Abstract
Kolmogorov theory—the widely-used theory that deals with light propagation and imaging through the atmosphere—is beset by troubling deficiencies, which include dimensional inconsistences and image predictions at odds with observed characteristics. Around 1990, it became clear to astronomers that much better resolution was possible from ground-based telescopes and the lax optical tolerances prescribed by this theory were promptly abandoned. Yet, in the absence of any better theory, most people simply ignore the problems and continue using Kolmogorov theory as though it were still fully viable. Plainly, a more substantial theory is needed. The new theory described in the book fills this need. In addition to providing a more comprehensive and precise understanding of imaging through the atmosphere with large telescopes (with and without AO) the new general theory also finds applications in the areas of laser communications and high energy laser beam propagation.
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Notes
- 1.
No doubt the propagation portions of the theory have applications to radio waves traveling through the ionosphere (Ratcliffe 1956), but this goes beyond the envisioned scope of the book.
- 2.
The philosopher, David Hume (1711–1776), an important figure in Western philosophy stated, “nothing can be proved except in mathematics; much of what we accept as fact is mere conjecture.” Arguably, mathematics is the only exact science.
- 3.
Exceptions arise when there are multiple solutions, some of which may not have obvious real-world interpretations. It is usually clear when this occurs and such solutions are simply ignored.
- 4.
- 5.
This resolution value is based on the Rayleigh angular resolution limit, \(1.22 \cdot \lambda /D,\) which applies to diffraction-limited telescopes with circular apertures.
- 6.
Coulman et al. made extensive turbulence structure size measurements over a multiyear period at various observatory sites in France, Chile, and the USA. They consistently measured significantly smaller average turbulence structure than assumed in Kolmogorov formulations.
- 7.
The father of dimensional analysis, James Clerk Maxwell (Appendix A), might have been the first to recognize the inherent problems of a formulation that is not dimensionally consistent.
- 8.
The use of the lower case in r 0 could give the mistaken impression that the quantity refers to the radius of the coherence patch. In fact, the quantity refers to the patch diameter; another frequently used name for r 0 is “coherence diameter.”
- 9.
Townes’ team used an 11-m baseline interferometer on Mt. Wilson to measure optical path differences over the baseline, inferring the atmospheric turbulence structure sizes from the measured differences. Their findings are contained in a number of papers, including “Atmospheric fluctuations: Empirical structure functions and projected performance of future instruments,” by Bester et al. (1992).
- 10.
The word “turbulence” generally refers to chaotic variations in fluid media, such as found in the churned wake of a ship. For turbulent fields of this sort, there are usually well-defined limits to the sizes of the constituent turbulence structures.
- 11.
The data were primarily obtained from images of the bright star, Vega, while it lay close to the zenith.
- 12.
A relatively recent example of this can be seen in the paper by Chanan et al. (1998). With reference to Fig. 1 in that paper, image size and shape are seen to change only marginally as wavelength ranges from 0.5 to 10 µm.
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McKechnie, T.S. (2016). Introduction. 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_2
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