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Encyclopedia > Astronomical seeing
Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. The vertical scale of the wavefronts plotted is highly exaggerated.

Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by the Earth's atmosphere. The astronomical seeing conditions on a given night at a given location describe how much the Earth's atmosphere perturbs the images of stars as seen through a telescope. The most common seeing measurement is the diameter (technically Full Width Half Maximum) of the seeing disc. The seeing disc diameter ("seeing") is a reference to the best possible angular resolution which can be achieved by an optical telescope in a long photographic exposure, and corresponds to the diameter of the fuzzy blob seen when observing a point-like star through the atmosphere. The size of the seeing disc is determined by the astronomical seeing conditions at the time of the observation. The best conditions give a seeing disc diameter of ~0.4 arcseconds and are found at high-altitude observatories on small islands such as Mauna Kea or La Palma. A detailed description of the seeing disc can be found in the FWHM of the seeing disc subsection of the following article. Image File history File links Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Image File history File links Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Scintillation or twinkling are generic terms for rapid variations in apparent brightness or color of a distant luminous object viewed through the atmosphere. ... In telecommunication, a full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. ... Angular resolution describes the resolving power of a telescope. ... An optical telescope is a telescope which is used to gather, and focus light, for directly viewing a magnified image, making a photograph, etc. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 â‰ˆ 7. ... The Mauna Kea Observatory, an institute of the University of Hawaii, is considered one of the most important land-based observatories in the world for its isolated, unobstructed views of space without interference from man-made light sources. ... The seeing statistics for Roque de los Muchachos Observatory make it the third best location for optical and infrared astronomy after Dome C, Antarctica and Mauna Kea Observatory, Hawaii. ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ...

Seeing is one of the biggest problems for Earth-based astronomy: while the big telescopes have theoretically milli-arcsecond resolution, the real image will never be better than the average seeing disc during the observation. This can easily mean a factor of 100 between the potential and practical resolution. 50 cm refracting telescope at Nice Observatory. ... Angular resolution describes the resolving power of a telescope. ...

## The Effects of Astronomical Seeing

Astronomical seeing has several effects:

1. It causes the images of point-sources (e.g., stars) to break up into speckle patterns, which change very rapidly with time (the resulting speckled images can be processed using speckle imaging)
2. Long exposure images of these changing speckle patterns result in a blurred image of the point source, called a seeing disc
3. The brightness of stars appears to fluctuate in a process known as scintillation or twinkling
4. Atmospheric seeing causes the fringes in an astronomical interferometer to move rapidly
5. The distribution of atmospheric seeing through the atmosphere (the CN2 profile described below) causes the image quality in adaptive optics systems to degrade the further you look from the location of reference star

The effects of atmospheric seeing were indirectly responsible for the belief that there were canals on Mars. In viewing a bright object such as Mars, occasionally a still patch of air will come in front of the planet, resulting in a brief moment of clarity. Before the use of charge-coupled devices, there was no way of recording the image of the planet in the brief moment other than having the observer remember the image and draw it later. This had the effect of having the image of the planet be dependent on the observer's memory and preconceptions which led the belief that Mars had linear features. Typical short-exposure image of a binary star (Zeta Bootis in this case) as seen through atmospheric seeing. ... Scintillation or twinkling are generic terms for rapid variations in apparent brightness or color of a distant luminous object viewed through the atmosphere. ... Optical interferometry is a technique of interferometry combining light from multiple sources in an optical instrument in order to make various precise measurements. ... A deformable mirror can be used to correct wavefront errors in an astronomical telescope. ... For a time in the late 19th and early 20th centuries, it was believed that there were canals on Mars. ... A specially developed CCD used for ultraviolet imaging in a wire bonded package. ...

The effects of atmospheric seeing are qualitatively similar throughout the visible and near infra-red wavebands. At large telescopes the long exposure image resolution is generally slightly higher at longer wavelengths, and the timescale (t0 - see below) for the changes in the dancing speckle patterns is substantially lower. Image of a small dog taken in mid-infrared (thermal) light (false color) Infrared (IR) radiation is electromagnetic radiation of a wavelength longer than visible light, but shorter than microwave radiation. ...

