Seeing is the astronomer"s term for the relative optical quality of the Earth"s atmosphere. Optical high quality is defined as the steadiness and absence of distortion in a telescopic image across an interval of monitoring. A motionmuch less and optically perfect photo suggests excellent seeing; a rapidly altering and also grossly distorted picture shows poor seeing.

You are watching: Which of the following effects is caused by atmospheric turbulence?

The cause of degraded or bad seeing is thermal turbulence in the environment. Seeing has actually nopoint to do through whether the night air is cloudy or clear, heat or cool, or even whether it is windy or calm. The important concern is only whether temperature differences in the environment are in movement.

The result of mixing air of various temperatures deserve to be watched in the appearance of objects behind convection currental fees, such as the air rising from an asphalt road on a hot day. Warm air increasing with cooler air produces a characteristic wavering or undulation in the appearance of objects behind the thermal curleas, equivalent to the appearance of objects below the surchallenge of rippling water. In the environment, as in air over a warm asphalt road, thermal turbulence is the reason of poor seeing.


Before delving that topic, yet, it is crucial to note that atmospheric aerosols (water vapor, dust, volcanic ash, coal and also oil burning byproducts) deserve to considerably degrade huge images. Aerosols produce a diffuse directional glow visible from the Moon, bbest earth or bbest star when the object is totally external the field of see in binoculars or a telescope. Monumental diffusion can be current also as soon as the skies appears dark and also faint stars are easily visible.

Thermal turbulence causes image perturbations on the order of 10–5 to 10–4 radians (2 to 20 arcseconds); the radius of the forward scatter brought about by diffusion have the right to be very huge, on the order of a radian (~60°, photo, ideal of water vapor diffusion).

To assess diffusion, cover the disk of the Sun or Moon through your thumb at arm"s size. The amount of stray light visible about the obstruction is an indication of the amount of diffusion. Viewing a bright star through a telescope will also present a nimbus of glare if diffusion is present. (Be sure that the objective and also eyeitem are not fogged or dewed.)

When the object is centered in the area of see, aerosols can significantly contribute to picture blurring and also contrast reduction, also as soon as thermal turbulence is negligible. And aerosols can be the major resource of image destruction also as soon as considerable thermal turbulence is existing.

A Topic of Recent Interest

Scientists have actually been conscious of optical disturbance given that English naturalist Robert Hooke in 1665 attributed the twinkling of stars to "small, moving areas of the atmosphere having actually various refracting powers which act choose lenses." Astronomer William Herschel was aware of optical turbulence and explicitly embraced procedures to cope through it, and also observational analyses of the trouble appear in the late 1ninth century. But the clinical research of astronomical seeing really takes off in the 1950"s, as soon as photoelectrical photometry, photomultipliers, oscilliscopes and sensitive photographic films made in-depth measurement of disturbance possible. Academic files execute not point out research study on the topic a lot prior to 1950 and also review short articles, summarizing previous studies of astronomical seeing, execute not show up till roughly 1960.

Regardless of the truth that Harvard Observatory astronomers approximately 1900 had actually figured out atmospheric disturbance as a "variable of prime importance" in planetary astronomy, amateur astronomical resources printed prior to 1950 either treat the problem not at all or only in passing — as the challenge of viewing under a "tremulous atmosphere" (Webb"s Celestial Objects, 1917). Amongst the first scientific research based descriptions of optical disturbance easily accessible to amateur astronomers were 2 articles on "Seeing" in Sky & Telescope (January/February, 1950; view Further Reading).

This reasonably current focus on atmospheric disturbance deserve to be traced in the evolving therapy of the topic found in Norton"s Star Atlas and Telescopic Handbook, then and also now. Here is the sole cite of the concern under the heading "Atmospheric Conditions" in the first edition (1910, p.17):

When the stars twinkle much it is an indication that the air is unsecure and also not altogether satisfactory for observation.

And right here the whole discussion under the heading "Twinkling of Stars" given in the fourteenth edition (1959, p.38):

Though pudepend atmospheric in its beginning, this phenomenon is of interest to astronomers, as it is affected by the nature of the light emitted by each star, e.g., by its spectrum. White stars (Types B and also A) twinkle most; yellow stars (Types F to K) slightly less, and red stars (Type M) least of all. Twinkling is leastern at the zenith, and in settled and also calm weather; best toward the horizon, and also in unsettled and also stormy weather; tbelow is also a seasonal waxing and waning from mid summer to mid winter and vice versa. Planets perform not commonly twinkle other than when close to the horizon — intended to be due to the fact that they have actually discs of an appreciable dimension.

