# Seeing

Scheme of the creation of optical turbulence (seeing) in the earth's atmosphere

In astronomy that's seeing ( Engl. : See ) both the fact and the amount of image blur due to air turbulence , mainly in the surface air layer , but also in the telescope dome and its immediate vicinity. It is usually in arcseconds indicated, and often on the half-width FWHM (full width at half maximum) of the imaging of a point source (eg. As distant star) measured.

When observing visually in a telescope, seeing is expressed by the star's rapid dancing back and forth in a fraction of a second, and in some weather conditions also by a blurred image. In astrophotography , it enlarges the almost point-shaped star disc depending on the duration of the exposure time. In order to determine the momentary seeing directly from a recording, the image must be exposed (integrated) for several seconds.

## overview

Values ​​below 1 "are referred to as good seeing, but in weather conditions with strong air turbulence it can be 5" and more. Typical values ​​for observatories on the European mainland are 1.5 to 2 arc seconds. At particularly favorable locations such as the Sierra Nevada in southern Spain, the Atacama Desert in Chile, on the Canary Islands or Hawaii, where the modern large telescopes are located, the mean value (median) is better than an arcsecond, in very good conditions it can even be below 0, 4 "sink.

Seeing is somewhat dependent on the wavelength of the light observed; longer-wave radiation has smaller values. Without specifying the wavelength, it mostly refers to 500 nm (turquoise light). Seeing is a direct result of the optical turbulence of the earth's atmosphere. If the perfectly planar light wave front from a distant star passes through the earth's atmosphere, the wave front is bent in the range of a few micrometers (0.001 mm). For visible light, these disturbances are usually larger than the light wavelength.

The current average value of the seeing can also change from one minute to the next, depending on the atmospheric conditions. The turbulence in the air is a consequence of changes in its refractive index, which changes both with time (wind speed) and with the location along the line of sight. Small optics like the human eye can observe the seeing through the twinkling of the stars. Small telescopes with a maximum opening of up to approx. 10 cm in diameter suffer mainly from the atmospheric image movement during long exposures. With short exposure times, diffraction-limited images with half-widths of around 1 arc second can be recorded. In general, the image movement decreases with larger openings. In telescopes with openings larger than approx. 10 cm in diameter, the image of a point source usually "breaks down" into several speckles and the half-width of a point source is no longer determined by the telescope size, but by the seeing.

In order to achieve an image that is independent of seeing and that is as diffraction-limited as possible, there are several technical compensatory measures such as speckle interferometry , lucky imaging or adaptive optics . These techniques lead to very good results with relatively small fields of view in the infrared range .

## Emergence

Cartoon: optical turbulence

Seeing deterioration is caused by turbulence in layers of air, which irregularly deflect (refract) the light arriving from outside the earth's atmosphere . When observing with the naked eye, the effect can be seen as blinking and twinkling of the stars ( scintillation ). On images with longer exposure times, seeing leads to the light beam from a point source being “smeared” over a larger area; the picture becomes blurred. The shorter the observed wavelength , the greater the deflection effect and the faster it changes . One extreme form of this turbulence effect is the shimmering air over hot asphalt.

Seeing has several causes. The jet stream in the high atmosphere is largely laminar and hardly contributes to seeing. However, the transition layer to deeper air layers is often turbulent and one of the main causes of seeing. Further transitional layers can strengthen it at a lower level. Close to the ground, winds are often turbulent because the air flows over bumps or obstacles. The weather also influences the seeing: in the back of a cold front (see backside weather ) the air is very pure, but very turbulent. The thermals close to the ground also contribute to the unrest in the air , which is caused by the temperature difference between the ground heated during the day and the cool night air . Thermal Bodenseeing is also worsened by changing vegetation , especially forests.

Bad seeing (4–5 ") when observing the lunar crater Clavius

These factors cannot be actively influenced, but can be minimized by a suitable choice of the telescope location. For example, the jet stream and the wind below are largely parallel over Chile, which reduces the turbulence. In addition, the wind comes from the sea, which means that the turbulence near the ground is also less. It is therefore a preferred location for modern giant telescopes .

