücken, Germany – 13 August 1896 in Munich, German Empire) was a German mathematician. He was the son of Julie Reinhold and Justus Christian Felix Seidel.
Lakatos credits von Seidel with di ...
(1821–1896) decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.
The five Seidel aberrations
;
Spherical aberration : The difference in focal length between paraxial rays and marginal rays, proportional to the square of the objective diameter.
;
Coma
A coma is a deep state of prolonged unconsciousness in which a person cannot be awakened, fails to respond normally to painful stimuli, light, or sound, lacks a normal wake-sleep cycle and does not initiate voluntary actions. Coma patients exhi ...
: A defect by which points appear as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from the
optical sine theorem In optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visibl ...
.
;
Astigmatism
Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at n ...
: The image of a point forms focal lines at the sagittal and tangental foci and in between (in the absence of coma) an elliptical shape.
;
Petzval field curvature
Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis (or a non-flat object past the hyperfocal distance) cannot be brought properly into focus on a flat image pl ...
: The Petzval field curvature means that the image, instead of lying in a plane, actually lies on a curved surface, described as hollow or round. This causes problems when a flat imaging device is used e.g., a photographic plate or CCD image sensor.
;
Distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signa ...
: Either barrel or pincushion, a radial distortion that must be corrected when combining multiple images (similar to stitching multiple photos into a
panoramic photo).
Optical defects are always listed in the above order, since this expresses their interdependence as first order aberrations via moves of the exit/entrance pupils. The first Seidel aberration, Spherical Aberration, is independent of the position of the exit pupil (as it is the same for axial and extra-axial pencils). The second, coma, changes as a function of pupil distance and spherical aberration, hence the well-known result that it is impossible to correct the coma in a lens free of spherical aberration by simply moving the pupil. Similar dependencies affect the remaining aberrations in the list.
Chromatic aberrations
: Longitudinal
chromatic aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...
: As with spherical aberration this is the same for axial and oblique pencils.
: Transverse chromatic aberration (chromatic aberration of magnification)
Astronomical research telescopes
![Two Unit Telescopes VLT](https://upload.wikimedia.org/wikipedia/commons/9/9f/Two_Unit_Telescopes_VLT.jpg)
Optical telescopes have been used in astronomical research since the time of their invention in the early 17th century. Many types have been constructed over the years depending on the optical technology, such as refracting and reflecting, the nature of the light or object being imaged, and even where they are placed, such as
space telescope
A space telescope or space observatory is a telescope in outer space used to observe astronomical objects. Suggested by Lyman Spitzer in 1946, the first operational telescopes were the American Orbiting Astronomical Observatory, OAO-2 launch ...
s. Some are classified by the task they perform such as
Solar telescopes.
Large reflectors
Nearly all large research-grade astronomical telescopes are reflectors. Some reasons are:
*In a lens the entire volume of material has to be free of imperfection and inhomogeneities, whereas in a mirror, only one surface has to be perfectly polished.
*Light of different colors travels through a medium other than vacuum at different speeds. This causes
chromatic aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...
.
*Reflectors work in a wider
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
of light since certain wavelengths are absorbed when passing through glass elements like those found in a refractor or catadioptric.
*There are technical difficulties involved in manufacturing and manipulating large-diameter lenses. One of them is that all real materials sag in gravity. A lens can only be held by its perimeter. A mirror, on the other hand, can be supported by the whole side opposite to its reflecting face.
![Comparison optical telescope primary mirrors](https://upload.wikimedia.org/wikipedia/commons/c/c5/Comparison_optical_telescope_primary_mirrors.svg)
Most large research reflectors operate at different focal planes, depending on the type and size of the instrument being used. These including the
prime focus
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 alternat ...
of the main mirror, the
cassegrain focus
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 ...
(light bounced back down behind the primary mirror), and even external to the telescope all together (such as the
Nasmyth and coudé focus).
A new era of telescope making was inaugurated by the
Multiple Mirror Telescope
The MMT Observatory (MMTO) is an astronomical observatory on the site of Fred Lawrence Whipple Observatory (IAU observatory code 696). The Whipple observatory complex is located on Mount Hopkins, Arizona, US (55 km south of Tucson) in the S ...
