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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 21 — Oct. 17, 2007
  • pp: 14115–14122
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Statistical analysis of measured free-space laser signal intensity over a 2.33 km optical path

Arnold Tunick  »View Author Affiliations


Optics Express, Vol. 15, Issue 21, pp. 14115-14122 (2007)
http://dx.doi.org/10.1364/OE.15.014115


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Abstract

Experimental research is conducted to determine the characteristic behavior of high frequency laser signal intensity data collected over a 2.33 km optical path. Results focus mainly on calculated power spectra and frequency distributions. In addition, a model is 2 developed to calculate optical turbulence intensity (Cn 2) as a function of receiving and transmitting aperture diameter, log-amplitude variance, and path length. Initial comparisons of calculated to measured Cn 2 data are favorable. It is anticipated that this kind of signal data analysis will benefit laser communication systems development and testing at the U.S. Army Research Laboratory (ARL) and elsewhere.

© 2007 Optical Society of America

1. Introduction

Optical turbulence is an important microphysical effect that acts on the propagation of light waves to distort optical propagation paths and intensity. It is brought about by fluctuations in the refractive index in air, i.e., air density, which affects the speed at which light wave-fronts propagate. Atmospheric refractions of electro-magnetic energy can cause spatial (directional) and temporal (intensity) variations in transmitted signals [1–5

1. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

]. In turn, these effects can severely impact the performance of Army free-space laser optics communication systems [6–8

6. Y. Han Oh, J. C. Ricklin, E. S. Oh, and F. D. Eaton, “Evaluating optical turbulence effects on free-space laser communication: modeling and measurements at ARL’s A_LOT facility,” Proc. SPIE 5550, 247–255 (2004). [CrossRef]

].

Hence, this paper presents new experimental research to examine the behavior of free-space laser signal intensity data collected at the Army Research Laboratory (ARL), Atmospheric Laser Optics Testbed (A_LOT) Facility [14

14. M. Vorontsov, G. Carhart, M. Banta, T. Weyrauch, J. Gowens, and J. Carrano, “Atmospheric Laser Optics Testbed (A_LOT): Atmospheric propagation characterization, beam control, and imaging results,” Proc. SPIE 5162, 37–48 (2003). [CrossRef]

]. Within the A_LOT, a near horizontal, 2.33 km optical path extends from the top of a tall water tower to the Intelligent Optics Laboratory (IOL) rooftop at ARL (Figs. 1 and 2). The A_LOT optical path traverses a non-uniform landscape, e.g., an open sand lot, a fairly continuous forest stand, several local roads, and various building arrays. Naturally, complex microphysical influences may (at times) affect the A_LOT measured data and research applications. Some microclimate influences may be due to irregular wind flow patterns around the IOL (High Bay building) and the water tower. Other effects may be due to varying wind shears, temperature gradients, and moisture changes across the top of nearby (and underlying) buildings and forest canopies. To this end, computer simulation models may provide some meaningful results even though all the pertinent landscape or canopy characterization data along the optical path may not yet be known or available [15

15. A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007). [CrossRef]

]. At the same time, detailed data analysis from a new laser-optics experiment may help us to better understand the physics relationships between refractive index structure and the behavior of high speed (~155 Mb/sec) laser signal propagation.

Fig. 1. A schematic of the ARL A_LOT optical path
Fig. 2. An aerial photo of the A_LOT propagation path (data from terrafly.com)

2. Experiment

The wave propagation geometry for this experiment is shown in Fig. 3. A high-speed, photo-detector sensitive to the wavelength of an A_LOT prototype laser transceiver was mounted behind a Schmidt-Cassegrain compound telescope (receiving aperture diameter, Dr = 127 mm; focal length, fl = 1347 mm), to record high frequency (f = 2000 Hz), aperture averaged signal intensities (Fig. 4). The laser transceiver (wavelength, λ= 808nm; transmitting aperture diameter, Dt = 60 mm) was located on top of the 73 m water tower ,while the receiving optics and photo-detector were located at 12 m (above ground level) within a climate controlled equipment shed (and optics table) located on the IOL rooftop. Note that the source for the optical transmitter at the water tower was a 100 mW laser diode (located at ground level) that was coupled to a 100 m long multimode fiber. Because this laser source propagates within a long multi-mode fiber, the exiting light can be considered a collimated, partially coherent beacon due to fiber vibrations [16

16. T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44, 6388–6401 (2005). [CrossRef] [PubMed]

]. Also note that the laser beam divergence was 2.8 mrad, which provided a 6.5 m footprint at the receiver plane.

