## Measurement of optical intensity fluctuation over an 11.8 km turbulent path

Optics Express, Vol. 16, Issue 10, pp. 6963-6973 (2008)

http://dx.doi.org/10.1364/OE.16.006963

Acrobat PDF (688 KB)

### Abstract

An 11.8km optical link is established to examine the intensity fluctuation of the laser beam transmission through atmosphere turbulence. Probability density function, fade statistic, and high-frequency spectrum are researched based on the analysis of the experimental data collected in each season of a year, including both weak and strong fluctuation cases. Finally, the daily variation curve of scintillation index is given, compared with the variation of refractive-index structure parameter *C*^{2}*
_{n}
*, which is calculated from the experimental data of angle of arrival. This work provides the experimental results that are helpful to the atmospheric propagation research and the free-space optical communication system design.

© 2008 Optical Society of America

## 1. Introduction

1. 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. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash “Theory of optical scintillation,” J. Opt. Soc. Am. **16**, 1417–1429 (1974). [CrossRef]

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

8. A. Tunick, “Statistical analysis of measured free-space laser signal intensity over a 2.33 km propagation path,” Opt. Express. **15**, 14115–14122 (2007). [CrossRef] [PubMed]

16. M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. **20**, 1359–1361 (1995). [CrossRef] [PubMed]

7. A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express. **15**, 3619–3628 (2007). [CrossRef] [PubMed]

8. A. Tunick, “Statistical analysis of measured free-space laser signal intensity over a 2.33 km propagation path,” Opt. Express. **15**, 14115–14122 (2007). [CrossRef] [PubMed]

## 2. Experimental setup

## 3. Data analysis

*σ*

^{2}

*<1) and two strong fluctuation (*

_{I}*σ*

^{2}

*>1) cases. Considering the dynamic range (60dB) of the AD card, data selection is mainly based on whether both high and low irradiance part of the intensity fluctuation can be included.*

_{I}### 3.1 Probability density function

*I*is light intensity and <·> means ensemble average. For weak fluctuations, scintillation index is equal to the Rytov variance which can be calculated as

*C*

^{2}

*is the refractive-index structure parameter,*

_{n}*k*=2

*π*/

*λ*is the wave-number,

*λ*is wavelength, and

*L*is the link distance. Probability density function (PDF) of the normalized intensity should be lognormal [3], and it can be described as

19. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. **40**, 1554–1562 (2001). [CrossRef]

*C*

^{2}

*lead to strong fluctuation in spring and winter. Histograms for T1–T4 and the lognormal fitting curves are shown in Fig. 4, with the light intensity normalized. The results of Fig. 4 are similar to the data analysis figures in Ref. [8*

_{n}8. A. Tunick, “Statistical analysis of measured free-space laser signal intensity over a 2.33 km propagation path,” Opt. Express. **15**, 14115–14122 (2007). [CrossRef] [PubMed]

*DY*and

*Dy*are variances of

*Y*and

*y*, respectively.

*R*

^{2}slightly falls down when

*σ*

^{2}

*rises (Fig. 7). It seems that in strong fluctuation region, the negative exponential approximation is less effective to larger*

_{I}*σ*

^{2}

*trials than to smaller*

_{I}*σ*

^{2}

*trials. However,*

_{I}*R*

^{2}is still above the level of 0.98 even though

*σ*

^{2}

*is greater than 3, so the negative exponential distribution is still a nice approximation for strong fluctuation trials.*

_{I}### 3.2 Probability of fade

*I*. It can be calculated as [3]

_{T}*p*(

*I*) is PDF of the intensity. The bit-error-rate (BER) of an on-off-keyed communication system can be given by multiplying the probability of fade with a factor of 0.5. It is customary to express

*I*in decibels, which can be described as the fade margin

_{T}*F*. Besides, the required

_{T}*F*for a given BER is larger for the trial that has a greater σ2I and the BER also rises with the increasing of

_{T}*σ*

^{2}

*for a given*

_{I}*F*. To achieve a BER of 10

_{T}^{-4}, about 13dB fade margin is required for T2 (

*σ*

^{2}

_{I}=0.4991), 20dB is required for T4 (

*σ*

^{2}

*=0.9074), and more than 35dB is required for T5 (*

_{I}*σ*

^{2}

*=1.2249). To achieve a BER of 10*

_{I}^{-5}, the required fade margin will be 15dB, 23dB and more than 40dB for T2, T4 and T5, respectively.