(MMT), with a mirror composed of six segments synthesizing a mirror of 4.5
meter
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
s diameter. This has now been replaced by a single 6.5 m mirror. Its example was followed by the
Keck telescope
The W. M. Keck Observatory is an astronomical observatory with two telescopes at an elevation of 4,145 meters (13,600 ft) near the summit of Mauna Kea in the U.S. state
In the United States, a state is a constituent political entit ...
s with 10 m segmented mirrors.
The largest current ground-based telescopes have a
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 ...
of between 6 and 11 meters in diameter. In this generation of telescopes, the mirror is usually very thin, and is kept in an optimal shape by an array of actuators (see
active optics). This technology has driven new designs for future telescopes with diameters of 30, 50 and even 100 meters.
Relatively cheap, mass-produced ~2 meter telescopes have recently been developed and have made a significant impact on astronomy research. These allow many astronomical targets to be monitored continuously, and for large areas of sky to be surveyed. Many are
robotic telescope
A robotic telescope is an astronomical telescope and detector system that makes observations without the intervention of a human. In astronomical disciplines, a telescope qualifies as robotic if it makes those observations without being operated ...
s, computer controlled over the internet (see ''e.g.'' the
Liverpool Telescope
The Liverpool Telescope (LT) is a two-metre-aperture robotic Ritchey–Chrétien telescope that observes autonomously (without human intervention). However professional astronomers, school groups and other credible registered users submit speci ...
and the
Faulkes Telescope North
The Faulkes Telescope North is a clone of the Liverpool Telescope, and is located at Haleakala Observatory in the U.S. state of Hawaii. It is a f/10 Ritchey-Chrétien telescope.
The telescope is owned and operated by LCOGT. This telescope and ...
and
South
South is one of the cardinal directions or Points of the compass, compass points. The direction is the opposite of north and is perpendicular to both east and west.
Etymology
The word ''south'' comes from Old English ''sūþ'', from earlier Pro ...
), allowing automated follow-up of astronomical events.
Initially the
detector
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
used in telescopes was the
human eye
The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm.
...
. Later, the sensitized
photographic plate
Photographic plates preceded photographic film as a capture medium in photography, and were still used in some communities up until the late 20th century. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinn ...
took its place, and the
spectrograph was introduced, allowing the gathering of spectral information. After the photographic plate, successive generations of electronic detectors, such as the
charge-coupled device
A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...
(CCDs), have been perfected, each with more sensitivity and resolution, and often with a wider wavelength coverage.
Current research telescopes have several instruments to choose from such as:
*imagers, of different spectral responses
*spectrographs, useful in different regions of the spectrum
*polarimeters, that detect light
polarization.
The phenomenon of optical
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
sets a limit to the resolution and image quality that a telescope can achieve, which is the effective area of the
Airy disc
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
, which limits how close two such discs can be placed. This absolute limit is called the
diffraction limit
The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to t ...
(and may be approximated by the
Rayleigh criterion
Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. ...
,
Dawes limit or
Sparrow's resolution limit
Sparrow's resolution limit is an estimate of the angular resolution limit of an optical instrument.
Rayleigh criterion
When a star is observed with a telescope, the light is diffracted or spread apart into an Airy disk
In optics, the Airy dis ...
). This limit depends on the wavelength of the studied light (so that the limit for red light comes much earlier than the limit for blue light) and on the
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of the telescope mirror. This means that a telescope with a certain mirror diameter can theoretically resolve up to a certain limit at a certain wavelength. For conventional telescopes on Earth, the diffraction limit is not relevant for telescopes bigger than about 10 cm. Instead, the
seeing, or blur caused by the atmosphere, sets the resolution limit. But in space, or if
adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
are used, then reaching the diffraction limit is sometimes possible. At this point, if greater resolution is needed at that wavelength, a wider mirror has to be built or aperture synthesis performed using an array of nearby telescopes.