At the same time, a boundary layer scintillometer [17

17. User’s Guide. LOA-004-xR Long Baseline Optical Anemometer and Atmospheric Turbulence Sensor. Revision 3/20/2003. Optical Scientific, Inc., Gaithersburg, MD (2003). http://www.opticalscientific.com/

] measured continuous, path-averaged values for the refractive index structure parameter, Cn 2, along the A_LOT line-of-sight. The scintillometer transmitter is mounted on top of the water tower and the receiver is located in front of the equipment shed on the IOL rooftop. Also, a single 3-axis sonic anemometer [18

18. Operating Instructions. Model 81000 Ultrasonic Anemometer. Revision 01/24/2007, R.M. Young Co., Traverse City, MI (2007). http://www.youngusa.com/

] was installed on a 2 m tripod on the IOL rooftop. The sonic sensor provided additional characterization of microclimate and turbulence conditions, e.g., mean and fluctuating wind velocity and temperature data.

Fig. 3. A schematic of the wave propagation geometry for this experiment.
Fig. 4. Photograph of the receiving optics. A high-speed photo-detector is mounted behind the telescope on the right. A video camera is attached to the telescope on the left.

3. Data analysis

Table 1 summarizes the turbulence and microclimate conditions for an initial data set consisting of eight cases collected during winter, spring, and summer months. Data selection was mainly based on whether both laser signal and scintillometer measurements were available for analysis. Another general section criterion was for fair weather conditions daytime and nighttime, i.e., no rain or snow. Signal intensity data were recorded for four (two-minute) periods for each 10–15 minute trial T1 – T8. Data were collected mainly during midday hours, with one exception, e.g., after sunset on 28 February 2007. In Table 1, the temperature and wind velocity data refer to 10–15 minute averages recorded on the IOL rooftop. Similarly, the measured Cn 2 data refer to 10–15 minute averages recorded along the 2.33 km A_LOT propagation path using an optical scintillometer. Finally, the calculated Rytov variance is included to help differentiate between weak (σ 1 2<1) and strong (σ 1 2 > 1) turbulence conditions. The Rytov variance was calculated as

σ12=1.23Cn2k76L116,
(1)

where k = 2π/λ is the wave-number, λ is wavelength, and L is path length [9

9. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001). [CrossRef]

].

Table 1. Microclimate and turbulence characteristics for the experimental data set

table-icon
View This Table
Fig. 5. Histograms of measured laser signal intensity data for trials (a) T3, (b) T4, (c) T5, and (d) T7. Log-normal regression coefficients, R2, are annotated on each graph.

Histograms and power spectra were computed for each case. Signal intensity bin counts and spectra power levels were derived and plotted using an average of the four (two-minute) periods collected for each trial to help suppress noise content. As an example, Fig. 5 presents the computed histograms for trials T3, T4, T5, and T7. Here, the frequency distributions are distinctly log-normal. This is confirmed by the calculated regression statistics annotated on each graph. In addition, these data show that the recorded signal intensities vary over a much broader range when the turbulence is strong and vise versa. A highly turbulent atmosphere is more likely to focus and defocus the transmitted laser light to bring about comparatively higher (and lower) received signal intensities. This characteristic is shown satisfactorily by the daytime and nighttime data collected on 28 February 2007 (i.e., trials T3 and T4). Similar log-normal characteristics were evidenced for the other data trials (not shown) as well.

Fig. 6. Spectral analysis for measured laser signal intensity data for trials (a) T3, (b) T4, (c) T5, and (d) T7. Turbulence power law curve fits for -5/3 and -17/3 are annotated on each graph.