### 3.3 High-frequency spectrum

**15**, 14115–14122 (2007). [CrossRef] [PubMed]

20. 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. A **16**, 2755–2762 (1999). [CrossRef]

21. R. Rao and Z. Gong, “High-frequency behavior of the temporal spectrum of laser beam propagating through turbulence,” Proc. SPIE **4926**, 175–180 (2002). [CrossRef]

**15**, 14115–14122 (2007). [CrossRef] [PubMed]

**15**, 14115–14122 (2007). [CrossRef] [PubMed]

*σ*

^{2}

*is smaller than 0.4. For weak fluctuation trials, α is in the interval of -21/3 to -13/3 mostly. For strong fluctuation trials,*

_{I}*α*is in the interval of -21/3 to -15/3. Mean values are -5.48 and -5.78 for weak fluctuation and strong fluctuation trials, respectively, close to the value of -17/3. It is hard to tell what makes the high-frequency power-law complicated. Beam parameter [21

21. R. Rao and Z. Gong, “High-frequency behavior of the temporal spectrum of laser beam propagating through turbulence,” Proc. SPIE **4926**, 175–180 (2002). [CrossRef]

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

23. Y. Wang, C. Fan, X. Wu, J. Zhan, and Z. Gong, “Effects of non-uniform wind on the arrival angle temporal spectrum of spherical wave,” Proc. SPIE **4125**, 98–101 (2000). [CrossRef]

20. 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. A **16**, 2755–2762 (1999). [CrossRef]

24. 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]

### 3.4 Daily variation of σ^{2}_{I} and C^{2}_{n}

*L*is the link distance,

*D*is the diameter of the receiving aperture, and

*F*(

*F*≈

*L*, if

*L*is long enough) and

*W*denote the receiver plane phase front radius of curvature and beam radius, respectively. In our experiment,

*k*and

*L*are on the order of 10

^{7}and 10

^{4}, respectively,

*W*is about 3–4m, and

*D*=0.127cm. Based on these parameters, the approximation of

*F*≈

*L*,

*a*≈1 and Λ≈0 can be made, and Eq. (8) can be simplified to

*C*

^{2}

*values can be calculated from the experimental data of AOA by*

_{n}*C*

^{2}

*can be calculated by Eq. (11).*

_{n}*σ*

^{2}

*and*

_{I}*C*

^{2}

*are presented in Fig. 11 and Fig. 12, respectively, which were measured in a complete diurnal period of 27 March 2007. In Fig. 11 and Fig. 12, both*

_{n}*σ*

^{2}

*and*

_{I}*C*

^{2}

*have greater values in the daytime than at night. In the daytime, two curves have similar profiles. Both of them increase before midday, maximize at noon and then decline in the afternoon. But at night,*

_{n}*C*

^{2}

*appears more stable than*

_{n}*σ*

^{2}

*. The*

_{I}*C*

^{2}

*curve of Fig. 12 is similar to the measurement results in reference [7*

_{n}7. A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express. **15**, 3619–3628 (2007). [CrossRef] [PubMed]

*σ*

^{2}

_{0}is the on-axis scintillation index and

*r*is the distance between the receiving point and the beam center. Equation (12) indicates that

*σ*

^{2}

*increases with square of distance transverse to the optical axis [25*

_{I}25. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A. **11**, 2719–2726 (1994). [CrossRef]

*σ*

^{2}

*will be larger, but the measured*

_{I}*C*

^{2}

*will not be different because it is independent of*

_{n}*r*. In our experiment, the beam direction will slowly drift with time, especially at night, which means

*r*increases with time. This can explain why two figures are inconsistent with each other in some period of time.

## 4. Summary and conclusions

## Acknowledgments

## References and links

1. | D. L. Fried, G. E. Mevers, and M. P. Keister, “Measurements of laser beam scintillation in the atmosphere,” J. Opt. Soc. Am. |

2. | T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. |

3. | L. C. Andrews and R. L. Phillips, |

4. | L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash “Theory of optical scintillation,” J. Opt. Soc. Am. |

5. | L. C. Andrews, R. L. Phillips, and C. Y. Hopen, |

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 |

7. | A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express. |

8. | A. Tunick, “Statistical analysis of measured free-space laser signal intensity over a 2.33 km propagation path,” Opt. Express. |

9. | I. I. Kim, B. McArthur, and E. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” Proc. SPIE |

10. | Y. E. Yenicea, R. Li, M. Takabeb, and T. Arugab, “Atmospheric turbulence measurements through stellar observations,” Proc. SPIE |

11. | D. Romain, M. Larkin, G. Ghayal, B. Paulson, and G. Nykolak, “Optical wireless propagation theory vs. experiment,” Proc. SPIE |

12. | A. Al-habash, K. W. Fischer, C. S. Cornish, K. N. Desmet, and J. Nash, “Comparison between experimental and theoretical probability of fade for free space optical communications,” Proc. SPIE |

13. | W. Brown, B. Wallin, D. Lesniewski, D. Gooding, and J. Martin, “The experimental determination of on-off keying laser communications probability models and a comparison with theory,” Proc. SPIE |

