Optical telescope

thumb|The [[Large Binocular Telescope at the Mount Graham International Observatory in Arizona uses two curved mirrors to gather light]]

An optical telescope gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.

There are three primary types of optical telescope :

Refracting telescopes, which use lenses and less commonly also prisms (dioptrics)
Reflecting telescopes, which use mirrors (catoptrics)
Catadioptric telescopes, which combine lenses and mirrors

An optical telescope's ability to resolve small details is directly related to the diameter (or aperture) of its objective (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 monoculars and binoculars) for outdoor activities such as observational astronomy, ornithology, pilotage, hunting and reconnaissance, as well as indoor/semi-outdoor activities such as watching performance arts and spectator sports.

History

The telescope is more a discovery of optical craftsmen than an invention of a scientist. The lens and the properties of refracting and reflecting light had been known since antiquity, and theory on how they worked was developed by ancient Greek 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. But the most significant step cited in the invention of the telescope was the development of lens manufacture for spectacles, first in Venice and Florence in the thirteenth century, 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, followed a few weeks later by claims by Jacob Metius, and a third unknown applicant, that they also knew of this "art".

Word of the invention spread fast and Galileo Galilei, 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 and a concave eye lens, a design is now called a Galilean telescope. Johannes Kepler proposed an improvement on the design that used a convex eyepiece, often called the Keplerian Telescope.

The next big step in the development of refractors was the advent of the Achromatic lens in the early 18th century, which corrected the chromatic aberration in Keplerian telescopes up to that time, allowing for much shorter instruments with much larger objectives. Chester Moor Hall is credited with designing the first achromatic lens in 1729, which consisted of a concave crown and a convex flint lens. However, it was John Dollond who received the first patent after further development of the design.

For reflecting telescopes, which use a curved mirror in place of the objective lens, theory preceded practice. The theoretical basis for curved mirrors behaving similar to lenses was probably established by Alhazen, whose theories had been widely disseminated in Latin translations of his work. Soon after the invention of the refracting telescope, Galileo, Giovanni Francesco Sagredo, 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) 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 has been generally credited with constructing the first practical reflecting telescopes, the Newtonian telescope, in 1668 although due to their difficulty of construction and the poor performance of the speculum metal 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 fabrication in the 18th century, silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century, 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 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 and space telescopes to overcome the problems of astronomical seeing.

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, 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 and faint stars as dim as an apparent magnitude of 15 with consumer-grade equipment.<!-- examples include the Stellina by Vaonis and the eVscope by Unistellar

Resolving power <math>R</math> is derived from the wavelength <math>{\lambda}</math> using the same unit as aperture; where 550 nm to mm is given by: <math>R = \frac{\lambda}{10^6} = \frac{550}{10^6} = 0.00055</math>.

<br />The constant <math>\Phi</math> is derived from radians to the same unit as the object's apparent diameter; where the Moon's apparent diameter of <math>D_{a} = \frac{313\Pi}{10800}</math> radians to arcsecs is given by: <math>D_{a} = \frac{313\Pi}{10800} \cdot 206265 = 1878</math>.

An example using a telescope with an aperture of 130 mm observing the Moon in a 550 nm wavelength, is given by: <math>F = \frac{\frac{2R}{D} \cdot D_{ob} \cdot \Phi}{D_{a = \frac{\frac{2 \cdot 0.00055}{130} \cdot 3474.2 \cdot 206265}{1878} \approx 3.22</math>

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 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) and optical imperfections of the telescope, the angular resolution of an optical telescope is determined by the diameter of the primary mirror or lens gathering the light (also termed its "aperture").

The Rayleigh criterion for the resolution limit <math>\alpha_R</math> (in radians) is given by

:<math>\sin(\alpha_R) = 1.22 \frac{\lambda}{D}</math>

where <math>\lambda</math> is the wavelength and <math>D</math> is the aperture. For visible light (<math>\lambda</math> = 550 nm) in the small-angle approximation, this equation can be rewritten:

:<math>\alpha_R = \frac{138}{D}</math>

Here, <math>\alpha_R</math> denotes the resolution limit in arcseconds and <math>D</math> 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 <math>\alpha_R</math>. This is taken into account by the Dawes limit

:<math>\alpha_D = \frac{116}{D}</math>

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. 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. Resolution limits can also be overcome by adaptive optics, speckle imaging or lucky imaging for ground-based telescopes.

