Abstract

The idea of projecting a laser beam onto a large area microcrystalline reflective film (3M film) for the visualization and measurement of atmospheric optical turbulence was proposed and investigated. The fold pass propagation of a laser beam by the reflection of a 3M film was theoretically analyzed and numerically simulated, which uncovers that the mechanism of bright dots, random in shape, brightness, and position, appears on the received laser speckle images. Experiments were performed to get the phenomena and explore the applications of the idea. An easy to implement laser speckle imaging system was set up for the qualitative experiments. As the result, the image of laser speckle patterns characterized by random dots and movable shadows were recorded, and the two-dimensional path averaged transverse wind field was retrieved. Also, a high-performance laser speckle imaging system cooperated with two professional optical turbulence monitoring instruments was set up for the qualitative experiments. Using the image data recorded in a clear sunny day, the probability distribution, spatial correlation coefficient, and scintillation index of the light intensity on the laser speckles were estimated. Meanwhile, the refractive index structure constant, aperture averaging factor, and inner scale of optical turbulence field were retrieved and compared with the monitored values and theoretical expectations. All the results are reasonable, which reveals the possibility and verifies the feasibility of using a fold pass laser speckle imaging system for optical turbulence research.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (2)

J. Ko and C.C. Davis, “Comparison of the plenoptic sensor and the Shack–Hartmann sensor,” Appl. Opt. 56(13), 3689–3698 (2017).
[Crossref]

G. S. Settles and M. J. Hargather, “A review of recent developments in schlieren and shadowgraph techniques,” Meas. Sci. Technol. 28(4), 042001 (2017).
[Crossref]

2015 (2)

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

X. Z. Ke and J. Wang, “Intensity of reflected wave from corner reflector illuminated by partially coherent beam in the atmospheric turbulence,” Acta Optical Sinica 35(10), 1001001 (2015).
[Crossref]

2014 (1)

W. Thielicke and E. J. Stamhuis, “PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB,” Journal of Open Research Software 2(1), e30 (2014).
[Crossref]

2012 (2)

2009 (1)

2008 (1)

H. Y. Wei, Z. S. Wu, and H. Peng, “Scattering from a diffuse target in the slant atmospheric turbulence,” Acta Physica Sinica 57(10), 6666–6672 (2008).

2006 (1)

2005 (1)

F. D. Eaton, “Recent developments of optical turbulence measurement techniques,” Proc. SPIE 5793, 68–72 (2005).

1999 (1)

1997 (2)

Y. X. Zhang, “Angle-of-arrival fluctuation of reflected laser beam in atmospheric turbulence,” Laser Technol. 21(1), 25–29 (1997).

L. C. Andrews, R. L. Phillips, and W. B. Miller, “Mutual coherence function for a double-passage retroreflected optical wave in atmospheric turbulence,” Appl. Opt. 36(3), 698–708 (1997).
[Crossref]

1995 (2)

L. C. Andrews, R. L. Phillips, and P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34(33), 7742–7751 (1995).
[Crossref]

L. C. Andrews and W. B. Miller, “The mutual coherence function and the backscatter amplification effect for a reflected Gaussian-beam wave in atmosphere turbulence,” Waves in Random Media 5(2), 167–182 (1995).
[Crossref]

1993 (1)

1992 (2)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random and Complex Media 2(3), 209–224 (1992).
[Crossref]

T. S. McKechnie, “Atmospheric turbulence and the resolution limits of large ground-based telescopes,” J. Opt. Soc. Am. A 9(11), 1937–1954 (1992).
[Crossref]

1991 (1)

1990 (1)

A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear 136(2), 313–327 (1990).
[Crossref]

1982 (1)

Al-Habash, M. A.

Andrews, L. C.

Chen, M.

Churnside, J. H.

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random and Complex Media 2(3), 209–224 (1992).
[Crossref]

Davis, C.C.

Dudorov, V. V.

Eaton, F. D.

F. D. Eaton, “Recent developments of optical turbulence measurement techniques,” Proc. SPIE 5793, 68–72 (2005).

Elsebelgy, B. H.

Fred Holmes, J.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random and Complex Media 2(3), 209–224 (1992).
[Crossref]

Hargather, M. J.

G. S. Settles and M. J. Hargather, “A review of recent developments in schlieren and shadowgraph techniques,” Meas. Sci. Technol. 28(4), 042001 (2017).
[Crossref]

M. J. Hargather and G. S. Settles, “Retroreflective shadowgraph technique for large-scale flow visualization,” Appl. Opt. 48(22), 4449–4457 (2009).
[Crossref]

Hopen, C. Y.

Ke, X. Z.

X. Z. Ke and J. Wang, “Intensity of reflected wave from corner reflector illuminated by partially coherent beam in the atmospheric turbulence,” Acta Optical Sinica 35(10), 1001001 (2015).
[Crossref]

Ko, J.