## Measures of Astronomical Seeing

There are three common descriptions of the astronomical seeing conditions at an observatory:

1. The FWHM of the seeing disc
2. r0 and t0
3. The CN2 profile

These are described in the sub-sections below:

### The FWHM of the seeing disc

Without an atmosphere, a small star would have an apparent size in a telescope image determined by diffraction and would be inversely proportional to the diameter of the telescope. However when light enters the Earth's atmosphere, the different temperature layers and different wind speeds distort the light waves leading to distortions in the image of a star. The effects of the atmosphere can be modelled as rotating cells of air moving turbulently. At most observatories the turbulence is only significant on scales larger than r0 (see below -- the seeing parameter r0 is 10-20 cm at visible wavelengths under the best conditions) and this limits the resolution of telescopes to be about the same as given by a space-based 10-20 cm telescope. Diffraction is the bending and spreading of waves when they meet an obstruction. ... Layers of Atmosphere (NOAA) Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by semi-random, stochastic property changes. ...

The distortion changes at a high rate, typically more frequently than 100 times a second. In a typical astronomical image of a star with an exposure time of seconds or even minutes, the different distortions average out as a filled disc called the seeing disc. The diameter of the seeing disc (technically the Full Width at Half Maximum intensity (FWHM)) is a common measure of the astronomical seeing conditions. The shutter speed dial of a Fujika STX-1. ... For the geometric term, see diameter. ... In telecommunication, a full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. ...

It follows from this definition that seeing is always a variable quantity, different from place to place, from night to night and even variable on a scale of minutes. Astronomers often talk about "good" nights with a low average seeing disc diameter, and "bad" nights where the seeing diameter was so high that all observations were worthless.

The FWHM of the seeing disc (or just Seeing) is usually measured in arcseconds, abbreviated with the symbol ("). A 1.0" seeing is a good one for average astronomical sites. The seeing of an urban environment is usually much worse. Good seeing nights tend to be clear, cold nights without wind gusts. Warm air rises (convection) degrading the seeing as does wind and clouds. At the best high-altitude mountaintop observatories the wind brings in stable air which has not previously been in contact with the ground, sometimes providing seeing as good as 0.4". A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 â‰ˆ 7. ... Convection is the transfer of heat by currents within a fluid. ... Observatory of Strasbourg An observatory is a location used for observing terrestrial and/or celestial events. ...

### r0 and t0

The astronomical seeing conditions at an observatory can be well described by the parameters r0 and t0. For telescopes with diameters smaller than r0, the resolution of long-exposure images is inversely proportional to the telescope diameter. For telescopes with diameters larger than r0, the image resolution is independent of telescope diameter, remaining constant at the value given by a telescope of diameter equal to r0. r0 also corresponds to the length-scale over which the turbulence becomes significant (10-20 cm at visible wavelengths at good observatories), and t0 corresponds to the time-scale over which the changes in the turbulence become significant. r0 determines the spacing of the actuators needed in an adaptive optics system, and t0 determines the correction speed required to compensate for the effects of the atmosphere. A deformable mirror can be used to correct wavefront errors in an astronomical telescope. ...

r0 and t0 vary with the wavelength used for the astronomical imaging, allowing slightly higher resolution imaging at longer wavelengths using large telescopes.

r0 is often known as the Fried parameter (pronounced freed), named after David L. Fried. David L. Fried is a scientist, best known for his contributions to optics. ...