Finally, below is simply the opening paragraph from the extfinished conversation of "Seeing" in Norton"s nineteenth edition (1998, p. 29):

Seeing is a term used to suggest the steadiness of the air, as judged by the appearance of the telescope picture. The two are connected by the fact that air currental fees are caused by masses of air at various temperatures, and the refractive index of air alters via temperature: therefore the currental fees cause the picture to flicker.

Fortunately a far-reaching body of research has actually collected given that 1970, generally urged by the should boost the yield from optical security and also mapping satellites and also to analyze turbulence at candiday sites for the modern-day generation of 10 meter and bigger terrestrial telescopes. This page summarizes some of the crucial ethics.

The Structure of Turbulence


All substances that transmit light also refract or bfinish the direction of the light by an amount proportional to the refrenergetic index of the tool. The refrenergetic index of air alters with its density, which close to the surconfront of the earth relies generally on temperature and to a lesser extent on humidity: warmer air, and even more humid air, is much less thick and also therefore refracts light less than cooler, drier air.

Two bodies of air of different temperatures and/or humidities produce a refrenergetic boundary that bends light in the same way as the boundary between air and also water or air and glass. If this boundary is distorted right into disturbance, it has a comparable (though weaker) optical effect as the surchallenge of water disturbed right into ripples by the wind, or glass with a randomly irconstant surface (photo, left).

Astronomers define this turbulence statistically, using an optical analysis developed by V.I. Tatarski from the mathematical description of disturbance cascades by Andrei Kolmogorov. This Kolmogorov-Tatarski model starts through the reality that disturbance in flowing media such as air or water relies on 3 factors: (1) the velocity of the flowing medium; (2) the boundary width or spatial dimensions of the flow; and also (3) the kinematic viscosity of the medium.

Due to the fact that the medium is in movement, it creates friction versus the boundaries roughly it. At low velocity and/or high viscosity, this friction just impedes the external layer of the flow: the inner circulation simply slides over this laggard external layer, developing layered or laminar flow. This distributes friction farther right into the circulation, layer by layer, the method playing cards slide over one an additional once the deck is spread out on a table.

The velocity limit at which laminar circulation deserve to no much longer dissipate friction is evaluated as a Reynolds number, calculated as the average viscosity and also physical dimension of the flow as a propercent of the circulation velocity. Air has a really low kinematic viscosity of around 0.15 cm2 per second, so also as soon as the physical scale of the circulation is as big as several hundred meters, disturbance appears at velocities of only a couple of kilometers per hour. Layers of relocating air are therefore nearly constantly turbulent.

Turbulence creates as boosting thermal energy — heat from the sunlight or warmth climbing from the earth — breaks laminar flows into extremely large cells that roll over themselves as whorls or eddies. Due to the fact that these whorls are relatively inefficient at dissipating power, the increased flow velocity breaks them right into smaller sized and also even more efficient whorls, and so on until the circulation viscosity impedes smaller sized divisions. At that suggest, the flow energy deserve to just be dissipated as warm from viscous friction. This turbulence cascade creates a disturbance frequency spectrum from the biggest, highest energy vortices to the smallest, low power eddies or whorls, which randomly arise and also mix within the flow. Louis Fry Richardson wittily summarized the disturbance cascade in a couplet:

Big whorls have actually little bit whorls that feed on their velocity,And bit whorls have lesser whorls and so on to viscosity.

The complicated texture of single turbulent boundaries is exquisitely visible in the light scattering contours of cumulus clouds — which create as convection currental fees of warmth, moist air surge into drier, cooler air over — and also in computer system simulations of unstable media. The imperiods (below) show sensations defined above: disturbance created by convection currents, turbulence resulting from boundary friction within a solitary moving layer, and the complex result of these factors in atmospheric turbulence.


computer simulation of thermal turbulence developed by burning at (left to right) low to high temperatures


computer simulation of boundary disturbance within a solitary flowing layer, perceived from the side (left) and from over (right)


comupter simulation of geostrophic (atmospheric) disturbance in air layers of two various temperatures

Tright here are 2 borders to the turbulence frequency spectrum. The biggest dimension or external scale of the turbulence (Lo) generally represents the thickness of the entire flowing tool, which in the setting have the right to be a layer of air 100 or more meters thick. The smallest eddies specify the inner range of disturbance (lo), which has been estimated to be as tiny as a few millimeters. Between these boundaries the disturbance develops a circulation of whorls wright here the variety of tiny whorls boosts significantly.


What is the effect of this turbulence on the light from a star? The diagram (right), adapted from the Lucky Imaging Internet Site, reflects that these tumbling eddies disrupt and refract the light in a facility but self similar or fractal pattern: from the biggest to the smallest range, the light fluctuates by random amounts across random intervals of time.