Furthermore, there are artificial contributions to seeing through the thermals of the telescope itself and the telescope dome ("dome seeing", in German hall refraction ). These can be prevented by painting the dome white, active cooling during the day to the expected night temperature and a clever design. In general, all heat sources inside the dome worsen the seeing. This also applies to the observer and its heat radiation, which is why large telescopes are increasingly being controlled from separate control rooms. In order to achieve the most laminar flow possible directly at the telescope, research telescopes are no longer built with a large, closed tube, but with an air-permeable tube tube . Furthermore, today's telescopic domes can be opened much wider than earlier designs.

Because seeing is caused by changing refractive index of the air and by irregular air movements, one speaks of optical turbulence in the atmosphere.

## Description of the optical disturbances

Many amateur astronomers classify seeing with values ​​from 1 to 5, analogous to the school grades (see Antoniadi scale ). More complex methods are described below.

### Visual versus photographic

Even when the air is very turbulent, there are usually short moments with a calm telescope image that an experienced observer can use to sketch fine details. In the above picture of the lunar crater Clavius , two small craters with 1 × 2 "(diameter 2 km) can be seen left and right of the middle crater for about 0.2 seconds, although the seeing is almost 5". In astrophotography , on the other hand, this is only possible with great effort, because the wobbling of the image adds up during the exposure.

With a modern webcam , this can be avoided with the moon and bright planets : you take at least 100 photos with a very short exposure time, look for the best 10 and average them on the PC to form an artificial image. This allows you to almost achieve the visual sharpness of the moment, or even exceed it for 500 to 1000 shots.

### r 0 and t 0

The seeing of a telescope location can be described by the location scale and the time scale . For telescopes with a diameter smaller than , the half-width of a point source is proportional to the wavelength and reciprocal to the telescope diameter for a long-term exposure : ${\ displaystyle r_ {0}}$${\ displaystyle t_ {0}}$${\ displaystyle D}$${\ displaystyle r_ {0}}$${\ displaystyle \ mathrm {FWHM}}$${\ displaystyle \ lambda}$

${\ displaystyle \ mathrm {FWHM} = {\ frac {\ lambda} {D}}}$

Telescopes with a larger diameter than , on the other hand, have a limited width at half maximum: ${\ displaystyle r_ {0}}$${\ displaystyle r_ {0}}$

${\ displaystyle \ mathrm {FWHM} = {\ frac {\ lambda} {r_ {0}}}}$

${\ displaystyle r_ {0}}$ for visible light under good visibility conditions is 10-20 cm and typically 5 cm at sea level.

${\ displaystyle r_ {0}}$is often referred to as the Fried parameter, after David L. Fried , and is proportional to . ${\ displaystyle \ lambda ^ {6/5}}$

The typical time scale for the atmospheric fluctuations results from dividing by the mean wind speed: ${\ displaystyle t_ {0}}$${\ displaystyle r_ {0}}$

${\ displaystyle t_ {0} \ approx {\ frac {0 {,} 3 \, r_ {0}} {v _ {\ mathrm {wind}}}}}$.

For visible light it is in the range of a few milliseconds. If the observation time is less than , the atmospheric disturbances are, so to speak, frozen, if it is significantly higher, an image averaged over the disturbances results. ${\ displaystyle t_ {0}}$

### The Kolmogorov turbulence model

According to Andrei Nikolajewitsch Kolmogorow , turbulence in the earth's atmosphere arises from the supply of energy from the sun in large balls of air ( eddies ) with the characteristic size L 0 . These finally disintegrate into smaller and smaller balls of air of the characteristic size l 0 , which convert their energy into heat via viscosity ( dissipation ). Typical values ​​for L 0 are in the range from a few tens to several hundred meters and for I 0 in the range of a few millimeters.

The mathematical-physical basis of the Kolmogorov model is based, among other things, on the concept of structural functions. It is assumed that for the statistical (turbulent) disturbances (phase disturbances, temperature disturbances, pressure disturbances) the respective spatial mean value (indicated by angle brackets) is zero, e.g. B. for the phase of electromagnetic waves φ the following applies: <φ> = 0. This model is supported by a large number of measurements and is often used to simulate astronomical images.

The structure function D describes the spatial properties of the turbulent medium. This is done by determining the mean difference of the statistical process at two locations ( r and r + ρ ):

${\ displaystyle D _ {\ phi} \ left (\ mathbf {\ rho} \ right) = \ left \ langle \ left | \ phi \ left (\ mathbf {r} \ right) - \ phi \ left (\ mathbf { r} + \ mathbf {\ rho} \ right) \ right | ^ {2} \ right \ rangle}$.