Lane, R. G.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random and Complex Media 2(3), 209–224 (1992).
[Crossref]

Liu, C.

Liu, L. Y.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Liu, Z.

Majumdar, A.

A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear 136(2), 313–327 (1990).
[Crossref]

McKechnie, T. S.

Mei, H. P.

S. M. Xiao, H. P. Mei, and R. Z. Rao, “Fiber optic turbulence sensing system,” Proc. SPIE 8417, 841733 (2012).
[Crossref]

Miller, W. B.

L. C. Andrews, R. L. Phillips, and W. B. Miller, “Mutual coherence function for a double-passage retroreflected optical wave in atmospheric turbulence,” Appl. Opt. 36(3), 698–708 (1997).
[Crossref]

L. C. Andrews and W. B. Miller, “The mutual coherence function and the backscatter amplification effect for a reflected Gaussian-beam wave in atmosphere turbulence,” Waves in Random Media 5(2), 167–182 (1995).
[Crossref]

Peng, H.

H. Y. Wei, Z. S. Wu, and H. Peng, “Scattering from a diffuse target in the slant atmospheric turbulence,” Acta Physica Sinica 57(10), 6666–6672 (2008).

Phillips, R. L.

Plonus, M. A.

Qian, X.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Rao, R. Z.

S. M. Xiao, H. P. Mei, and R. Z. Rao, “Fiber optic turbulence sensing system,” Proc. SPIE 8417, 841733 (2012).
[Crossref]

Rao Gudimetla, V. S.

Rui, D.

Settles, G. S.

G. S. Settles and M. J. Hargather, “A review of recent developments in schlieren and shadowgraph techniques,” Meas. Sci. Technol. 28(4), 042001 (2017).
[Crossref]

M. J. Hargather and G. S. Settles, “Retroreflective shadowgraph technique for large-scale flow visualization,” Appl. Opt. 48(22), 4449–4457 (2009).
[Crossref]

G. S. Settles, “Schlieren and shadowgraph techniques,” (Springer-Verlag, 2001).

Stamhuis, E. J.

W. Thielicke and E. J. Stamhuis, “PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB,” Journal of Open Research Software 2(1), e30 (2014).
[Crossref]

Thielicke, W.

W. Thielicke and E. J. Stamhuis, “PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB,” Journal of Open Research Software 2(1), e30 (2014).
[Crossref]

Tien, C. L.

A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear 136(2), 313–327 (1990).
[Crossref]

Vernin, J.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Wang, H. S.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Wang, J.

X. Z. Ke and J. Wang, “Intensity of reflected wave from corner reflector illuminated by partially coherent beam in the atmospheric turbulence,” Acta Optical Sinica 35(10), 1001001 (2015).
[Crossref]

Wei, H. Y.

H. Y. Wei, Z. S. Wu, and H. Peng, “Scattering from a diffuse target in the slant atmospheric turbulence,” Acta Physica Sinica 57(10), 6666–6672 (2008).

H. Y. Wei, “Laser beam propagation on the slant path through the turbulent atmosphere and the characteristics of returned waves by targets”, (Paper for Doctor’s degree, Xidian University, Xi’an, 2009).

Wu, Z. S.

H. Y. Wei, Z. S. Wu, and H. Peng, “Scattering from a diffuse target in the slant atmospheric turbulence,” Acta Physica Sinica 57(10), 6666–6672 (2008).

Xian, H.

Xiao, S. M.

S. M. Xiao, H. P. Mei, and R. Z. Rao, “Fiber optic turbulence sensing system,” Proc. SPIE 8417, 841733 (2012).
[Crossref]

Yang, C. C.

Yao, Y. Q.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Yi, X.

Yin, J.

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Yu, P. T.

Yue, P.

Zhang, Y. X.

Y. X. Zhang, “Angle-of-arrival fluctuation of reflected laser beam in atmospheric turbulence,” Laser Technol. 21(1), 25–29 (1997).

Acta Optical Sinica (1)

X. Z. Ke and J. Wang, “Intensity of reflected wave from corner reflector illuminated by partially coherent beam in the atmospheric turbulence,” Acta Optical Sinica 35(10), 1001001 (2015).
[Crossref]

Acta Physica Sinica (1)

H. Y. Wei, Z. S. Wu, and H. Peng, “Scattering from a diffuse target in the slant atmospheric turbulence,” Acta Physica Sinica 57(10), 6666–6672 (2008).