Figure 6 shows the power spectra computed for trials T3, T4, T5, and T7. For low frequencies, data are fairly well represented by the Kolmogorov model [19

19. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds’ numbers,” in Turbulence, Classic Papers on Statistical Theory (Wiley-Interscience, New York, 1961), 151–155.

], i.e., the -5/3 turbulence power law. Alternately, for higher frequencies, e.g., where f > 60–100 Hz, the measured laser signal data appear to follow the -17/3 power law of Batchelor et al. [20

20. G. K. Batchelor, I. D. Howells, and A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II: The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959). [CrossRef]

], which has been examined in several papers on scalar fluctuations in turbulent fluids [21–23

21. R. H. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 945–953 (1968). [CrossRef]

]. At the same time, it is not clear what brings about a marked curvature in the calculated power spectra. One can plausibly fit different segments of these power spectra, e.g., in the inertial-convective and dissipation regions, by using alternative power law exponents [21–25

21. R. H. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 945–953 (1968). [CrossRef]

]. However, the turbulence (eddy) scales and boundaries for each segment are likely to vary from experiment to experiment depending on the experimental setup, wavelength, propagation path length, microclimate, and terrain [23

23. E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004). [CrossRef] [PubMed]

,25

25. R. Rao, S. Wang, X. Liu, and Z. Gong, “Turbulence spectrum effect on wave temporal-frequency spectra for light propagating through the atmosphere,” J. Opt. Soc. Am. 16, 2755–2762 (1999). [CrossRef]

]. Undoubtedly, the turbulence scales that influence the A_LOT data shown here are unique due to some or all of these external conditions. Similar power spectra were calculated for the other data trials (not shown).

Finally, a model is developed to calculate optical turbulence intensity (Cn 2) as a function of the log-amplitude variance of the measured laser signal data. The model is based on an expression derived by Wang et al. [26

26. T-i Wang, G. R. Ochs, and S. F. Clifford, “A saturation-resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978). [CrossRef]

], i.e.,

Cn2=Cσ2Dt73L3
(2)

where C = 4.48Dr/Dt, Dt= 0.060 m is the transmitting aperture, Dr= 0.127 m is the receiving aperture, σ 2 is the measured log amplitude variance of the free-space laser (808 nm) signal, and L = 2330 m is the A_LOT propagation path length. According to Wang et al. [26

26. T-i Wang, G. R. Ochs, and S. F. Clifford, “A saturation-resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978). [CrossRef]

], the algorithm in Eq. (2) requires that the light source be incoherent and uniformly illuminated across the transmitting aperture. In this experiment, the light source was a collimated, partially coherent beacon, as mentioned in Sect. 2.

Fig. 7. Modeled versus measured Cn 2 data for trials T1 – T8.

4. Summary and conclusions

Acknowledgements

The author would like to thank Mikhail Vorontsov, Gary Carhart, and Ronald Meyers of the Army Research Laboratory (ARL) and Thomas Weyrauch of the University of Maryland (UMD) for providing helpful comments on this study, particularly with regard to the experimental setup. In addition, the author gratefully acknowledges Mikhail Vorontsov and Gary Carhart of the ARL, Nikolay Tikhonov (Army Research Office, STAS), and Ernst Polnau (UMD) for A_LOT hardware and software development and for keeping the A_LOT facility in operation. Partial funding for A_LOT development and operations was provided by the Joint Technology Office. Partial funding for this study was provided by the U.S. Army Engineer Research and Development Center (ERDC) and the ARL.

References and links

1.

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

2.

T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. 10, 2456–2461 (1971). [CrossRef] [PubMed]

3.

D. L. Fried, G. E. Mevers, and M. P. Keister, “Measurements of laser beam scintillation in the atmosphere,” J. Opt. Soc. Am. 57, 787–797 (1967). [CrossRef]

4.

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, (Springer-Verlag, 1978), pp. 129–170 [CrossRef]

5.

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuation in a laser beam,” Opt. Acta. 28, 715–728 (1981). [CrossRef]

6.