In recent years, a number of technologies to overcome the distortions caused by
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
on ground-based telescopes have been developed, with good results. See
adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
,
speckle imaging
Speckle imaging describes a range of high-resolution astronomical imaging techniques based on the analysis of large numbers of short exposures that freeze the variation of atmospheric turbulence. They can be divided into the shift-and-add ("'' ...
and
optical interferometry
Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
.
See also
*
Astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
*
Astrophotography
Astrophotography, also known as astronomical imaging, is the photography or imaging of astronomical objects, celestial events, or areas of the night sky. The first photograph of an astronomical object (the Moon) was taken in 1840, but it was no ...
*
Amateur telescope making
''Amateur Telescope Making'' (''ATM'') is a series of three books edited by Albert G. Ingalls between 1926 and 1953 while he was an associate editor at ''Scientific American''. The books cover various aspects of telescope construction and obser ...
*
Bahtinov mask
The Bahtinov mask is a device used to focus small astronomical telescopes accurately.
Although masks have long been used as focusing aids, the distinctive pattern was invented by Russian amateur astrophotographer Pavel Bahtinov (russian: Пав ...
*
Binoculars
*
Carey mask
A Carey mask (named after the inventor, George F. Carey) is a focusing aid for astronomical telescopes. The mask is in the form of a thin card or sheet that is placed over the front aperture of the telescope. There are four series of slits in ...
*
Chinese Future Giant Telescope
The Chinese Future Giant Telescope is a proposed optical telescope with a primary mirror that has a 30-meter diameter.
Major characteristics
The Chinese Future Giant Telescope has a primary focal ratio of 1.2. Its primary mirror is segmented wi ...
*
Depth of field
The depth of field (DOF) is the distance between the nearest and the furthest objects that are in acceptably sharp focus in an image captured with a camera.
Factors affecting depth of field
For cameras that can only focus on one object dist ...
*
Dipleidoscope
Dipleidoscope
A dipleidoscope is an instrument used to determine true noon; its name comes from the Greek for ''double image viewer''. It consists of a small telescope and a prism that creates a double image of the sun. When the two images overlap ...
*
Globe effect
*
Hartmann mask
Hartmann mask is a tool to help focusing telescopes, mainly used by amateur astronomers. It is named after the German astronomer Johannes Franz Hartmann (1865–1936), who developed it around 1900.
Theory and practice
Every part of a mirror o ...
*
History of optics
Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek philosophers, and the development of geometrical optics in the Greco-Roman world. The w ...
*
List of optical telescopes
* List of largest optical reflecting telescopes - List of large optical telescopes
* List of largest optical refracting telescopes
* List of space telescopes
* List of solar telescopes
* List of telescope types
* List of largest optical telescope ...
*
List of largest optical reflecting telescopes
A ''list'' is any set of items in a row. List or lists may also refer to:
People
* List (surname)
Organizations
* List College, an undergraduate division of the Jewish Theological Seminary of America
* SC Germania List, German rugby union ...
(with mirrors)
*
List of largest optical refracting telescopes
Refracting telescopes use a lens to focus light. The largest refracting telescope in the world is the Yerkes Observatory 40 inch (102 cm) refractor, used for astronomical and scientific observation for over a century. The Swedish 1-m S ...
(with lenses)
*
List of largest optical telescopes historically
Telescopes have grown in size since they first appeared around 1608. The following tables list the increase in size over the years. Different technologies can and have been used to build telescopes, which are used to magnify distant views especia ...
*
List of solar telescopes
This is a list of solar telescopes built in various countries around the world. A solar telescope is a specialized telescope that is used to observe the Sun.
This list contains ground-based professional observatory telescopes at optical wavelengt ...
(for the Sun)
*
List of space telescopes
This list of space telescopes (astronomical space observatories) is grouped by major frequency ranges: gamma ray, x-ray, ultraviolet, visible, infrared, microwave and radio. Telescopes that work in multiple frequency bands are included in all ...
*
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 ...
References
External links
Notes on AMATEUR TELESCOPE OPTICSThe Resolution of a Telescopeskyandtelescope.com – What To Know (about telescopes)
{{DEFAULTSORT:Optical Telescope
Telescopes