The Kolmogorov model of turbulence leads to a simple relation (by Valerian Illich Tatarskii ) between the phase structure function D φ and a single parameter, the so-called coherence length r 0 (also called Fried parameter). The following applies:

${\ displaystyle D _ {\ phi} \ left ({\ mathbf {\ rho}} \ right) = 6 {,} 88 \ left ({\ frac {\ left | \ mathbf {\ rho} \ right |} {r_ {0}}} \ right) ^ {5/3}}$

${\ displaystyle r_ {0}}$is a measure of the strength of the turbulence or the phase change. Fried (1965) and Noll (1976) found that this also corresponds to the diameter for which the variance of the phase averaged over the opening (telescope diameter ) d reaches 1: ${\ displaystyle r_ {0}}$${\ displaystyle \ sigma ^ {2}}$

${\ displaystyle \ sigma ^ {2} = 1 {,} 03 \ left ({\ frac {d} {r_ {0}}} \ right) ^ {5/3}}$

This equation is the common definition for . ${\ displaystyle r_ {0}}$

### Representation of optical disturbances by Zernike polynomials

In optics, imaging errors (aberrations) are often represented as the sum of special polynomials, so-called Zernike polynomials . The same can be done for the statistical, atmospheric aberrations; however, in this case the coefficients of the Zernike polynomials, e.g. B. Describe defocus, coma, astigmatism, etc., now also statistical functions that change over time. The following table (based on Noll 1976) gives the mean square amplitudes of the aberrations Δ j and the remaining phase disturbance after eliminating the first j terms:

${\ displaystyle Z_ {j}}$ n m equation description ${\ displaystyle \ Delta _ {j}}$ ${\ displaystyle \ Delta _ {j} - \ Delta _ {j-1}}$
Z1 0 0 ${\ displaystyle 1}$ 1,030 S -
Z2 1 1 ${\ displaystyle 2r \ cos \ phi}$ tilt 0.582 S 0.448 S
Z3 1 1 ${\ displaystyle 2r \ sin \ phi}$ tilt 0.134 S 0.448 S
Z4 2 0 ${\ displaystyle {\ sqrt {3 (2r ^ {2} -1)}}}$ Defocus 0.111 S 0.023 S
Z5 2 2 ${\ displaystyle {\ sqrt {6r ^ {2} \ sin 2 \ phi}}}$ astigmatism 0.0880 S 0.023 S
Z6 2 2 ${\ displaystyle {\ sqrt {6r ^ {2} \ cos 2 \ phi}}}$ astigmatism 0.0648 S 0.023 S
Z7 3 1 ${\ displaystyle {\ sqrt {8 (3r ^ {3} -2r) \ sin \ phi}}}$ coma 0.0587 S 0.0062 S
Z8 3 1 ${\ displaystyle {\ sqrt {8 (3r ^ {3} -2r) \ cos \ phi}}}$ coma 0.0525 S 0.0062 S
Z9 3 3 ${\ displaystyle {\ sqrt {8r ^ {3} \ sin 3 \ phi}}}$ 0.0463 S 0.0062 S
Z10 3 3 ${\ displaystyle {\ sqrt {8r ^ {3} \ cos 3 \ phi}}}$ 0.0401 S 0.0062 S
Z11 4th 0 ${\ displaystyle {\ sqrt {5 (6r ^ {4} -6r ^ {2} +1)}}}$ Spherical aberration 0.0377 S 0.0024 S

In the table, the abbreviations mean: , the distance from the center, the azimuth angle. ${\ displaystyle S = (D / r_ {0}) ^ {5/3}}$${\ displaystyle r}$${\ displaystyle \ phi}$

## Scales

There are different scales for assessing seeing. They differ in the effort required to determine the seeing value and in whether they are instrument-dependent or not.

Since different atmospheric disturbance factors are present at different locations , a location-specific specification of a seeing scale is helpful when it comes to the choice of the observation location. Such a statement about the unrest in the atmosphere is also part of every observation report of an astronomical object .

Seeing on a seeing scale is primarily assessed using optical aids. However, since the assessment of the seeing depends heavily on its appearance, information about the instrument used (type of instrument and magnification) is part of every observation report.

