Abstract

In the near-infrared and visible bandpasses optical propagation theory conventionally assumes that humidity does not contribute to the effects of atmospheric turbulence on optical beams. While this assumption may be reasonable for dry locations, we demonstrate that there is an unequivocal effect owing to the presence of humidity upon the strength of turbulence parameter, Cn2, from data collected in the Chesapeake Bay area over 100 m length horizontal propagation paths. We describe and apply a novel technique, Hilbert phase analysis, to the relative humidity, temperature, and Cn2 data to show the contribution of the relevant climate variable to Cn2 as a function of time.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Roddier, "The effects of atmospheric turbulence in optical astronomy," Prog. Opt. XIX, 281-377 (1981).
  2. V. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  3. V. Tatarskii, The Effects of a Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).
  4. R. R. Beland, Propagation through Atmospheric Optical Turbulence (SPIE Optical Engineering Press, 1993).
  5. M. Miller and P. L. Zieske, Turbulence Environmental Characterization, RADC-TR-79-131, ADA072379 (Rome Air Development Center, 1976).
  6. M. C. Roggeman and B. Welsh, Imaging through Turbulence (CRC Press, 1996).
  7. P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).
  8. K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, "Verification of the bulk method for calculating overwater optical turbulence," Appl. Opt. 20, 2919-2924 (1981).
  9. G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
    [CrossRef]
  10. E. L. Andreas, "Estimating Cn2 over snow and sea ice from meteorological data," J. Opt. Soc. Am. A 5, 481-494 (1988).
  11. G. R. Ochs and T.-I. Wang, "Finite aperture optical scintillometer for profiling wind and Cn2," Appl. Opt. 17, 3774-3778 (1979).
  12. T.-I. Wang, "Optical flow sensor," U.S. patent 6,369,881 (9 April 2002).
  13. S. F. Clifford, G. R. Ochs, and R. S. Lawrence, "Saturation of optical scintillation by strong turbulence," J. Opt. Soc. Am. 64, 148-154 (1974).
  14. E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
    [CrossRef]
  15. S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
    [CrossRef]
  16. E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
    [CrossRef]
  17. C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
    [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  19. L. Cohen, Time Frequency Analysis (Prentice Hall, 1995).
  20. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).
  21. M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
    [CrossRef]
  22. C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
    [CrossRef]
  23. H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
    [CrossRef]

2006

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

2004

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

1999

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

1998

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

1997

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

1996

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

1988

1981

1979

1974

Aime, C.

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

Andreas, E. L.

Aristidi, E.

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

Beaumont, H.

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

Beland, R. R.

R. R. Beland, Propagation through Atmospheric Optical Turbulence (SPIE Optical Engineering Press, 1993).

Bendall, C. S.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Chang, M. P. J. L.

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

Clifford, S. F.

Cohen, L.

L. Cohen, Time Frequency Analysis (Prentice Hall, 1995).

Davidson, K. L.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, "Verification of the bulk method for calculating overwater optical turbulence," Appl. Opt. 20, 2919-2924 (1981).

de Leeuw, G.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

Doss-Hammel, S.

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Doss-Hammell, S.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Eaton, F.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Eaton, F. D.

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Fairall, C. W.

Font, C. O.

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

Frederickson, P. A.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

Fritz, P. J.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

Gilbreath, C.

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Gilbreath, G. C.

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Goroch, A. K.

Huang, N. E.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Kunz, G. J.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

Lantéri, H.

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

Lawrence, R. S.

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Long, S. R.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Miller, M.

M. Miller and P. L. Zieske, Turbulence Environmental Characterization, RADC-TR-79-131, ADA072379 (Rome Air Development Center, 1976).

Moerman, M. M.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

Moore, C.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Murphy, J.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Ochs, G. R.

Oh, E.

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Oh, Y. H.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Ricklin, J.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Ricklin, J. C.

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Roddier, F.

F. Roddier, "The effects of atmospheric turbulence in optical astronomy," Prog. Opt. XIX, 281-377 (1981).

Roggeman, M. C.

M. C. Roggeman and B. Welsh, Imaging through Turbulence (CRC Press, 1996).

Roura, E. A.

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

Schacher, G. E.

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Stell, M.

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

Tatarskii, V.

V. Tatarskii, The Effects of a Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

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

Tsintikidis, D.

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Vallestero, N. J.

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

Wang, T.-I.

Welsh, B.

M. C. Roggeman and B. Welsh, Imaging through Turbulence (CRC Press, 1996).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wu, M. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Yen, N.-C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Zeisse, C. R.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Zieske, P. L.

M. Miller and P. L. Zieske, Turbulence Environmental Characterization, RADC-TR-79-131, ADA072379 (Rome Air Development Center, 1976).