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys.: Conf. Ser. (1)

L. Y. Liu, Y. Q. Yao, J. Vernin, H. S. Wang, J. Yin, and X. Qian, “Multi-instrument characterization of optical turbulence at the Ali observatory,” J. Phys.: Conf. Ser. 595, 012019 (2015).
[Crossref]

Journal of Open Research Software (1)

W. Thielicke and E. J. Stamhuis, “PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB,” Journal of Open Research Software 2(1), e30 (2014).
[Crossref]

Laser Technol. (1)

Y. X. Zhang, “Angle-of-arrival fluctuation of reflected laser beam in atmospheric turbulence,” Laser Technol. 21(1), 25–29 (1997).

Meas. Sci. Technol. (1)

G. S. Settles and M. J. Hargather, “A review of recent developments in schlieren and shadowgraph techniques,” Meas. Sci. Technol. 28(4), 042001 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (2)

F. D. Eaton, “Recent developments of optical turbulence measurement techniques,” Proc. SPIE 5793, 68–72 (2005).

S. M. Xiao, H. P. Mei, and R. Z. Rao, “Fiber optic turbulence sensing system,” Proc. SPIE 8417, 841733 (2012).
[Crossref]

Waves in Random and Complex Media (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random and Complex Media 2(3), 209–224 (1992).
[Crossref]

Waves in Random Media (1)

L. C. Andrews and W. B. Miller, “The mutual coherence function and the backscatter amplification effect for a reflected Gaussian-beam wave in atmosphere turbulence,” Waves in Random Media 5(2), 167–182 (1995).
[Crossref]

Wear (1)

A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear 136(2), 313–327 (1990).
[Crossref]

Other (4)

H. Y. Wei, “Laser beam propagation on the slant path through the turbulent atmosphere and the characteristics of returned waves by targets”, (Paper for Doctor’s degree, Xidian University, Xi’an, 2009).

L. C. Andrews and R. L. Phillips, “Laser beam propagation through random media, second edition,” (SPIE press, 2005), P.159.

https://www.researchgate.net/profile/Elena_Masciadri2/publication/252209187_OPTICAL_TURBULENCE_Astronomy_Meets_Meteorology/links/551acd480cf251c35b4fe46c/OPTICAL-TURBULENCE-Astronomy-Meets-Meteorology.pdf

G. S. Settles, “Schlieren and shadowgraph techniques,” (Springer-Verlag, 2001).

Supplementary Material (3)

NameDescription
» Visualization 1       The shadow of hot air flow on the random dot speckle pattern.
» Visualization 2       The shadow of natural turbulence field added on the random dots.
» Visualization 3       Movie of recorded laser speckle images, the sampling frequency was 1000fps.

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Figures (13)

Fig. 1.
Fig. 1. Schematic diagram of fold pass laser transmission through the turbulence field
Fig. 2.
Fig. 2. The (a) composition, (b) mechanism and (c), (d) photograph of prisms in a 3M film
Fig. 3.
Fig. 3. Kolmogorov phase screen simulated under the condition (a) $C_n^2 = {10^{ - 15}}{m^{ - 2/3}}$ and (b) $C_n^2 = {10^{ - 14}}{m^{ - 2/3}}$, the distance $L = 250m$
Fig. 4.
Fig. 4. An example of simulated height distribution for the Gaussian distributed rough surface
Fig. 5.
Fig. 5. The laser speckle patterns of single trip and fold pass transmitted laser beam: (a), (b) in vacuum; (c), (d) in $C_n^2 = {10^{ - 15}}{m^{ - 2/3}}$; (e), (f) in $C_n^2 = {10^{ - 14}}{m^{ - 2/3}}$; (g) the binary speckle in vacuum; (h) the difference of speckle pattern between turbulence in $C_n^2 = {10^{ - 15}}{m^{ - 2/3}}$ and in vacuum; (i) the difference of speckle pattern between turbulence in $C_n^2 = {10^{ - 14}}{m^{ - 2/3}}$ and in vacuum
Fig. 6.
Fig. 6. Experimental setup for air flow visualization, the sampling frequency was 170fps, (a) experiment performed in a floor corridor within 42 m, a cup of hot water was placed beneath the laser beam in the middle; (b) the shadow of hot air flow on the random dot speckle pattern (see Visualization 1); (c) experiment performed 1.5 m above the grass land within 100 m; (d) the shadow of natural turbulence field added on the random dots (see Visualization 2), the upward, downward, left, right are respectively sky, ground, south and north
Fig. 7.
Fig. 7. Image of laser speckle patterns estimated by the algorithm of frequency decomposition and cross correlation, (a) the original images; (b) the low frequency component of shadows; (c) the binarized high frequency component of the bright dots; (d) the movement of shadows in weak turbulence, its averaged speeds were -3.0 mm/s horizontally and -5.7 mm/s vertically; (e) the movement of shadows in strong turbulence, the averaged speeds were 14.0 mm/s horizontally and -15.5 mm/s vertically, the vector vortexes noted as the arrow length and pseudo color was caused by the transversal wind field, and the size in the image was calibrated as 0.22 mm/pixel
Fig. 8.
Fig. 8. Schematic diagram of the experimental setup for the quantitative experimentation
Fig. 9.
Fig. 9. Movie of recorded laser speckle images (see Visualization 3), the sampling frequency was 1000 fps
Fig. 10.
Fig. 10. The probability density function of laser intensity represented by digital number, (a) (c): the single pixel at different axis offset d; (b) (d): the centered rectangle area with different side length L
Fig. 11.
Fig. 11. Variation of normalized correlation coefficient with axis offset r
Fig. 12.
Fig. 12. (a) variation of scintillation index with the diameter D and Fried number ${r_0}$; (b) comparing of refractive index structure constant measured by three methods, the x coordinate is the Beijing time from 14:30 (T1) to the same time next day (T49), T10∼T36 refers to the night time from 19:00 to 7:00 next day, the sampling time of scintillometer, coherence meter and laser speckle imaging system are respectively 1 min, 20s, and 6s, they are determined by the instruments
Fig. 13.
Fig. 13. Comparison of measured and fitted aperture averaging factor with the inner scales retrieved from the fittings, the same turbulence strength is noted with the same color, they match well when the aperture is larger than 120mm