#### Mathematical Description of r0 and t0

Simulated negative image showing what a single (point-like) star would look like through a ground-based telescope with a diameter of 2r0. Diffraction makes the image appear blurred. The atmosphere would make the blob move around very rapidly, so that in a long-exposure photograph it would appear more blurred.
Simulated negative image showing what a single (point-like) star would look like through a ground-based telescope with a diameter of 7r0, on the same angular scale as the 2r0 image above. The atmosphere makes the image break up into several blobs (speckles). The speckles move around very rapidly, so that in a long-exposure photograph the star would appear as a single blurred blob.
Simulated negative image showing what a single (point-like) star would look like through a ground-based telescope with a diameter of 20r0. The atmosphere makes the image break up into several blobs (speckles). The speckles move around very rapidly, so that in a long-exposure photograph the star would appear as a single blurred blob.

In reality the pattern of blobs (speckles) in the images changes very rapidly, so that long exposure photographs would just show a single large blurred blob in the centre for each telescope diameter. The diameter (FWHM) of the large blurred blob in long exposure images is called the seeing disc diameter, and is independent of the telescope diameter used (as long as adaptive optics correction is not applied). A deformable mirror can be used to correct wavefront errors in an astronomical telescope. ...

It is first useful to give a brief overview of the basic theory of optical propagation through the atmosphere. In the standard classical theory, light is treated as an oscillation in a field ψ. For monochromatic plane waves arriving from a distant point source with wave-vector $mathbf{k}$: $psi_{0} left(mathbf{r},tright) = A_{u}e^{ileft (phi_{u} + 2pinu t + mathbf{k}cdotmathbf{r} right )}$ where ψ0 is the complex field at position $mathbf{r}$ and time t, with real and imaginary parts corresponding to the electric and magnetic field components, φu represents a phase offset, ν is the frequency of the light determined by $nu=cleft | mathbf{k} right | / left ( 2 pi right )$, and Au is the amplitude of the light.

The photon flux in this case is proportional to the square of the amplitude Au, and the optical phase corresponds to the complex argument of ψ0. As wavefronts pass through the Earth's atmosphere they may be perturbed by refractive index variations in the atmosphere. The diagram at the top-right of this page shows schematically a turbulent layer in the Earth's atmosphere perturbing planar wavefronts before they enter a telescope. The perturbed wavefront ψp may be related at any given instant to the original planar wavefront $psi_{0} left(mathbf{r}right)$ in the following way: $psi_{p} left(mathbf{r}right) = left ( chi_{a} left(mathbf{r}right) e^{iphi_{a} left(mathbf{r}right)}right ) psi_{0} left(mathbf{r}right)$

where $chi_{a} left(mathbf{r}right)$ represents the fractional change in wavefront amplitude and $phi_{a} left(mathbf{r}right)$ is the change in wavefront phase introduced by the atmosphere. It is important to emphasise that $chi_{a} left(mathbf{r}right)$ and $phi_{a} left(mathbf{r}right)$ describe the effect of the Earth's atmosphere, and the timescales for any changes in these functions will be set by the speed of refractive index fluctuations in the atmosphere.

#### The Kolmogorov model of turbulence

A description of the nature of the wavefront perturbations introduced by the atmosphere is provided by the Kolmogorov model developed by Tatarski (1961), based partly on the studies of turbulence by the Russian mathematician Andreï Kolmogorov (see references below by Kolmogorov). This model is supported by a variety of experimental measurements (see e.g. references below by Buscher et al 1995, Nightingale and Buscher 1991, O’Byrne 1988, Colavita et al 1987) and is widely used in simulations of astronomical imaging. The model assumes that the wavefront perturbations are brought about by variations in the refractive index of the atmosphere. These refractive index variations lead directly to phase fluctuations described by $phi_{a} left(mathbf{r}right)$, but any amplitude fluctuations are only brought about as a second-order effect while the perturbed wavefronts propagate from the perturbing atmospheric layer to the telescope. For all reasonable models of the Earth's atmosphere at optical and infra-red wavelengths the instantaneous imaging performance is dominated by the phase fluctuations $phi_{a} left(mathbf{r}right)$. The amplitude fluctuations described by $chi_{a} left(mathbf{r}right)$ have negligible effect on the structure of the images seen in the focus of a large telescope. Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Andrey Kolmogorov Andrey Nikolaevich Kolmogorov (ÐÐ½Ð´Ñ€ÐµÌÐ¹ ÐÐ¸ÐºÐ¾Ð»Ð°ÌÐµÐ²Ð¸Ñ‡ ÐšÐ¾Ð»Ð¼Ð¾Ð³Ð¾ÌÑ€Ð¾Ð²) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Soviet mathematician who made major advances in the fields of probability theory and topology. ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ...

