Earth’s atmosphere places serious limitations upon as-
tronomical observations for two primary reasons. First,
the atmosphere is not equally transparent at all wave-
lengths and certain wavelength regimes are completely in-
accessible from the ground. Observations from telescopes
orbiting above the atmosphere have to a certain extent cir-
cumvented this obstacle. Second, turbulence within the at-
mosphere produces image blurring that seriously degrades
the ability of telescopes to resolve detail in images. Be-
ginning in the late 19th century, astronomers realized the
importance of locating observatories at sites with excep-
tionally stable air in order to achieve the best possible
seeing conditions. It is fortunate that the properties that
lend favorable astronomical seeing are also consistent with
transparency, and modern observatories are typically lo-
cated at relatively high elevations in very dry climates.
The intrinsic limiting ability of a telescope to resolve
fine angular detail is set by the diffraction properties of
light. For a telescope such as the 4-m-aperture Mayall
reflector on Kitt Peak in southern Arizona observing at a
wavelength of 550 nm, the center of the visible region of
the spectrum, the Rayleigh limit is approximately 0.035
arcsec, an angle equivalent to that subtended by a nickel
seen from a distance of 75 miles.
Unfortunately, the atmosphere thwarts the realization
of such resolution and imposes an effective limiting res-
olution from 1 to 2 arcsec, a degradation in resolution
by a factor of roughly 50. Some locations on Earth offer
seeing that is occasionally as good as 0.2–0.3 arcsec, but
even these rare and superb seeing conditions are an order
of magnitude worse than what would be obtained under
ideal circumstances. One obvious option is to put tele-
scopes into orbit above the atmosphere. Indeed, a primary
justification for the 2.5-m Hubble Space Telescope (HST)
has been its ability completely to avoid atmospheric blur-
ring. For the foreseeable future, ground-based telescopes
will continue to be built with apertures significantly larger
than their far more expensive space-borne counterparts.
The two 10-m Keck telescopes on Mauna Kea in Hawaii
as well as the new 8-m-class telescopes in the northern
and southern hemispheres offer three to four times higher
resolution than HST if the challenge of atmospheric blur-
ring can be overcome. Thus, extensive resources have been
expended to exploit methods for correcting turbulent blur-
ring by special imaging techniques and especially through
adaptive optics.
In 1970, the French astronomer and optical physi-
cist Antoine Labeyrie pointed out an elegantly sim-
ple method for circumventing atmospheric seeing condi-
tions to achieve diffraction-limited resolution. Labeyrie’s
method, which he named speckle interferometry, takes
advantage of the detailed manner in which the blurring
occurs in order to cancel out the seeing-induced effects.
The atmosphere is a turbulent medium with scales of
turbulence ranging from perhaps hundreds of meters down
to turbulent eddies as small as a few centimeters. Theturbulence arises from the dynamics of the atmosphere as
driven by Earth’s rotation and the absorption of solar ra-
diant energy, which is converted into the thermal energy
content of the atmosphere. Turbulence along does not in-
duce “bad seeing,” rather it is the variation in density from
one turbulence region to another that causes rays of light to
be refracted from otherwise straight paths to the telescope.
Light from a star spreads out in all directions to fill
a spherical volume of space. The distances to stars are
so great that a typical star can be envisioned as a point
source illuminating a spherical surface on which the
telescope is located. Because the radius of this imagi-
nary sphere is so enormously large in comparison with
the telescope aperture, the light entering the telescope at
any instant can be pictured as a series of parallel and plane
wave fronts. Equivalently, all rays of light from the star to
the telescope can be considered as parallel rays perpen-
dicular to the incoming wave fronts. To this simple picture
we must add the effects of the atmosphere.
A telescope accepts the light from a star passing through
a cylindrical column of air pointing to the source and hav-
ing a diameter equal to the telescope’s aperture. If the
column of air were perfectly uniform, the incoming wave
fronts would remain flat, and a perfect Airy pattern could
be formed. The density variations accompanying turbu-
lence exist at elevations throughout the troposphere. The
cumulative effect of these fluctuations can be modeled as
being equivalent to patches across the telescope entrance
aperture, or pupil, such that within one such patch, rays
of light remain roughly parallel (or alternately, the wave
front remains nearly flat). A given patch, or coherence cell,
will produce some net tilt of the parallel bundle of rays
and will retard the entire bundle by some amount referred
to as a piston error. A telescope whose aperture is stopped
down to match the diameter of these cells, a quantity com-
monly referred to as r0, would produce an instantaneous
image in the form of an Airy pattern. From one instant to
the next, a given r0-size cell moves because of winds and
will even dissolve on a slightly longer time scale because
of the dynamics of turbulence.
A telescope with an aperture larger than r0 will at any
time contain (D/r0)
2 coherence cells, each of which pro-
duces some random tilt and piston deviations on its bundle
of rays from the mean of these deviations. At any instant,
there will be some fraction of these deviations arising from
points distributed randomly throughout the aperture that
have nearly identical tilt and piston errors. The light from
these coherent subapertures undergoes interference to pro-
duce a fringe pattern that shows regions of brightness and
darkness. These bright regions are called speckles, and
each speckle is in essence a distorted or noisy version of
an Airy pattern. The entire distribution of speckles at any
instant fills a region whose size corresponds to the Airy
disk of a single r0-size aperture. Under typical seeing con-
ditions, the coherence cell size r0 is from 8 to 15 cm, with
seeing conditions degrading asr0 becomes smaller. When
r0 = 15 cm, the seeing disk diameter will be about 1 arcsec.
The parameter r0 improves with wavelength to the expo-
nent 6/5, making turbulent blurring a nonissue at infrared
wavelengths longer than 10µm. The twinkling of starlight
as observed by the unaided eye is produced by the rapid
passage of individual coherence cells, each of which is
significantly larger than the pupil of the eye, across the
line of sight with the resultant apparent rapid motion of
the star arising from the random tilts from each successive
cell. Planets do not appear to twinkle because their disks
are sufficiently extended in angular size to average out the
tilts from a number of cells at any instant.
The rapid motion and dissolution of seeing cells re-
quires the use of short exposure times in order to record
a speckle pattern. For exposures longer than the atmo-
spheric redistribution time t0, speckle patterns will blur
into the classic long-exposure image of a star in which the
image profile intensity drops off in a Gaussian-like man-
ner to fill the arcsecond-scale seeing disk. Experience has
shown that exposure times no longer than about 0.01 sec
are typically sufficient to freeze the speckles. Atmospheric
conditions vary considerably from place to place and from
time to time, and values of t0 less than 0.001 sec have
been encountered. Exposures on such a short time scale
will permit the detection of so few photons, even from
a bright object with a large telescope, that speckles can-
not effectively be recorded. Fortunately, such rapid seeing
conditions are rare.
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