14. | M. J. Curley, B. H. Peterson, J. C. Wang, S. S. Sarkisov, S. S. Sarkisov II, G. R. Edlin, R. A. Snow, and J. F. Rushing, “Statistical analysis of cloud-cover mitigation of optical turbulence in the boundary layer,” Opt. Express. |

15. | H. Yuksel and C. C. Davis, “Aperture averaging for studies of atmospheric turbulence and optimization of free space optical communication links” Proc. SPIE |

16. | M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. |

17. | C. Rao, W. Jiang, and N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” Proc. SPIE |

18. | R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE |

19. | M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. |

20. | 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. A |

21. | R. Rao and Z. Gong, “High-frequency behavior of the temporal spectrum of laser beam propagating through turbulence,” Proc. SPIE |

22. | B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE |

23. | Y. Wang, C. Fan, X. Wu, J. Zhan, and Z. Gong, “Effects of non-uniform wind on the arrival angle temporal spectrum of spherical wave,” Proc. SPIE |

24. | E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. |

25. | W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A. |

**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: January 30, 2008

Revised Manuscript: February 26, 2008

Manuscript Accepted: April 11, 2008

Published: May 1, 2008

**Citation**

Yijun Jiang, Jing Ma, Liying Tan, Siyuan Yu, and Wenhe Du, "Measurement of optical intensity fluctuation over an 11.8 km turbulent path," Opt. Express **16**, 6963-6973 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-6963

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### References

- 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]
- T. Chiba, "Spot dancing of the laser beam propagated through the turbulent atmosphere," Appl. Opt. 10, 2456-2461 (1971). [CrossRef] [PubMed]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 1998).
- L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1974). [CrossRef]
- L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001). [CrossRef]
- 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]
- A. Tunick, "Statistical analysis of optical turbulence intensity over a 2.33 km propagation path," Opt. Express 15, 3619-3628 (2007). [CrossRef] [PubMed]
- A. Tunick, "Statistical analysis of measured free-space laser signal intensity over a 2.33 km propagation path," Opt. Express 15, 14115-14122 (2007). [CrossRef] [PubMed]
- I. I. Kim, B. McArthur, and E. Korevaar, "Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications," Proc. SPIE 4214, 26-37 (2001). [CrossRef]
- Y. E. Yenicea, R. Li, M. Takabeb, and T. Arugab, "Atmospheric turbulence measurements through stellar observations," Proc. SPIE 3615, 316-324 (1999). [CrossRef]
- D. Romain, M. Larkin, G. Ghayal, B. Paulson, and G. Nykolak, "Optical wireless propagation theory vs. experiment," Proc. SPIE 4214, 38-45 (2001). [CrossRef]
- A. Al-habash, K. W. Fischer, C. S. Cornish, K. N. Desmet, and J. Nash, "Comparison between experimental and theoretical probability of fade for free space optical communications," Proc. SPIE 4873, 79-89 (2002). [CrossRef]
- W. Brown, B. Wallin, D. Lesniewski, D. Gooding, and J. Martin, "The experimental determination of on-off keying laser communications probability models and a comparison with theory," Proc. SPIE 6105, 61050U (2006). [CrossRef]
- M. J. Curley, B. H. Peterson, J. C. Wang, S. S. Sarkisov, S. S. SarkisovII, G. R. Edlin, R. A. Snow, and J. F. Rushing, "Statistical analysis of cloud-cover mitigation of optical turbulence in the boundary layer," Opt. Express. 14, 8929-8946 (2006). [CrossRef] [PubMed]
- H. Yuksel and C. C. Davis, "Aperture averaging for studies of atmospheric turbulence and optimization of free space optical communication links" Proc. SPIE 5892, 58920P (2005). [CrossRef]
- M. S. Belen'kii, "Effect of the stratosphere on star image motion," Opt. Lett. 20, 1359-1361 (1995). [CrossRef] [PubMed]
- C. Rao, W. Jiang, and N. Ling, "Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor," Proc. SPIE 3763, 84-91 (2006). [CrossRef]
- R. R. Beland, "Some aspects of propagation through weak isotropic non-Kolmogorov turbulence," Proc. SPIE 2375, 6-16 (1995). [CrossRef]
- M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001). [CrossRef]
- 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. A 16, 2755-2762 (1999). [CrossRef]
- R. Rao and Z. Gong, "High-frequency behavior of the temporal spectrum of laser beam propagating through turbulence," Proc. SPIE 4926, 175-180 (2002). [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]
- Y. Wang, C. Fan, X. Wu, J. Zhan, and Z. Gong, "Effects of non-uniform wind on the arrival angle temporal spectrum of spherical wave," Proc. SPIE 4125, 98-101 (2000). [CrossRef]
- 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]
- W. B. Miller, J. C. Ricklin, and L. C. Andrews, "Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam," J. Opt. Soc. Am. A. 11, 2719-2726 (1994). [CrossRef]

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