Across time (temporal frequency), the biggest variations in the turbulence (L0) can extfinish across intervals of 20 seconds or even more, while the troughs between those peaks are churned by successively smaller sized and also more rapid fluctuations down to the minimum time interval (l0) shown by a solitary vertical line, which represents fluctuations that occur numerous hundred times a 2nd. Within the photo, the dimension or amplitude of the optical distortions varies from biggest to smallest in the very same way.

In addition, atmospheric disturbance often mirrors intermittency or gusts of greater turbulence separated by intervals of much less disturbance.

Temperature distinctions as tiny as 0.1 to 1 K deserve to develop noticeable optical effects, but just in air masses warmer than about 10°F (–12°C). In addition to offering the energy that creates the disturbance, wind shear and also convection currental fees additionally move the turbulence throughout the landscape and also telescope line of sight, sometimes at high rate.

Atmospheric disturbance is the random combination of 2 sepaprice kinds of variation: amplitude, or the amount of change in refracting result (created by the width of the eddies and the distinction in temperature between them), and also frequency, or the moment interval in between amplitude alters of the same dimension (produced by the movement of eddies throughout the optical path). Both the mathematical models and also visual inspection of star images present that the refracting impact (red brackets) and tempdental spacing (blue brackets) of atmospheric disturbance fluctuate randomly throughout scales exceeding 100,000 to 1.

The Location of Turbulence


The Komolgorov-Tatarski version represents turbulence at a solitary boundary in between thermally different layers of air. But turbulence actually arises in a number of different locations, throughout several various atmospheric layers.

The most basic meteorological design of atmospheric disturbance was proposed by Hufnagel (1974) and also revised by Valley (1979), and also (via allowances for regional geography and climate) this model has actually been primarily sustained in subsequent research study — through the caution that dimensions at specific sites around the year deserve to decomponent from it extensively, and turbulence will be focused in atmospheric layers at almost any kind of altitude as much as the tropopausage.

The Hufnagel Valley design locates the majority of atmospheric turbulence in two regimes (chart, left): turbulence within the surchallenge boundary layer, which occurs in dense, relatively low velocity (as much as 50 kilometers per hour) convection and layered air currents relocating within a kilometer or two of the earth"s surconfront, and high altitude turbulence roughly the tropopausage, which occurs in reasonably rarefied, high velocity (as much as 500 kilometers per hour) air currents at the temperature invariation between the tropospright here and also stratosphere.

François Roddier (1981), adopting the discussion in Jean Texereau (1961; 1984), elaborated this model into four categories: "disturbance associated with the telescope and the dome, turbulence in the surface boundary layer or because of ground convection, disturbance in the planetary boundary layer or linked through orographic disturbances, and turbulence in the tropopausage or above" (1981, p. 288). Schematically I will certainly refer to these as instrument, surconfront, geographical and high environment turbulence.

1. Instrument turbulence occurs inside the telescope and also any type of framework that shelters it. It is most regularly produced by convection layers climbing at the surconfront of a reflecting mirror created by heat inside the cooling glass (mirror seeing), by air currental fees crawling alengthy the sides of a closed telescope tube (telescope framework seeing), by convection currental fees from the observer"s body wafting across the optical path (specifically in cold weather), by warmth rising via the restrictive opening of an observatory dome (structure seeing), and by warm rising from pavement, masonry or steel automatically under and also about the telescope (site seeing). Several research studies imply that mirror seeing dequalities the picture in a 25 cm telescope by around 0.1 arcsecond for eextremely level Centigrade that mirror temperature exceeds ambient temperature; the effect is much less in bigger apertures.

2. Surchallenge turbulence extends from the ground approximately a few hundred meters in the landscape roughly the telescope, which as soon as viewing at a zenith angle over 60° is within fifty percent a kilometer of the observing website. Surconfront turbulence frequently represents up to fifty percent of all the oboffered optical distortion; it is mostly because of convection currental fees rising from warmth stored in the sunlit earth throughout the day. Particular concentrations of convection curleas have the right to aincrease from nearby residences, led roadways, surdeals with of stonework or concrete, commercial structures, and also from disturbance between low lying layers that develop temperature invariation limits. At many locations, surconfront disturbance follows a diurnal cycle from a minimum just after sunincrease, steeply rising to a peak throughout early afternoon, decreasing to a second minimum soon after suncollection, boosting in the time of the beforehand evening to an additional peak at approximately midnight, prior to returning to a minimum in the hour or two before morning.

