Abstract
Atmospheric turbulence that affects propagating light waves is described. A model of the atmosphere that distorts the wavefront of light waves is outlined, and the energy cascade theory of turbulence and the structure function of wind velocity are presented along with definitions of the outer scale and the inner scale. Structure functions are introduced to treat random quantities, where the relationship between the structure function of refractive index and the structure function of temperature is denoted. The Kolmogorov spatial power spectral density of refractive index fluctuations is expressed with the structure parameter of the refractive index. Representative models of the refractive index structure parameters as a function of altitude are shown with examples of calculations. Assuming that the atmosphere is a plane perpendicular to the direction of light wave propagation, the coherence length of the atmosphere, or Fried’s parameter, is derived from the wave structure function. The isoplanatic angle is presented as an indicator to show that two wavefronts with different propagation angles can be considered approximately equivalent, and the Greenwood frequencies at which two wavefronts measured can be considered approximately equivalent are introduced. For the phenomena observed in light waves propagating in atmospheric turbulence, theoretical expressions of intensity fluctuation, focal point variation, and movement of the irradiated area of the transmitted light waves are shown.
References
J.C. Owens, Optical refractive index of air: dependence on pressure, temperature and composition. Appl. Opt. 6(1), 51–59 (1967)
S.F. Clifford, The classical theory of wave propagation in a turbulent medium, in Laser Beam Propagation in the Atmosphere, ed. by J.W. Strohbehn, (Springer, New York, 1978). Chap. 2
L.C. Andrews, R.L. Phillips, Laser Beam Propagation Through Random Media, 2nd edn. (SPIE Press, Washington, 2005). Chap. 3
O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Proc. R. Soc. Lond. 35, 84–99 (1883)
L.F. Richardson, Weather Prediction by Numerical Process (Cambridge University Press, Cambridge, UK, 1922). Chap. 4
L.F. Richardson, Some measurements of atmospheric turbulence. Philos. Trans. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Character 221, 1–28 (1921)
J. Vernin, F. Roddier, Experimental determination of two-dimensional spatiotemporal power spectra of stellar light scintillation. Evidence for a multilayer structure of the air turbulence in the upper troposphere. J. Opt. Soc. Am. 63(3), 270–273 (1973)
C.E. Coulman, J. Vernin, Y. Coqueugniot, J.L. Caccia, Outer scale of turbulence appropriate to modelling refractive-index structure profiles. Appl. Opt. 27(1), 155–160 (1988)
A.N. Kolmogorov, Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18 (1941). Reprinted in Proceedings of the Royal Society of London A 434, 15–17, 1991
A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 9–13 (1941). Reprinted in Proceedings of the Royal Society of London A 434, 9–13, 1991
A. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers, in Turbulence, Classic Papers on Statistical Theory, ed. by S.K. Friedlander, L. Topper, (Interscience Publishers, New York, 1961), pp. 151–155
R.H. Tyson, Principles of Adaptive Optics, 4th edn. (CRC Press, New York, 2016). Chap. 2
V. I. Tatarski, The Effect of the Turbulent Atmosphere on Wave Propagation (U.S. Dept. of Commerce, National Technical Information Service, Springfield, 1971). Chap. 1. Translated by Israel Program for Scientific Translations; originally published in 1967
S. Corrsin, On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473 (1951)
J.W. Strohbehn, Line-of-sight wave propagation through the turbulent atmosphere. Proc. IEEE, 1301–1318 (1968)
L.C. Andrews, R.L. Phillips, Laser Beam Propagation Through Random Media, 2nd edn. (SPIE Press, Washington, 2005). Chap. 12
M.G. Miller, P.L. Zieske, Turbulence Environmental Characterization, Rome Air Development Center, RADC-TR-79-131, ADA072379 (1979)
D.H. Tofsted, S.G. O’Brien, G.T. Vaucher, An Atmospheric Turbulence Profile Model for Use in Army Wargaming Applications I, Army Research Laboratory, ARL-TR-3748, ADA509431 (2006)
D.L. Fried, Optical heterodyne detection of an atmospherically distorted signal wave front. Proc. IEEE 55(1), 57–67 (1967)
D.L. Fried, Optical resolution through a randomly inhomogeneous medium for very long and very short exposures. J. Opt. Soc. Am. 56(10), 1372–1379 (1966)
D.L. Fried, Statistics of a geometric representation of wavefront distortion. J. Opt. Soc. Am. 55(11), 1427–1435 (1965)
A. Muschinski, Phase-factor spectra of turbulent phase screens. J. Opt. Soc. Am. A 38(9), 1339–1348 (2021)
V.I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961). Chap. 8. Translated by R. A. Silverman, Dover publications, Inc., New York, 1967
L.C. Andrews, R.L. Phillips, Laser Beam Propagation Through Random Media, 2nd edn. (SPIE Press, Washington, 2005). Chap. 6
D.L. Fried, Anisoplanatism in adaptive optics. J. Opt. Soc. Am. 72(1), 52–61 (1982)
L.C. Andrews, R.L. Phillips, Laser Beam Propagation Through Random Media, 2nd edn. (SPIE Press, Washington, 2005). Chap. 14
D.P. Greenwood, Bandwidth specification for adaptive optics systems. J. Opt. Soc. Am. 67(3), 390–393 (1977)
H.T. Yura, W.G. McKinley, Optical scintillation statistics for IR ground-to-space laser communication systems. Appl. Opt. 22(21), 3353–3358 (1983)
R.S. Lawrence, J.W. Strohbehn, A survey of clear-air propagation effects relevant to optical communications. Proc. IEEE 58(10), 1523–1545 (1970)
Y. Cheon, A. Muschinski, Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence. J. Opt. Soc. Am. A 24(2), 415–422 (2007)
J.H. Churnside, R.J. Lataitis, Wander of an optical beam in the turbulent atmosphere. Appl. Opt. 29(7), 926–930 (1990)
T. Chiba, Spot dancing of the laser beam propagated through the turbulent atmosphere. Appl. Opt. 10(11), 2456–2461 (1971)
L.C. Andrews, R.L. Phillips, R.J. Sasiela, R.R. Parenti, Strehl ratio and scintillation theory for uplink Gaussian-beam waves: beam wander effects. Opt. Eng. 45(7), 076001-1–076001-12 (2006)
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Takayama, Y. (2024). Lightwave Propagation in the Air. In: Kawanishi, T. (eds) Handbook of Radio and Optical Networks Convergence. Springer, Singapore. https://doi.org/10.1007/978-981-33-4999-5_55-1
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