Abstract

The relationship between the non-Kolmogorov refractive-index structure constant and the Kolmogorov refractive-index structure constant is derived by using the refractive-index structure function and the variance of refractive-index fluctuations. It shows that the non-Kolmogorov structure constant is proportional to the Kolmogorov structure constant and the scaling factor depends on the outer scale and the spectral power law. For a fixed Kolmogorov structure constant, the non-Kolmogorov structure constant increases with a increasing outer scale for the power law less than 11/3, the trend is opposite for the power law greater than 11/3. This equivalent relation provides a way of obtaining the non-Kolmogorov structure constant by using the Kolmogorov structure constant.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (1)

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

2012 (4)

2011 (2)

2010 (1)

2008 (1)

2007 (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

2005 (1)

R. Rao, “Optical properties of atmospheric turbulence and their effects on light propagation (invited paper),” Proc. SPIE 5832, 1–11 (2005).

2002 (1)

V. P. Lukin, “Estimation of behavior of outer scale of turbulence from optical measurements,” Proc. SPIE 4538, 74–84 (2002).
[Crossref]

1999 (1)

1997 (1)

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

1995 (1)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

1994 (1)

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

1941 (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers,” C. R. Acad. Sci. 30, 301–305 (1941).

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Bai, X.

Baykal, Y.

Belen’kii, M. S.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Bishop, K. P.

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Brown, J. M.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Cao, L.

Cao, X.

Charnotskii, M.

Cui, C.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Cui, L.

Du, W.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Gerçekcioglu, H.

Golbraikh, E.

Han, Q.

Huang, H.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Huang, Y.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Jiang, W.

Karis, S. J.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Keating, D. D. B.

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers,” C. R. Acad. Sci. 30, 301–305 (1941).

Kopeika, N. S.

Kyrazis, D. T.

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Ling, N.

Lukin, V. P.

V. P. Lukin, “Estimation of behavior of outer scale of turbulence from optical measurements,” Proc. SPIE 4538, 74–84 (2002).
[Crossref]

Ma, J.

Mei, H.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Preble, A. J.

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Qian, X.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Rao, C.

Rao, R.

R. Rao, “Optical properties of atmospheric turbulence and their effects on light propagation (invited paper),” Proc. SPIE 5832, 1–11 (2005).

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Shao, S.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Tan, L.

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Wissler, J. B.

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Wu, X.

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Xue, B.

Xue, W.

Yu, S.

Zheng, S.

Zhou, F.

Zilberman, A.

Acta Opt. Sin. (1)

X. Wu, Y. Huang, H. Mei, S. Shao, H. Huang, X. Qian, and C. Cui, “Measurement of non-Kolmogorov turbulence characteristic parameter in atmospheric surface layer,” Acta Opt. Sin. 34(6), 0601001 (2014).
[Crossref]

Appl. Opt. (1)

C. R. Acad. Sci. (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers,” C. R. Acad. Sci. 30, 301–305 (1941).

J. Opt. Soc. Am. A (4)

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (7)

R. Rao, “Optical properties of atmospheric turbulence and their effects on light propagation (invited paper),” Proc. SPIE 5832, 1–11 (2005).

V. P. Lukin, “Estimation of behavior of outer scale of turbulence from optical measurements,” Proc. SPIE 4538, 74–84 (2002).
[Crossref]

D. T. Kyrazis, J. B. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Other (3)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Medium, 2nd ed. (SPIE, 2005).

R. Rao, Light Propagation in the Turbulent Atmosphere (AnHui Science and Technology, 2005).

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Figures (4)

Fig. 1
Fig. 1 The non-Kolmogorov structure constant as a function of Kolmogorov structure constant with different outer scales at three spectral power laws: (a) α = 3.1 , (b) α = 11 / 3 , (c) α = 3.9 .
Fig. 2
Fig. 2 The time series of the power laws of the three-dimensional spectrum of temperature fluctuations
Fig. 3
Fig. 3 The time series of measurements of Kolmogorov structure constants C n 2 ( z ) and non-Kolmogorov structure constants C ˜ n 2 ( α , z ) .
Fig. 4
Fig. 4 The comparisons of the time series of the non-Kolmogorov structure constants between the measurement results and the equivalent results.

Equations (27)

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D v ( r ) = [ v ( r 1 + r ) v ( r 1 ) ] 2 = C v 2 r 2 / 3 , l 0 r L 0 ,
D n ( r ) = [ n ( r 1 + r ) n ( r 1 ) ] 2 = C n 2 r 2 / 3 , l 0 r L 0 ,
D n ( r ) = 8 π 0 d κ Φ n ( κ ) κ 2 [ 1 sin ( κ r ) κ r ] ,
Φ n ( κ ) = 1 4 π 2 κ 2 0 sin ( κ r ) κ r d d r [ r 2 d d r D n ( r ) ] ,
Φ n ( κ , z ) = 0.033 C n 2 ( z ) κ 11 / 3 , 2 π / L 0 κ 2 π / l 0 ,
D n ( r , z ) = C ˜ n 2 ( γ , z ) r γ , l 0 r L 0 ,
Φ n ( α , κ ) = A ( α ) C ˜ n 2 ( α , z ) κ α , 2 π / L 0 κ 2 π / l 0 ,
A ( α ) = 2 α 6 ( α 2 5 α + 6 ) π 3 / 2 Γ [ 3 α 2 ] Γ [ 5 α 2 ] , 3 < α < 5 ,
D n ( L 0 , z ) = [ n ( r + L 0 ) n ( r ) ] 2 = n 2 ( r + L 0 ) + n 2 ( r ) 2 n ( r + L 0 ) n ( r ) = 2 σ n 2 = C n 2 ( z ) L 0 2 / 3 ,
C n 2 ( z ) = 2 σ n 2 L 0 2 / 3 ,
σ n 2 = 0.5 C n 2 ( z ) L 0 2 / 3 .
D n ( r , z ) = 2 σ n 2 ( r / L 0 ) 2 / 3 , l 0 r L 0 ,
D n ( r , z ) = 2 σ n 2 ( r / L 0 ) 3 α , l 0 r L 0 ,
C ˜ n 2 ( α , z ) = 2 σ n 2 L 0 3 α .
C ˜ n 2 ( α , z ) = L 0 11 / 3 α C n 2 ( z ) .
C n 2 = [ n ( x ) n ( x + r ) ] r 2 / 3 , l 0 r L 0 ,
C T 2 = [ T ( x ) T ( x + r ) ] r 2 / 3 , l 0 r L 0 ,
C n 2 = ( 79 × 10 6 P T 2 ) 2 C T 2 ,
T = T s 1 + 0.51 q ,
T s = c 2 γ d R d 273.15 ,
ψ T ( κ ) = V 2 π ψ T ( f ) ,
ψ T ( f ) = B f α 1 ,
α = α 1 + 2.
log [ ψ T ( f ) ] = log ( B ) α 1 log ( f ) ,
ψ T ( κ ) = 0.125 C T 2 κ 5 / 3 .
Φ T ( κ ) = 1 2 π d ψ T ( κ ) d κ .
Φ T ( α , κ ) = A ( α ) C ˜ T 2 ( α , z ) κ α , 2 π / l 0 κ 2 π / L 0 ,

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