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.
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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 105 to 104 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
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 ~1020 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.