3. Geographic turbulence exoften tends from a couple of hundred meters to a few kilometers over the ground; for viewing at a zenith angle of 60° or better this implies a geographic radius from the observing site of up to 7 km. Geographic turbulence commonly forms as numerous overlying layers of air 100 to 200 meters thick that have the right to extfinish horizontally for a number of kilometers; over 4 kilometres it is primarily independent of the landscape and becomes less significant as much as a minimum at around 6 to 9 kilometers. It is caused not only by air curleas forced upward by mountainous terrain however by the displace of various other big landscape functions — huge bodies of water, expanses of bare ground or sand also, conmetropolitan breakthrough, huge areas of snow — as these form the thermal and also moisture content of the weather bearing atmosphere.

4. High atmosphere turbulence is primarily linked through the jet stream, which is commonly confined to latitudes over 30° north or south of the equator at altitudes of approximately 10 to 15 kilometres. (At higher latitudes the jet stream altitude is much much less, and near the poles it disshows up near the surconfront.) Stratospheric layers over about 20 kilometres are rarefied and thermally homogenous, and also have a negligible effect on seeing. The jet stream contributes to disturbance both straight through its high velocity movement against lower atmospheric layers, and also indirectly via the amount of cold or moist air it brings from north latitudes and ocean surfaces, the affect of its movement on the formation of high and low pressure areas, and the weather turbulence created by the energetic mixture of moisture, temperature and also barometric pressure. The jet stream is high enough so that, even if it is not directly overhead, it deserve to cause substantial distinctions in the amount of disturbance checked out in opposite directions of the sky — at ranges of up to 25 km from the observing website as soon as viewing at a 60° zenith angle.

The relative scale and also location of these four sources of disturbance is nicely summarized in predictive models of optical disturbance (making use of the disturbance framework index Cn2, explained in the next section) arisen by Trinquet & Vernin (2009; below).


Although this is the graphical depiction of a forespreading design, not of actual dimensions, it reproduces the pattern of disturbance as it has actually been measured at various sites roughly the human being and as summarized in the previous graph: large, undulating turbulence (red) close to the ground, and small, vibrating disturbance (cyan) in the high atmosphere. It also illustprices the amazing variability in seeing over time, both across days and within a solitary evening. This reveals the chaotic top quality of optical disturbance throughout bigger physical and tempdental scales. (Compare via the simulation of boundary disturbance, over.)

The Optics of Turbulence

To the naked eye, optical disturbance produces the twinkling of stars. In telescopes, turbulence produces a range of effects on the photo of stars and planets that has actually been otherwise explained as "wavering" and also "wobbling" in small telescopes and also "boiling" or "churning" in large telescopes. This is a clue that the optical impacts of turbulence vary via the aperture of the observing instrument.


The easiest model of optical disturbance represents it as the boundary between 2 layers of air at different temperatures (as diagrammed by Dorrit Hoffleit, right). The refracting effect of a solitary small area of the boundary is tantamount to the refracting result of an air/glass optical surface. The whole layer disrupts the light from a star right into moving light and dark bands, similar to the caustics or network-related of light bands and shadow cells visible at the bottom of a rippling swimming pool on a sunny day. These shadows have the right to be viewed in a telescope superimplemented on the image of a bbest star carried much out of focus; the focused imperiods of extfinished surencounters such as the Moon appear as if under relocating water. (See for instance this brief computer animation of turbulence imaged in a large telescope.)


As a simplification a lot of useful to the visual astronomer, the optical impacts of this turbulence layer have the right to be contrasted as 3 kinds of distortion in the star diffractivity artitruth (diagram, right):

• Oscillating is a wavering or jumping of the star photo around an average location within the image area, which is slow enough that the eye have the right to perceive and follow a solitary systematic star image. The "undistorted" star image shows up largely intact, as a recognizable Airy disk and initially diffraction ring, yet it is in constant motion from place to location. Oscillations are resulted in by modeprice power (tool scale) disturbance wbelow F = H and v is not rapid, and is typical of turbulence within a kilometer or two of the ground; it is likewise characteristic of poor seeing in tiny aperture (below ~10–20 cm) telescopes. The angular displacement created by oscillation is normally tiny, much less than a few arcseconds. As an outcome, star imeras execute not seem to oscillate once L > D — in small aperture telescopes and also the naked eye; instead a shadow band also momentarily fills the little aperture, which produces a brief dimming or twinkling in brightness by about 10%, well-known as scintillation. In apertures higher than or approaching the diameter of the disturbance cells (L = D) the tilting occurs completely within the aperture diameter and the focused photo shows up to wobble or dance roughly a central allude.