In professional astronomy, seeing is nowadays determined with a so-called seeing monitor (DIMM, Differential Image Motion Monitor, and MASS, Multi-Aperture Scintillation Sensor) as standard. Older scales like the ones described below are practically only used in amateur astronomy.

### Pickering scale

The Pickering scale according to William Henry Pickering provides information about the degree of air turbulence compared to a perfect picture without atmospheric disturbances. Therefore, the indication of the seeing is also given in the form 1/10 (for the worst), 2/10 etc. Pickering used a refractor with a 5 inch (12.7 cm) aperture when creating his scale .

The classification takes place in ten categories:

1. Very bad: the star is twice as large as the diameter of the third diffraction ring . The star appears 13 ″ in diameter.
2. Very bad: the star is occasionally larger than the diameter of the third diffraction ring.
3. Bad to very bad: The star is about the same size as the diameter of the third diffraction ring (6.7 ″) and brighter in the middle.
4. Bad: The central star disc can often be seen. Parts of the diffraction rings (arcs) can sometimes be seen.
5. Inexpensive: the central star disc is always visible. Arches of the diffraction rings are often visible.
6. Inexpensive to good: the central star disc is always visible. Short arcs of the diffraction rings are always visible.
7. Good: The central star disc is sometimes sharply defined. The diffraction rings can be seen as long arcs or complete circles.
8. Good to excellent: The central star disc is always sharply defined. The diffraction rings can be seen as complete circles or long arcs, but in motion.
9. Excellent: the inner diffraction ring is calm. The outer rings are occasionally at rest.
10. Excellent / perfect: The entire diffraction pattern is completely calm.

9 and 10 can not be reached in Central Europe .

The Antoniadi scale according to Eugène Michel Antoniadi enables a rough classification of seeing. It is mainly used in amateur astronomy and is based on school grades .

The evaluation is from I to V:

• I perfect picture without the slightest picture disturbance
• II slight flushing, but phases of calm lasting at least a few seconds
• III mediocre air rest, noticeable trembling of the image
• IV bad seeing, constantly disturbing wobbling
• V very poor seeing, which hardly allows a rough sketch to be made.

## Seeing at observatories

Observatories are preferably set up at locations with particularly low atmospheric disturbances. At the vast majority of research astronomy sites with large optical telescopes of the 8-10 m class, the median seeing at a wavelength of 500 nm is less than 0.8 arc seconds.

## Crossing the seeing barrier

With conventional optical telescopes, seeing limits the angular resolution to approx. 1 arc second. This corresponds to the theoretical resolution limit of a 12.5 cm telescope at a wavelength of 0.5 µm (green light). The first step in breaking this barrier was speckle interferometry , which allows the observation of bright objects with high resolution. For this purpose, a large number of recordings of the same object are made, each with an exposure time of less than t 0 . The phase deviation ( bispectrum ) is averaged through a mathematical image analysis so that the temporary deviations cancel each other out. Simplified methods, such as “ Image Stacking ”, which eliminate the two Zernike modes of tilt by simply shifting the image, already allow an improvement by a factor of 8; " Lucky Imaging " is even better , which also only uses the images in which the remaining phase disturbances are just low. The basic limitation of the process lies in the short exposure times required. During this time, the observed object must provide enough light for a low-noise image that is suitable for post-processing. This limit has been shifted significantly downwards, in particular through the development of highly sensitive, almost noise-free " Electron Multiplying CCD " image sensors.

At the beginning of 1990, the first large telescopes were equipped with adaptive optics that compensate for the phase disturbance. The larger the telescope mirror and the shorter the wavelength of the observation, the more degrees of freedom the system must have in order to achieve a complete correction. Here, too, a bright object must be at least in the vicinity of the examined object in order to provide sufficient information for setting the optics. This limit can be overcome by using a laser guide star .

From the NASA 1990 was Hubble Space Telescope into orbit. It is not affected by seeing because it works outside of the atmosphere. Due to its mirror diameter of 2.4 m, its resolution is below that of larger terrestrial telescopes. The planned successor, the James Webb Space Telescope, is to have a primary mirror with a diameter of 6.5 m.

## Individual evidence

1. A. Tokovinin and V. Kornilov: Accurate measurements seeing with MASS and DIMM MNRAS 381, pp 1179-1189 (2007) doi : 10.1111 / j.1365-2966.2007.12307.x