Abstract
In this chapter an expression is developed for calculating the isoplanatic angles of a generalized atmosphere. The expression is evaluated for vertical atmospheric paths for two types of turbulence: (1) Kolmogorov turbulence and (2) the smaller turbulence measured in 1988 by Coulman et al. For the former, isoplanatic angles are disappointingly small (~ 10 arcsec). For the latter, the angles are similarly small for images comprised only of speckle; however, for images containing cores—which are routinely anticipated at near-IR wavelengths for this type of turbulence—preliminary experiments indicate that isoplanatic angles might be as large as 10 arcmin. If confirmed, such angles would greatly lessen the need for expensive laser guide star systems. By simply using star image cores as reference features (as opposed to the traditional light energy centroid) the sky coverage fraction provided by the limited number of suitably bright natural reference stars in the sky for carrying out AO corrections could increase by a factor ~1000. The chapter concludes with a quantitative examination of the age-old enigma: “Why do stars twinkle but not planets?”.
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Notes
- 1.
The experiment was supported by Sandia National Laboratories. Others who attended the three-night experiment included, D.R. Neal, M. Kaufmann, and R. Michie. National Optical Astronomy Observatory (NOAO) kindly provided the use of the telescope and the assistance of technical personnel, F.F. Forbes, R.G. Probst, and R. Kraus.
- 2.
The isoplanatic measurement activity was carried out under the umbrella of the Falcon Nuclear Laser development program.
- 3.
Focal anisoplanatism is a phenomenon caused by the conically convergent projected beam that forms a laser guide star in the upper atmosphere exploring a slightly different atmospheric path than the collimated image-forming light beams from distant astronomical objects. The resulting non-common path regions lead to residual uncorrected OPD fluctuation that ultimately limits the sharpness of the AO-corrected image.
- 4.
At the time Coulman et al. made their measurements, the 5/3-power law was commonly assumed. The crucial difference noticed by these authors is that the measured outer scale limits, rather than being larger than the largest telescope apertures, were significantly smaller than these apertures.
- 5.
- 6.
The scintillation patterns shown in Fig. 3.11 were obtained by the author in the backyard of his home in Albuquerque, New Mexico. Partly due to the relatively high, 1850-m, altitude of the site, stars lying near zenith rarely appear to twinkle, and likewise neither do planets. However, it is still possible to see strong twinkling (as in Fig. 3.11) by viewing stars at large zenith angles.
- 7.
The van Cittert-Zernike theorem indicates that the spatial coherence patch size of visible light from Sirius as it arrives at the Earth’s surface is about 20 m. To resolve the 0.006-arcsec disc of this, the brightest of all stars at visible wavelengths would require a telescope diameter >20 m.
- 8.
The planetary disc is assumed here, as previously, to be approximately circular as well as being uniformly illuminated by sunlight. The superior planets, Mars, Jupiter, and Uranus, may be considered suitably circular for present purposes. A modified analysis would be required to deal with the inferior planets, Mercury and Venus, which show phase-like behavior when not at opposition. Saturn would also require a modified analysis because of its ring system.
- 9.
For the Poisson noise dealt with here, in the case where the average number of photons falling on a detector during a prescribed integration period is large (say ≫10), the rms variation of the observed number is given approximately by the square root of that number.
- 10.
The 3.8-m Mayall telescope in spite of its significant aberrations (circa 1990) could routinely produce well-defined cores at 2.2 μm even in 1.25-arcsec visible seeing conditions (average Kitt Peak seeing). On Mauna Kea where average seeing is about 0.7 arcsec, it may reasonably be assumed that a 1.8-m-wide diffraction-limited telescope primary mirror segment would produce image cores at 2.2 μm with Strehl intensities approaching 0.8.
- 11.
In fact, a disproportionate number of stars lie in the direction of the galactic center. However, an equally disproportionate number of interesting objects may also lie in the same direction.
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McKechnie, T.S. (2016). Atmospheric Isoplanatic Angle. In: General Theory of Light Propagation and Imaging Through the Atmosphere. Springer Series in Optical Sciences, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-18209-4_17
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