• Speckling is produced by high energy, high frequency disturbance (little angular size and also exceptionally fast fluctuation) wbelow F > L so that the aperture can sample the imeras from many turbulence cells at the same time. This breaks the star photo right into multiple, simultaneous Airy disks superapplied on each other at random little ranges from a addressed central location within the image area. The very same wave interference that produces the dark rings in the undistorted star diffraction artireality creates dark borders in between the superapplied Airy disks of the simultaneous star imperiods, developing plenty of visibly distinctive beads of light, called speckles. Since these images of the star are developed all at once, the "dancing" areas of the star are linked as a solitary photo — causing a bloated, boiling mass of speckles that continues to be fixed at a solitary location. At this range the angular width of turbulence cells is so little that even carefully spaced binary stars of equal magnitude will display different speckle fads moment to minute, and matched magnitude double stars will certainly merge right into an unresolved oblengthy mass.

Temporal scale contributes to the scintillation appearance: photo fluctuations or flickers that are much faster than around 50 cycles per second are not visible to the eye, which instead perceives the flickers as a consistent light, yet this thresorganize declines to a rate of a few flickers per second in incredibly faint imperiods. Consequently the visible "boiling" of speckles in negative seeing has a characteristic maximum perceptible price at different visual magnitudes, and also appears the majority of vigorous and also insystematic in bright stars regarded at high magnification with a big aperture.

Keep in mind that this temporal scale indicates that naked eye twinkling is diagnostic just of low frequency turbulence (commonly, heat from the ground or swiftly altering weather) which may have actually bit effect on the telescopic image; the amount of low frequency disturbance is additionally not indicative of the amount of high frequency disturbance. If many of the atmospheric disturbance is high frequency, the scintillation deserve to be too fast to be discerned by the naked eye in bideal stars, although the telescopic photo will certainly be seriously degraded.

• Flashing is an abrupt expansion of the star image accompanied by a loss of emphasis and also enhanced illumination in the bordering aerosol diffusion. It led to by extremely big fluctuations in disturbance wbelow F > H and also the angular air speed v is slow-moving. These conditions imply that the optical path is via a thickening in a refracting air layer or an abnormally large turbulence cell, which can be either in instrument or surface disturbance turbulence or (rarely) in high altitude turbulence. If the flashing does not also create a simultaneous brightening in the aerosol illumicountry (the diffusion nimbus roughly the star image), the disturbance is probably in the instrument or observatory structure.

In general, all three forms of distortion have the right to integrate in different proportions to develop the complicated and also moment to moment alters in a star picture, although it is not inexplicable for a visual astronomer to suffer distortion as a mixture of adjacent forms in the diagram. Therefore, on exceptionally fine nights, an undistorted star image will certainly be disturbed by brief dancing or rippling movement, on average nights a dancing Airy disk will integrate via speckling of the diffraction rings, and on bad nights tbelow can be frequent flashing in a scintillating star picture.

Although disturbance have the right to be explained in terms of atmospheric models, for instance as superapplied disturbance layers of various frequencies, it is not convenient to apply it to imaging on those terms. Instead, subsequent study has analyzed the cumulative impacts of turbulence on the wavefront and also as optical distortions in the picture. To briefly summarize this extremely technical literature: R.E. Hufnagel and also N.R. Stanley (1964) derived the alters in the modulation transfer attribute (MTF) and Strehl proportion or point spread feature (PSF) that outcome from the transmission of a diffractivity limited image with unstable media. David Fried (1965, 1966) applied their occupational to the difficulty of "looking down" through the setting via optical (armed forces or mapping) satellites. These advancements were summarized and also applied to the astronomical difficulties of "looking up" with the environment by François Roddier (1981).

Vladimir Sacek"s web page on Atmospheric Turbulence summarizes the thrust of a strict optical analysis, which attributes oscillation effects to wavefront tilt and also scintillation results to roughness. Roughness in turn deserve to be explained in regards to traditional optical aberrations — a random mixture of deemphasis, spherical aberration, astigmatism and also coma.

Rather tha strategy the technical analysis, it is valuable to visualize the optical effects of atmospheric disturbance in regards to a Newtonian reflector mirror divided up right into thousands of tiny hexagonal airplane mirror cells. Undisturbed, these tiny mirrors align to create a perfect paraboloid surchallenge that creates a diffractivity limited telescopic image.

However before each mirror have the right to oscillate independently from side to side by a miniscule angle that represents the refractivity included by the environment. If we looked throughout the mirror from one side, we would certainly watch the surconfront appear to ripple consistently, with an overall motion across the mirror from one side to the other however with a range of smaller sized disturbances and eddies in the flow. These oscillations deflect the light falling on each mirror amethod from the optical course vital for perfect focus by the entire aperture.