Recently, it has become practical to perform aperture synthesis 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.

Focal length and focal ratio

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus. A system with a shorter focal length has greater optical power 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 <math>N</math>. The focal ratio of a telescope is defined as the focal length <math>f</math> of an objective divided by its diameter <math>D</math> 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, 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:

<math>N = \frac {f}{D} = \frac {1200}{254} \approx 4.7</math>

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 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 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 with the purpose of gathering more photons in a given time period than a slower system, allowing time lapsed photography to process the result faster.

Wide-field telescopes (such as astrographs), are used to track satellites and asteroids, for cosmic-ray research, and for astronomical surveys of the sky. It is more difficult to reduce optical aberrations in telescopes with low f-ratio than in telescopes with larger f-ratio.

Light-gathering power

thumb|The [[W. M. Keck Observatory|Keck II telescope gathers light by using 36 segmented hexagonal mirrors to create a 10 m (33 ft) aperture primary mirror]]

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 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 <math>P</math> compared against a human eye is the squared result of the division of the aperture <math>D</math> over the observer's pupil diameter <math>D_{p}</math>, Most observers' eyes instantly respond to darkness by widening the pupil to almost its maximum, although complete adaption to night vision generally takes at least a half-hour. (There is usually a slight extra widening of the pupil the longer the pupil remains dilated / relaxed.)

The improvement in brightness with reduced magnification has a limit related to something called the exit pupil. The exit pupil is the cylinder of light exiting the eyepiece and entering the pupil of the eye; hence the lower the magnification, the larger the exit pupil. It is the image of the shrunken sky-viewing aperture of the telescope, reduced by the magnification factor, <math>\ M\ ,</math> of the eyepiece-telescope combination:

:<math>\ M = \frac{\ L\ }{ \ell }\ ,</math>

where <math>\ L\ </math> is the focal length of the telescope and <math>\ \ell\ </math> is the focal length of the eyepiece.

Ideally, the exit pupil of the eyepiece, <math>\ d_\mathsf{ep}\ ,</math> matches the pupil of the observer's eye: If the exit pupil from the eyepiece is larger than the pupil of individual observer's eye, some of the light delivered from the telescope will be cut off. If the eyepiece exit pupil is the same or smaller than the pupil of the observer's eye, then all of the light collected by the telescope aperture will enter the eye, with lower magnification producing a brighter image, as long as all of the captured light gets into the eye.

The minimum <math>\ M_\mathsf{min}\ </math> can be calculated by dividing the telescope aperture <math>\ D\ </math> over the largest tolerated exit pupil diameter <math>\ d_\mathsf{ep} ~.</math>

Eyepiece field stop method given by <math>v_{t} = \frac {d_f}{f_t} \times 57.3</math>, where <math>v_{t}</math> is the true FOV, <math>d_{f}</math> is the eyepiece field stop diameter in millimeters and <math>f_{t}</math> is the focal length of the telescope in millimeters.

A new era of telescope making was inaugurated by the Multiple Mirror Telescope (MMT), with a mirror composed of six segments synthesizing a mirror of 4.5 meters diameter. This has now been replaced by a single 6.5 m mirror. Its example was followed by the Keck telescopes with 10 m segmented mirrors.

The largest current ground-based telescopes have a primary mirror 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.

thumb|[[Harlan J. Smith Telescope reflecting telescope at McDonald Observatory, Texas]]

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 telescopes, computer controlled over the internet (see e.g. the Liverpool Telescope and the Faulkes Telescope North and South), allowing automated follow-up of astronomical events.

Initially the detector used in telescopes was the human eye. Later, the sensitized photographic plate 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 (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 sets a limit to the resolution and image quality that a telescope can achieve, which is the effective area of the Airy disc, which limits how close two such discs can be placed. This absolute limit is called the diffraction limit (and may be approximated by the Rayleigh criterion, Dawes limit or Sparrow's resolution limit). 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 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 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 on ground-based telescopes have been developed, with good results. See adaptive optics, speckle imaging and optical interferometry.

References

External links

Notes on AMATEUR TELESCOPE OPTICS
Online Telescope Math Calculator
The Resolution of a Telescope
skyandtelescope.com – What To Know (about telescopes)