The phase fluctuations in Tatarski's model are usually assumed to have a Gaussian random distribution with the following second order structure function: $D_{phi_{a}}left(mathbf{rho} right) = left langle left | phi_{a} left ( mathbf{r} right ) - phi_{a} left ( mathbf{r} + mathbf{rho} right ) right | ^{2} right rangle _{mathbf{r}}$

where $D_{phi_{a}} left ({mathbf{rho}} right )$ is the atmospherically induced variance between the phase at two parts of the wavefront separated by a distance $mathbf{rho}$ in the aperture plane, and < ... > represents the ensemble average.

The structure function of Tatarski (1961) can be described in terms of a single parameter r0:

$D_{phi_{a}} left ({mathbf{rho}} right ) = 6.88 left ( frac{left | mathbf{rho} right |}{r_{0}} right ) ^{5/3}$

r0 indicates the strength of the phase fluctuations as it corresponds to the diameter of a circular telescope aperture at which atmospheric phase perturbations begin to seriously limit the image resolution. Typical r0 values for I band (900 nm wavelength) observations at good sites are 20---40 cm. Fried (1965) and Noll (1976) noted that r0 also corresponds to the aperture diameter for which the variance σ2 of the wavefront phase averaged over the aperture comes approximately to unity: $sigma ^{2}=1.0299 left ( frac{d}{r_{0}} right )^{5/3}$ Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ...

This equation represents a commonly used definition for r0, a parameter frequently used to describe the atmospheric conditions at astronomical observatories.

r0 can be determined from a measured CN2 profile (described below) as follows:

$r_{0}=left ( 16.7lambda^{-2}( cos gamma )^{-1}int_{0}^{infty}dh C_{N}^{2}(h) right )^{-3/5}$

where the turbulence strength $C_{N}^{2}(h)$ varies as a function of height h above the telescope, and γ is the angular distance of the astronomical source from the zenith (from directly overhead). The zenith, in astronomy, is the point in the sky which appears directly above the observer. ...

The timescale t0 is simply proportional to r0 divided by the mean wind speed.

#### References

Astronomical observatories are generally situated on mountaintops, as the air at ground level is usually more convective. A light wind bringing stable air from high above the clouds and ocean generally provides the best seeing conditions (telescope shown: NOT).

Much of the above text is taken (with permission) from http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/ Image File history File links Download high resolution version (1477x979, 454 KB)The NOT telescope at sunset in June 2001. ... Image File history File links Download high resolution version (1477x979, 454 KB)The NOT telescope at sunset in June 2001. ... The dome of the Nordic Optical Telescope. ...

• BUSCHER, D. F., ARMSTRONG, J. T., HUMMEL, C. A., QUIRRENBACH, A., MOZURKEWICH, D., JOHNSTON, K. J., DENISON, C. S., COLAVITA, M. M., & SHAO, M. 1995. Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales. Applied Optics, 34(Feb.), 1081-1096.
• COLAVITA, M. M., SHAO, M., & STAELIN, D. H. 1987. Atmospheric phase measurements with the Mark III stellar interferometer. Applied Optics, 26(Oct.), 4106-4112.
• FRIED, D. L. 1965. Statistics of a Geometric Representation of Wavefront Distortion, Optical Society of America Journal, 55, 1427-1435.
• KOLMOGOROV, A. N. 1941. Dissipation of energy in the locally isotropic turbulence. Comptes rendus (Doklady) de l'Académie des Sciences de l'U.R.S.S., 32, 16-18.
• KOLMOGOROV, A. N. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynold's numbers. Comptes rendus (Doklady) de l'Académie des Sciences de l'U.R.S.S., 30, 301-305.
• NIGHTINGALE, N. S., & BUSCHER, D. F. 1991. Interferometric seeing measurements at the La Palma Observatory. Monthly Notices of the Royal Astronomical Society, 251(July), 155-166.
• NOLL, R. J. 1976. Zernike polynomials and atmospheric turbulence. Optical Society of America Journal, 66(Mar.), 207-211.
• O'BYRNE, J. W. 1988. Seeing measurements using a shearing interferometer. Publications of the Astronomical Society of the Pacific, 100(Sept.), 1169-1177.
• TATARSKI, V. I. 1961. Wave Propagation in a Turbulent Medium. McGraw-Hill Books.