When a big propercentage of these mirrors tilt in the very same direction at the same moment throughout the whole objective diameter, the image at the emphasis is disput to one side ("tilt") and oscillation results. When some of the mirrors tilt at the exact same moment toward or amethod from the optical axis by an amount proportional to their distance from the optical axis, defocus or flashing outcomes. When mirrors on one side of the aperture tilt to a much shorter emphasis than mirrors on the opposite side, coma results. When the mirrors alengthy one diameter tilt outward at the very same time mirrors along the perpendicular diameter tilt inwards, astigmatism outcomes. Extremely facility and also chaotic patterns of disturbance have the right to in this way be attributed to distinctive aberration categories, and also as each category result is subtracted from the whole the remainder can be defined by other kinds of aberration, till we are left through the mirror cells in perfect alignment again.

The Statistical Description of Turbulence

Atmospheric turbulence has actually been successfully analyzed and also explained in sepaprice models of unstable flows and optical aberrations. These deserve to be offered to derive descriptive statistics for the degree of turbulence, which can be done both for the turbulence itself and also its effect on photo top quality.

Due to the fact that optical disturbance and optical aberrations are separate complex phenomena produced by many type of different resources of distortion, it is not feasible to attach them in detail. Instead, the connection is conveniently identified as an average disturbance in relation to an average photo aberration.

A star diffractivity artifact is composed of the Airy disk surrounded by concentric diffraction rings. This Airy disk has actually an angular (visual) radius resolved by the telescope aperture and also a direct (photographic) radius addressed by the telescope loved one aperture. In perfect optical device, the Airy disk comprises about 86% of the complete light from the star. The cumulative effect of the many kind of small mirrors (in the previous analogy) tilting in divergent directions is to randomly change light that would develop inside a compact Airy disk ameans from the optically perfect place, spreading the light throughout a broader area. This lowers the Strehl ratio (the proportion of total light that is focused into the Airy disk) and also inflates the point spread function, both technical signs of degraded optical high quality.

Since optical speckling bloats the star picture, and oscillation shifts the image around on the image aircraft during a time expocertain, the full width fifty percent maximum of a star picture (explained in the page on seeing measurement methods) is a concrete and also empirical measure of the all at once impact of atmospheric turbulence in a provided aperture. Seeing that is listed below a FWHM of 1 arcsecond is taken into consideration wonderful, and also seeing that is over 5 arcsecond is considered bad. (Keep in mind that FWHM is based on the cumulative photo dispersion measured by a CCD sensor and also is not straight a measure of appearance to the visual astronomer.)

The statistical summary of the average atmospheric disturbance begins with the temperature structure coreliable, which is a variance identified on a 3 dimensional average squared distance. It is calculated as:

CT2 = <T(x) – T(x+r)>2/r2/3

where x is any type of point within the turbulence, and also r is the 3 dimensional distance from x to any type of second allude of the very same temperature. Referring to the middle series of turbulence simulations (above), it is obvious that better power disturbance breaks isothermal cells right into smaller sized devices, reducing the average distance in between points of the exact same temperature: as disturbance becomes even more extreme, the average CT2 becomes smaller.

This can be applied to estimate the refractive index structure coeffective Cn2 of the turbulence, which is the average distinction in the refrenergetic index between between 2 points in the unstable layer. Mathematically it is sindicate the temperature framework coefficient scaled by the average air press and temperature:

Cn2 = CT2·<7.9x10-5·P / T2>2

wbelow P is the atmospheric pressure in millibars and T is the temperature (in Kelvins). The refrenergetic index becomes smaller as the dimension of turbulence cells decreases, yet significantly smaller as pressure decreases and also temperature rises.

Next the refractive index coeffective can be used to estimate the average physical width of a turbulence cell having actually a unidevelop optical result, well-known variously as Fried"s seeing parameter, Fried"s coherence size or Fried"s r0 (pronounced R naught):

r0 = <0.184λ6/5·(cos γ)3/5∫dh·Cn2(h)>–3/5 meters

σ2 = 1.0299·(d / r0)5/3

wbelow h is altitude in meters, γ is the zenith angle, and also Cn2(h) is the refrenergetic index framework coeffective at a certain altitude, incorporated throughout all atmospheric layers in the optical path; σ2 is the two dimensional variance of the coherence size roughly the average. The vital points are that the optical results of seeing are less (Fried"s r0 gets larger) at smaller zenith angles and also much longer wavelengths, but that turbulence impacts are additive (cumulative) across the entire atmospheric layer to maximum h, from the mirror surconfront to the stratospright here.

Finally the isoplanatic angle θo of Fried"s r0 is the average angular width of an isoplanatic patch alengthy the optical route of a ground based observer:

θo = 0.6*ro/h

where h is the altitude of the unstable layer.

