Light-gathering power

Light-gathering power


An optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum to directly view a magnified image for making a photograph, or collecting data through electronic image sensors.

There are three primary types of optical telescope: refractors which use lenses (dioptrics), reflectors which use mirrors (catoptrics), and catadioptric telescopes which use both lenses and mirrors in combination.

A telescope's light gathering power and ability to resolve small detail is directly related to the diameter (or aperture) of its objective (the primary lens or mirror that collects and focuses the light). The larger the objective, the more light the telescope can collect and the finer detail it can resolve.

Telescopes and binoculars can be used for activities such as observational astronomy, ornithology, pilotage and reconnaissance, or watching sports or performance arts.

History

Further information: History of the telescope

The telescope is more a discovery of optical craftsmen than an invention of scientist.[1][2] The lens and the properties of refracting and reflecting light had been known since antiquity and theory on how they worked were 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.[3][4] But the most significant step cited in the invention of the telescope was the development of lens manufacture for spectacles,[2][5][6] first in Venice and Florence in the thirteenth century,[7] and later in the spectacle making centers in both the Netherlands and Germany.[8] It is in the Netherlands in 1608 where the first recorded optical telescopes (refracting telescopes) appeared. The invention is credited to the spectacle makers Hans Lippershey and Zacharias Janssen in Middelburg, and the instrument-maker and optician Jacob Metius of Alkmaar.[9]

Galileo greatly improved upon these designs the following year and is generally credited with being the first to use a telescope for astronomical purposes. Galileo's telescope used Hans Lippershey's design of a convex objective lens and a concave eye lens and this design has come to be called a Galilean telescope. Johannes Kepler proposed an improvement on the design[10] 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[11] that corrected chromatic aberration seen in Keplerian telescopes up to that time, allowing for much shorter instruments with much larger objectives.

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.[12] 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 as lenses, discussed the idea of building a telescope using a mirror as the image forming objective.[13] 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,[14] the most notable of which was published in 1663 by James Gregory and came to be called the Gregorian telescope,[15][16] but no working models were built. Isaac Newton has been generally credited with constructing the first practical reflecting telescopes, the Newtonian telescope, in 1668[17] 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,[18] silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century,[19] 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.

Principles

For detailed information on specific designs of reflecting, refracting, and catadioptric telescopes: see the main articles on Reflecting telescopes, Refracting telescopes, and Catadioptrics.

The basic scheme is that the primary light-gathering element the objective (1) (the convex lens 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 (2) which acts like a magnifying glass. The eye (3) then sees an inverted magnified virtual image (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 inverted and reverted, or rotated 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 everted (reversed left to right). In terrestrial telescopes such as Spotting scopes, monoculars and binoculars, prisms (e.g., Porro prisms), 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, 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.

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 \alpha_R (in radians) is given by

\sin(\alpha_R) = 1.22 \frac{\lambda}{D}

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

\alpha_R = \frac{138}{D}

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

\alpha_D = \frac{116}{D}

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 balloon 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 f-ratio

The focal length determines how wide an angle the telescope can view with a given eyepiece or size of a CCD detector or photographic plate. The f-ratio (or focal ratio, or f-number) of a telescope is the ratio between the focal length and the diameter (i.e., aperture) of the objective. Thus, for a given objective diameter, low f-ratios indicate wide fields of view. 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

The light-gathering power of an optical telescope is proportional to the area of the objective lens or mirror, or proportional to the square of the diameter (or aperture). For example, a telescope with a lens which has a diameter three times that of another will have nine times the light-gathering power.

A bigger telescope can have an advantage over a smaller one, because their sensitivity increases as the square of the entrance diameter.[20] For example, a 7 meter telescope would be about ten times more sensitive than a 2.4 meter telescope.[20]

For a survey of a given area, the field of view is just as important as raw light gathering power. Survey telescopes such as Large Synoptic Survey Telescope therefore try to maximize the product of mirror area and field of view (or etendue) rather than raw light gathering ability alone.

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 (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

Main article: Optical aberration
Spherical aberration 
The difference in focal length between paraxial rays and marginal rays, proportional to the square of the objective diameter.
Coma 
A most objectionable defect by which points are imaged as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from the optical sine theorem.
Astigmatism 
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.
Curvature of Field
The Petzval field curvature means that the image instead of lying in a plane actually lies on a curved surface which is 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
Either barrel or pincushion, a radial distortion which must be corrected for if multiple images are to be combined (similar to stitching multiple photos into a panoramic photo).

They 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.

The chromatic aberrations

Longitudinal chromatic aberration: As with spherical aberration this is the same for axial and oblique pencils.
Transverse chromatic aberration (chromatic aberration of magnification)

Astronomical research telescopes

Optical telescopes have been used in astronomical research since the time of their invention in the early 17th century. Many types have be 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 telescopes. 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.
  • Reflectors work in a wider spectrum 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.

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 of the main mirror, the cassegrain focus (light bounced back down behind the primary mirror), and even external to the telescope all together (such as the Nasmyth and coudé focus).[21]

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.

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.

See also

Notes

External links

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