Seeing and Atmospheric Turbulence


Here are some quick notes on seeing and atmospheric turbulence.

The theory of atmospheric seeing was developed in the ’60’s-’80’s and is now well proven. Measuring the temperature structure coefficient predicts image quality (essentially, a plot of index of refraction versus altitude).

Seeing


Seeing is directly related to high-frequency temperature fluctuations associated with turbulence.
Atmosphere above a site is divided into four layers: surface, planetary boundary, atmospheric boundary and the free atmosphere.
Turbulence is generated in the surface layer by wind shear due to frictional/topographic effects from the surface. Height of this layer set by the roughness of the ground, eg, trees and boulders. Layer's extent is 10 to 100 feet high. Telescopes at Apache Point are situation up in the air so that the optics sit above this layer. Isolated peaks (not ridges) are best because air flows around rather than over the surface.
The planetary layer holds the air that's heated by the Sun and moves up and down vertically. The upper limit is the inversion layer, typically 3000 feet.
The atmospheric boundary layer sits on top of the planetary layer and is free of convention but is affected somewhat by the ground, eg, mountains.
The free atmosphere is unaffected by the ground. Turbulence is caused by the jet stream, creating vertical temperature gradients above and below the jet stream, 7 miles up. Jet stream velocity is highest in the mid-latitudes, so best to observe on nights when the jet stream is 'elsewhere'.

Inland sites can be quite good as long as they face into undisturbed air. Large flat plains downwind from mountain ranges can be as good as coastal or island sites.

Turbulence


Direction of light affected by differences in index of refraction of air.
Index of refraction of air changes with air temperature (not humidity, and not wind speed) in the free atmospheric layer or in the surface layer next to the scope.
Seeing depends on temperature differences and not on wind. The temperature difference between the adiabatic cooling rate and the actual air temperature is dissipated by the creation of smaller and smaller eddies on a fractal scale that eventually transform into heat. Turbulence occurs in very thin 10-20 feet deep layers.

What is the structure of thermal turbulence?
Turbulent energy in atmosphere produced by buoyancy and wind shear on scale of tens of meters.

Turbulence in the Inertial Subrange


Energy created by turbulent eddies, and passes through the Inertial Subrange, where smaller and smaller eddies are created.
Eventually eddies on scale of millimeters created.  Sheers in these small eddies are so large that air viscosity transforms their kinetic energy into heat, stopping the eddy creation process.
It’s in the thermal subrange where thermal fluctuations occur.

Characteristics of Seeing


R0, called the “Fried Length” or “coherence length”, permits simple characterization of seeing.
R0 is the diameter of light rays that stay parallel through the atmosphere.
R0 at best sites range from 10-30cm [4-12 inches]. Seeing disk is 1/2 to 1/3 arcsecond. The coherence time is 10-50 milliseconds and the isoplanatic angle is 2-10 arcseconds.
Image degradation comes in two forms: image motion and image blur. Smaller apertures suffer from image motion and large apertures suffer from image blur.
Can be observed by noting the largest aperture where stars appear to shimmer yet are sharply defined.  Larger apertures show steady but bloated stars.

What Aperture is Best?


R0, the Fried Length, suggests that best aperture is 10-30cm [4-12 inches]. However, seeing is highly variable. For us in Oregon, in northwestern USA, when the jetstream is overhead seeing is atrocious, confirming the notes above. When the jetstream is elsewhere (British Columbia or California) seeing can be quite good. Further, locally, at my house, when the nighttime mountain breezes start, seeing disintegrates. Nonetheless, the breeze is not continuous and patience is rewarded with good views. There are nights of near perfect seeing, where magnifications from 750x upward can be used. Finally, there are the rare nights of perfect seeing. On one such night I double barlowed with a very high power eyepiece and reached 6000x on my 20 inch [51cm] F5. The stars showed perfect Airy disks. What was interesting, besides the weird effect of such a small exit pupil, was that fainter stars still looked relatively pinpoint-ish. The rings around the Airy disk were too faint to be seen and indeed, the Airy disk itself was not of equal brightness throughout and instead tapered towards the edge. Of course, resolution was not changed.
This matches my experiences observing through 40 inch [1m] telescopes on nights of good seeing at 750-1200x. The stars were pinpoints, aesthetically very appealing. Also visual observers favorably comment on viewing through 80 and 90 inch [2m and 2.3m] Cassegrains.
Therefore there is a subjective factor of up to 8X in visual observing depending on seeing conditions and observer patience.
The percentage of nights with excellent seeing versus average seeing is a probability function with a long tail. Nights of excellent seeing are one in ten to one in fifty, or several times a year.

Scopes larger than the Fried Length are also preferred when digitally imaging the planets. Perhaps the median scope here is a 16 inch [40cm]. MacEvoy says that the best aperture is 3.5 * R0, or ~ 14 inches [35cm] for R0 of 10cm. At this aperture it is virtually certain that lucky imaging will greatly increase image quality. That is because the extra aperture allows short exposures that freeze the seeing, the hundreds to thousands of images taken are gone through after the fact where the worst ones discarded and the best ones are stacked into a single image of exquisite detail.

References


Bely: The Design and Construction of Large Optical Telescopes, 2003, section 1.3.4 pg 13-, section 12.2.1 pg 394- (contains citations)
Measuring Seeing, Marc Sarazin (European Southern Observatory) http://www.eso.org/astclim/espas/iran/zanjan/zanjan04.ppt
For a thorough and excellent treatment on the subject, see Astronomical Seeing, Bruce MacEvoy, 2012, part 1 http://www.handprint.com/ASTRO/seeing1.html, part 2 http://www.handprint.com/ASTRO/seeing2.html, part 3 http://www.handprint.com/ASTRO/seeing3.html
Jetstream analysis http://squall.sfsu.edu/crws/jetstream.html and animation http://squall.sfsu.edu/scripts/jetstream_modelsml_fcst.html


Mel Bartels, 2012