Fried"s r0 is approximately the average physical dimension of a solitary isoplanatic patch (a turbulence cell refracting light in the very same direction). Observational outcomes suggest r0 varies from around 2 to 21 cm for visible wavelengths perceived at the zenith, through 10 cm provided as a dominion of thumb average worth. The following table, adjusted from Roddier (1981), converts Fried"s r0 via direct steps of seeing at wavelengths around λ = 500 nm ("blue green").

Fried"s parameterr0 (cm)Coherence areaλ2σ (cm2)Seeing angleω (arcsecond)

The diffractivity limit DL in turbulence of a provided r0 at wavelength λ for a focal length ƒ and spatial frequency νc is approximated as:

DLr0 = 1/νc·1/ƒ = 2.1·λ/r0

and the diameter and variety of speckles as:

Ns = (D / r0)2

Ds = (λ / Do)·206265 arcseconds

This can be compared to the unperturbed diffraction limit λ/Do to identify the loved one deterioration in average resolution. However, if seeing is proclaimed in terms of an image FWHM, a rough preeminence of thumb is that Fried"s r0 is 22 cm once the FWHM seeing is about 0.5 arcseconds, is 11 cm once the seeing is around 1 arcsecond, and so on.


The chart (right) is based upon a number of years of atmospheric dimensions at the ESO observatory at Cerro Paranal, Chile; the basic develop of the curve is typical of atmospheric dimensions at other areas.

Perspective scaling — turbulence becomes visually smaller sized the farther it is from the viewer — accounts for fundamental dependence of turbulence size on altitude. This is portrayed by the oselection curve, which plots the noticeable angular width to a ground observer of a consistent 1 meter width located at the equivalent altitudes. Comparing the angular width of the two curves at the very same altitude reflects that the average dimension of atmospheric turbulence can be rather big near the ground, on the order of a number of meters or more, but decreases in size from the surconfront boundary as much as an altitude of around 5 kilometres.

Fried"s r0 is frequently interpreted as the telescope aperture at which the change occurs from scintillation or oscillation to speckling as the leading photo distortion. Thus big r0 suggests fairly great seeing, and also for any type of particular telescope, as soon as D 0, the setting does not substantially degrade the photo, though it might affect the stcapability the picture (as oscillation). In that instance the telescope is said to be diffraction limited quite than seeing restricted. The consensus endure is that telescopes over about 10–20 cm in aperture are, on the majority of nights, continuously seeing limited.

The context for the previous "little mirrors" analogy is that some of the newest generation of large aperture (10+ meters) telescopes are designed as little segmented mirrors attached to servomechanisms that deserve to independently tilt each mirror segment to compensate for local tilt aberrations measured in genuine time in the side to side variations in the place of a laser beam reflected off a refracting layer high in the environment. These adaptive optics mechanisms cannot respond easily enough to remove the "roughness" components of disturbance, but they can cancel the results of the relatively broad and also sluggish "tilt" oscillations. At the various other extreme, speckle interferometry enables analysis of incredibly tiny details through the computational filtering of speckle fads backwards to isolate the original Airy disk (or identical object detail).

If the huge object is a bbest star or earth, the alternate strategy of lucky imaging can be applied: an extremely huge number of imeras are captured and only those imeras are offered in which the turbulence has lapsed for a portion of a 2nd right into a glimpse of minimal distortion. This is made feasible by modern CCD imaging that allows consistent, quick video capture of telescope imperiods, which deserve to be evaluated, selected and averaged ("stacked") into a single photo by computer system software application. The probcapacity of obtaining a brief expocertain diffraction restricted image is connected to

Prob ~ 5.6*exp<–0.1557*(D/r0)2>

which suggests a probability of 1 in 1 once D = 3.5r0, about 1 in 400 once D = 7r0 and also becomes exponentially impractical (1 in 1 million) as soon as D = 10r0. (In these analyses the expocertain time is roughly 1/3 the fluctuation period of a single Fried size, which is a lot of feasibly derived via video capture.) These steeply escalating prices of huge apertures are a primary reason for the advance of adaptive optics.


Astronomers evaluate seeing by a variety of methods: radar imaging, imaging the variations in a laser reflected off a high atmosphere layer, or observing a star simultaneously via parallel apertures of different sizes (which therefore sample r0 at various values). Statistical analyses applied to each kind of information deserve to isolate the various ranges or spatial and temporal frequencies in the picture, and also from these estimate the family member vertical place, scale parameters and lateral velocity of the turbulence.

Some of the ideal observing sites in the world average an r0 of 10 to 15 cm, which implies that all telescopes of aperture higher than about 6" would percreate at less than their diffractivity borders.