Tables (1)

Tables Icon

Table 1. Parameters of numerical simulation

Equations (21)

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2 i k A ( r , z , t ) z = 2 A ( r , z , t ) + 2 k 2 n 1 ( r , z , t ) A ( r , z , t ) ,
2 i k ψ ( r , z , t ) z = 2 ψ ( r , z , t ) + 2 k 2 n 1 ( r , z , t ) ψ ( r , z , t ) .
U ( r , z = 0 , t ) = A 0 ( r , t ) exp [ i φ 0 ( r , t ) ] ,
A 0 ( r ) = exp [ r 2 / W 0 2 i k r 2 / ( 2 F 0 ) ] .
Θ 1 = 1 L / F 1 = Θ 0 / ( Θ 0 2 + Λ 0 2 ) ,
Λ 1 = 2 L / k W 1 2 = Λ 0 / ( Θ 0 2 + Λ 0 2 ) .
A ( r , z = L ) = 1 Θ 1 + i Λ 1 exp ( r 2 W 1 2 i k r 2 2 F 1 ) exp ( i k L ) ,
A ( r , z = L ) = i k 2 π L exp ( i k L ) d ρ A 0 ( ρ ) exp ( i k | r ρ | 2 2 L + φ 1 ( r , ρ ) ) .
ψ ( r , z = L , t ) = T ( r , t ) A ( r , z = L , t ) ,
T ( r , t ) = n = 1 N V n ( r n , t ) exp ( i φ n ( r n , t ) ) .
U ( ρ , z i + 1 ) = f 2 1 { exp ( i Δ z k z ) f 2 [ [ U ( ρ , z i ) exp [ i S i ( ρ ) ] ] } .
φ ( x , y ) = Δ κ x Δ κ y κ x κ y R ( κ x , κ y ) F φ ( κ x , κ y ) e j ( κ x x + κ y y ) .
F φ ( κ x , κ y ) = 2 π k 2 Δ z C n 2 ( κ x 2 + κ y 2 ) 11 / 6
φ h i g h ( m , n ) = 2 π N ( 0.033 π Δ z C n 2 Δ x Δ y ) 1 / 2 × m = N / 2 N / 2 1 n = N / 2 N / 2 1 exp ( 2 π j m m N + 2 π j n n N ) × R ( m , n ) [ ( 2 π m N Δ x ) 2   +   ( 2 π n N Δ y ) 2 ] 11 / 12
φ l o w ( m , n ) = p = 1 N p m = 1 1 n = 1 1 exp [ 2 π j 3 p ( m m N + n n N ) ] × R ( m , n ) × f ( m , n )
φ ( m , n ) = φ h i g h ( m , n ) + φ l o w ( m , n )
B h ( ρ 1 , ρ 2 ) = h ( ρ 1 ) h ( ρ 2 ) = σ h 2 exp ( Δ ρ 2 / ρ h 2 ) ,
Φ h ( κ ) = π σ h 2 exp ( κ 2 ρ h 2 / 4 ) .
U s ( ρ ) = R d W ( ρ ) U ( ρ ) exp [ i 2 k h ( ρ ) ]
x c = i = 1 M ( i j = 1 M I i , j ) / i = 1 M j = 1 M I i , j , y c = j = 1 M ( j i = 1 M I i , j ) / i = 1 M j = 1 M I i , j .
B I ( r ) = C I ( r ) / [ σ I ( 0 ) σ I ( r ) ] ,

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