Y. Han Oh, J. C. Ricklin, E. S. Oh, and F. D. Eaton, “Evaluating optical turbulence effects on free-space laser communication: modeling and measurements at ARL’s A_LOT facility,” Proc. SPIE 5550, 247–255 (2004). [CrossRef]

7.

G.W. Carhart, M.A. Vorontsov, L.A. Beresnev, P.S. Paicopolis, and F.K. Beil, “Atmospheric laser communication system with wide-angle tracking and adaptive compensation,” Proc. SPIE 5892 (2005). [CrossRef]

8.

A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express 15, 3619–3628 (2007) http://www.opticsexpress.org/abstract.cfm?id=131583. [CrossRef] [PubMed]

9.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001). [CrossRef]

10.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber Comm. Rep. 3, 111–158 (2006). [CrossRef]

11.

D. Dayton, B. Pierson, B. Spielbusch, and J. Gonglewski, “Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor,” Opt. Lett. 17, 1737–1739 (1992). [CrossRef] [PubMed]

12.

C. Rao, W. Jiang, and N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” Proc. SPIE 3763, 84–91 (1999). [CrossRef]

13.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotrophy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999). [CrossRef]

14.

M. Vorontsov, G. Carhart, M. Banta, T. Weyrauch, J. Gowens, and J. Carrano, “Atmospheric Laser Optics Testbed (A_LOT): Atmospheric propagation characterization, beam control, and imaging results,” Proc. SPIE 5162, 37–48 (2003). [CrossRef]

15.

A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007). [CrossRef]

16.

T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44, 6388–6401 (2005). [CrossRef] [PubMed]

17.

User’s Guide. LOA-004-xR Long Baseline Optical Anemometer and Atmospheric Turbulence Sensor. Revision 3/20/2003. Optical Scientific, Inc., Gaithersburg, MD (2003). http://www.opticalscientific.com/

18.

Operating Instructions. Model 81000 Ultrasonic Anemometer. Revision 01/24/2007, R.M. Young Co., Traverse City, MI (2007). http://www.youngusa.com/

19.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids for very large Reynolds’ numbers,” in Turbulence, Classic Papers on Statistical Theory (Wiley-Interscience, New York, 1961), 151–155.

20.

G. K. Batchelor, I. D. Howells, and A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II: The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959). [CrossRef]

21.

R. H. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 945–953 (1968). [CrossRef]

22.

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996). [CrossRef]

23.

E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004). [CrossRef] [PubMed]

24.

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

25.

R. Rao, S. Wang, X. Liu, and Z. Gong, “Turbulence spectrum effect on wave temporal-frequency spectra for light propagating through the atmosphere,” J. Opt. Soc. Am. 16, 2755–2762 (1999). [CrossRef]

26.

T-i Wang, G. R. Ochs, and S. F. Clifford, “A saturation-resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978). [CrossRef]

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.3310) Atmospheric and oceanic optics : Laser beam transmission

ToC Category:
Atmospheric and oceanic optics

History
Original Manuscript: July 31, 2007
Revised Manuscript: October 1, 2007
Manuscript Accepted: October 6, 2007
Published: October 11, 2007

Citation
Arnold Tunick, "Statistical analysis of measured free-space laser signal intensity over a 2.33 km optical path," Opt. Express 15, 14115-14122 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-14115