### The CN2 profile

A more thorough description of the astronomical seeing at an observatory is given by producing a profile of the turbulence strength as a function of altitude, called a CN2 profile. CN2 profiles are generally performed when deciding on the type of adaptive optics system which will be needed at a particular telescope, or in deciding whether or not a particular location would be a good site for setting up a new astronomical observatory. Typically, several methods are used simultaneously for measuring the CN2 profile and then compared. Some of the most common methods include:

1. SCIDAR (imaging the shadow patterns in the scintillation of starlight)
2. LOLAS (a small aperture variant of SCIDAR designed for low-altitude profiling)
3. SLODAR
4. RADAR mapping of turbulence
5. Balloon-borne thermometers to measure how quickly the air temperature is fluctuating with time due to turbulence

There are also mathematical functions describing the CN2 profile. Some are empirical fits from measured data and others attempt to incorporate elements of theory. One common model for continental land masses is known as Hufnagel-Valley after two workers in this subject. Scintillation or twinkling are generic terms for rapid variations in apparent brightness or color of a distant luminous object viewed through the atmosphere. ...

## Overcoming Atmospheric Seeing

The first answer to this problem was speckle imaging, which allowed bright objects to be observed with very high resolution. Later came NASA's Hubble Space Telescope, working outside the atmosphere and thus not have any seeing problems and allowing observations of faint targets for the first time (although with poorer resolution than speckle observations of bright sources from ground-based telescopes because of Hubble's smaller telescope diameter). The highest resolution visible and infrared images currently come from imaging optical interferometers such as the Navy Prototype Optical Interferometer or Cambridge Optical Aperture Synthesis Telescope. Typical short-exposure image of a binary star (Zeta Bootis in this case) as seen through atmospheric seeing. ... NASA Logo Listen to this article Â· (info) This audio file was created from the revision dated 2005-09-01, and does not reflect subsequent edits to the article. ... The Hubble Space Telescope is a telescope in orbit around the Earth. ... Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ... The Navy Prototype Optical Interferometer (NPOI) is an interferometer operated by the US Naval Observatory, the Naval Research Laboratory and The Lowell Observatory. ... COAST, the Cambridge Optical Aperture Synthesis Telescope, is a multi-element optical interferometer with baselines of up to 100 metres, designed to observe stars with angular resolution as high as one thousandth of one arcsecond (much higher resolution than can be obtained with individual telescopes such as the Hubble Space...

Starting in the 1990s, many telescopes have begun to develop adaptive optics systems that partially solve the seeing problem, but none of the systems so far built or designed completely removes the atmosphere effect, and observations are usually limited to a small region of the sky surrounding relatively bright stars. The 1990s decade refers to the years from 1990 to 1999, inclusive, the last decade of the 20th Century. ... A deformable mirror can be used to correct wavefront errors in an astronomical telescope. ...

A more recently implemented and much cheaper technique Lucky Imaging has had very good results. This idea dates back to Fried in 1978. Basically this technique relies on the fact that every so often the sky will momentarily be clear, and hence by recording the image in realtime, an excellent image can be picked out. This technique can outperform adaptive optics in many cases and is even accessible to amateurs. The best 1% of exposures of the 0. ...

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