How often do nights of fantastic seeing occur? The graph (left) summarizes four years of night r0 dimensions at the William Herschel Telescope site in the Canary Islands. Even this superb viewing area has many nights of relatively poor seeing: the distribution is positively skewed, and also the cumulative probcapability reflects only a 50% opportunity on any night of values of r0 above 14 cm, and only a 10% possibility of worths above 25 cm or 10 inches. Therefore, at this terrific site, a 10 inch telescope will suffer at least some seeing limitation on 9 out of 10 nights.

Due to the fact that this graph specifies a website preferred as having the finest seeing among many kind of feasible sites in the human being, it deserve to be generalised to various other locations by moving the average or median value to the ideal (to reexisting worse average seeing). However the standard form of the graph — as soon as seeing is incredibly great, it much a lot better than average seeing, yet once seeing is poor, it is just slightly worse than average seeing — might be typical of all sites at all times. Indeed the low probcapability of a large worth of r0 at La Palma is continual via astronomer E.M. Antoniadi"s comment that nights of terrific seeing are only "one in fifty".

Additional Reading

"Seeing" by Dorrit Hoffleit. Sky & Telescope, January, 1950, pp. 57-58.

"Seeing - II" by Dorrit Hoffleit. Sky & Telescope, February, 1950, pp. 88-89. - perhaps the initially seeing study evaluation post for the nonprofessional reader.

"The Atmospbelow and also "Seeing"". Section 27 in Amateur Astronomer"s Handbook by J.B. Sidgwick. (New York: Dover, 1980; pp.445-470.) - an early yet still valuable summary of atmospheric seeing, as construed circa 1970.

"Atmospheric Turbulence". Chapter 15 in How to Make a Telescope by Jean Texereau. (Richmond, VA: Willmann-Bell, 1984; pp. 289-307. Translation of 1961 French edition.) - a qualitative analysis of seeing for the visual astronomer.

"Atmospheric Optics". Chapter 5.1 in Reflecting Telescope Optics II (second ed.) by Ray Wilkid. (Berlin, DE: Springer Verlag, 2001; pp. 373-396.) - a amazing summary of the mathematical theory and also empirical measurement of atmospheric disturbance.

Atmospheric Turbulence by J.B. Calvert - A useful explanation of the statistical description of turbulence.

Atmospheric Turbulence: "Seeing" by Kees Dullemond - a concise and intelligble advent to the mathematics of turbulence.

"Atmospheric Turbulence" by Vladimir Sacek - focus on the theoretical evaluation of optical disturbance.

The Effects of Atmospheric Turbulence in Optical Astronomy (1981) by F. Roddier - a classical testimonial paper that pulls together the basic analytical ethics and also draws important conclusions from them.

High Resolution Imaging from the Ground by N.J. Woolf - one more helpful testimonial article from the 1980s.The Physics of Astronomical Seeing by Suprit Singh (PowerPoint presentation) - focus on the physics of turbulence.

Optical Resolution Thstormy a Randomly Inhomogeneous Medium for Very Long and also Very Short Exposures (1965) by D.L. Fried.

The Effects of Atmospheric Turbulence on Astronomical Observations (2002) by Andreas Quirrenbach.

An Investigation of the Effects of Mirror Temperature Upon Telescope Seeing by C.M. Lowne - the first experimental research of mirror seeing.

Mechanism of Formation of Atmospheric Turbulence Relevant for Optical Astronomy (1998) by R. Avila and also J. Vernin.

Exceptional expensive seeing over Dome C in Antarctica (2004) by Jon S. Lawrence, Michael Ashley, Andrei Tokovinin & Tony Travoullion.

Measurement of the Turbulence in the Free Atmosphere over Mt. Maidanak (2000) by V.G. Kornilov and also A.A Tokovinin.

The Intrinsic Seeing Quality at the WHT Site by the Half Arcsecond Programme.

Atmospheric Intensity Scintillation of Stars. I: Statistical Distributions and Temporal Properties (1997a) by D. Dravins, L. Lindegren, E. Mezey and A. Young.

Atmospheric Intensity Scintillation of Stars. II: Dependence on Optical Wavelength (1997b) by D. Dravins, L. Lindegren, E. Mezey and also A. Young.

Atmospheric Intensity Scintillation of Stars. III: Effects for Different Telescope Apertures (1998) by D. Dravins, L. Lindegren and also E. Mezey.

Field Guide to Atmospheric Optics by Larry Andrews.

Experipsychological Comparison of Turbulence Modulation Transfer Function and Aerosol Modulation Transfer Function Thunstable the Open Atmospright here by I. Dror & N.S. Kopeika.

See more: A Switch Is Typically Preconfigured With One _______________ That Includes All Its Ports.

Using Meteorological Forecasts to Predict Astronomical "Seeing". (2009) by Hervé Trinquet & Jean Vernin.