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References

  1. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).
  2. T. Chiba, "Spot dancing of the laser beam propagated through the turbulent atmosphere," Appl. Opt. 10, 2456-2461 (1971). [CrossRef] [PubMed]
  3. D. L. Fried, G. E. Mevers, and M. P. Keister, "Measurements of laser beam scintillation in the atmosphere," J. Opt. Soc. Am. 57, 787-797 (1967). [CrossRef]
  4. A. Ishimaru, "The beam wave case and remote sensing," in Laser Beam Propagation in the Atmosphere, (Springer-Verlag, 1978), pp. 129-170 [CrossRef]
  5. G. Parry, "Measurement of atmospheric turbulence induced intensity fluctuation in a laser beam," Opt. Acta. 28, 715-728 (1981). [CrossRef]
  6. Y. Han Oh, J. C. Ricklin, E. S. Oh and F. D. Eaton, "Evaluating optical turbulence effects on free-space laser communication: modeling and measurements at ARL’s A_LOT facility," Proc. SPIE 5550, 247-255 (2004). [CrossRef]
  7. G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide-angle tracking and adaptive compensation," Proc. SPIE 5892, 346-357 (2005). [CrossRef]
  8. A. Tunick, "Statistical analysis of optical turbulence intensity over a 2.33 km propagation path," Opt. Express 15, 3619-3628 (2007). [CrossRef] [PubMed]
  9. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001). [CrossRef]
  10. J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, "Atmospheric channel effects on free-space laser communication," J. Opt. Fiber Commun. Rep. 3, 111-158 (2006). [CrossRef]
  11. D. Dayton, B. Pierson, B. Spielbusch, and J. Gonglewski, "Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor," Opt. Lett. 17, 1737-1739 (1992). [CrossRef] [PubMed]
  12. C. Rao, W. Jiang, and N. Ling, "Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor," Proc. SPIE 3763, 84-91 (1999). [CrossRef]
  13. M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, "Preliminary experimental evidence of anisotrophy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics," Proc. SPIE 3762, 396-406 (1999). [CrossRef]
  14. M. Vorontsov, G. Carhart, M. Banta, T. Weyrauch, J. Gowens, and J. Carrano, "Atmospheric Laser Optics Testbed (A_LOT): Atmospheric propagation characterization, beam control, and imaging results," Proc. SPIE 5162, 37-48 (2003). [CrossRef]
  15. A. Tunick, "Modeling microphysical influences on optical turbulence in complex areas," Meteorol. Atmos. Phys. 96, 293-304 (2007). [CrossRef]
  16. T. Weyrauch and M. A. Vorontsov, "Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications," Appl. Opt. 44, 6388-6401 (2005). [CrossRef] [PubMed]
  17. User’s Guide. LOA-004-xR Long Baseline Optical Anemometer and Atmospheric Turbulence Sensor. Revision 3/20/2003. Optical Scientific, Inc., Gaithersburg, MD (2003). http://www.opticalscientific.com/
  18. Operating Instructions. Model 81000 Ultrasonic Anemometer. Revision 01/24/2007, R.M. Young Co., Traverse City, MI (2007). http://www.youngusa.com/
  19. A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds’ numbers," in Turbulence, Classic Papers on Statistical Theory (Wiley-Interscience, New York, 1961), 151-155.
  20. G. K. Batchelor, I. D. Howells, and A. A. Townsend, "Small-scale variation of convected quantities like temperature in turbulent fluid. Part II: The case of large conductivity," J. Fluid Mech. 5, 134-139 (1959). [CrossRef]
  21. R. H. Kraichnan, "Small-scale structure of a scalar field convected by turbulence," Phys. Fluids 11, 945-953 (1968). [CrossRef]
  22. T. Elperin, N. Kleeorin, and I. Rogachevskii, "Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow," Phys. Rev. E 53, 3431-3441 (1996). [CrossRef]
  23. E. Golbraikh and N. S. Kopeika, "Behavior of structure function of refraction coefficients in different turbulent fields," Appl. Opt. 43, 6151-6156 (2004). [CrossRef] [PubMed]
  24. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, "Optical propagation in non-Kolmogorov atmospheric turbulence," Proc. SPIE 2471, 181-196 (1995). [CrossRef]
  25. R. Rao, S. Wang, X. Liu, and Z. Gong, "Turbulence spectrum effect on wave temporal-frequency spectra for light propagating through the atmosphere," J. Opt. Soc. Am. 16, 2755-2762 (1999). [CrossRef]
  26. T-i Wang, G. R. Ochs, and S. F. Clifford, "A saturation-resistant optical scintillometer to measure Cn2," J. Opt. Soc. Am. 68, 334-338 (1978). [CrossRef]

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