Appl. Opt.

J. Appl. Meteorol.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, "Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods," J. Appl. Meteorol. 39, 1770-1783 (1999).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Proc. R. Soc. London Ser. A

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998).

Proc. SPIE

M. P. J. L. Chang, E. A. Roura, C. O. Font, C. Gilbreath, and E. Oh, "Applying the Hilbert-Huang decomposition to horizontal light propagation Cn2 data," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683E (2006).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "On the relationship between Cn2 and humidity," in Advances in Stellar Interferometry, J. D. Monnier, M. Schoeller, and W. C. Danchi, eds., Proc. SPIE 6268, 62683D (2006).
[CrossRef]

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, "Validation of a bulk turbulence model with thermal images of a point source," in Image Propagation through the Atmosphere, C. Dainty and L. R. Bissonnette, eds., Proc. SPIE 2828, 108-116 (1996).
[CrossRef]

E. Oh, J. Ricklin, F. Eaton, C. Gilbreath, S. Doss-Hammell, C. Moore, J. Murphy, Y. H. Oh, and M. Stell, "Estimating optical turbulence using the PAMELA model," in Remote Sensing and Modeling of Ecosystems for Sustainability, W. Gao and D. R. Shaw, eds., Proc. SPIE 5550, 256-266 (2004).
[CrossRef]

S. Doss-Hammel, E. Oh, J. C. Ricklin, F. D. Eaton, G. C. Gilbreath, and D. Tsintikidis, "A comparison of optical turbulence models," in Remote Sensing and Modeling of Ecosystems for Sustainability, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 236-246 (2004).
[CrossRef]

E. Oh, J. C. Ricklin, G. C. Gilbreath, N. J. Vallestero, and F. D. Eaton, "Optical turbulence model for laser propagation and imaging applications," in Free-Space Laser Communication and Active Laser Illumination III, D. G. Voelz and J. C. Ricklin, eds., Proc. SPIE 5160, 25-32 (2004).
[CrossRef]

C. O. Font, M. P. J. L. Chang, E. Oh, and C. Gilbreath, "Humidity contribution to the refractive index structure function Cn2," in Atmospheric Propagation III, C. Y. Young and G. C. Gilbreath, eds., Proc. SPIE 6215, 621502 (2006).
[CrossRef]

Prog. Opt.

F. Roddier, "The effects of atmospheric turbulence in optical astronomy," Prog. Opt. XIX, 281-377 (1981).

Pure Appl. Opt.

H. Beaumont, C. Aime, E. Aristidi, and H. Lantéri, "Image quality and seeing measurements for long horizontal overwater propagation," Pure Appl. Opt. 6, 15-30 (1997).
[CrossRef]

Other

T.-I. Wang, "Optical flow sensor," U.S. patent 6,369,881 (9 April 2002).

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

V. Tatarskii, The Effects of a Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

R. R. Beland, Propagation through Atmospheric Optical Turbulence (SPIE Optical Engineering Press, 1993).

M. Miller and P. L. Zieske, Turbulence Environmental Characterization, RADC-TR-79-131, ADA072379 (Rome Air Development Center, 1976).

M. C. Roggeman and B. Welsh, Imaging through Turbulence (CRC Press, 1996).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

L. Cohen, Time Frequency Analysis (Prentice Hall, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Effects of solar insolation on C n 2 as measured on 9 March 2006 in Puerto Rico. Solar radiation measurements are superimposed at an arbitrary scale on top of the C n 2 data. (Left) The full 24 h period. The vertical axis values are of order 10 12 m 2 / 3 . (Right) Close up of the evening period. The vertical axis values are of order 10 14 m 2 / 3 . The C n 2 data were obtained at an urban site 1.75 km from the sea. These values are in agreement with measurements of seeing over the sea by alternative means (Ref. [23]).

Fig. 2
Fig. 2

Graph of n / ( A t ) versus Bowen ratio for λ = 0.93 μ m .

Fig. 3
Fig. 3

Example correlograms of C n 2 and relative humidity in the absence of solar insolation. The upper and lower bounds indicate the 50% confidence level. The C n 2 magnitudes are 10 15 m 2 / 3 , in agreement with measurements of seeing over the sea by alternative means (Ref. [23]).

Fig. 4
Fig. 4

(Left) Hilbert phase space plot of the trajectory of the C n 2 signal vector of Fig. 1. The signal vector's start point drifts arbitrarily around the phase space making the determination of a physically reasonable instantaneous frequency impossible over the whole path. (Right) Hilbert phase space plot of the trajectory of a single IMF derived from the C n 2 signal. The IMF vector's start point is stable, and its trajectory does not change direction, so a positive instantaneous frequency can be determined at all points.

Fig. 5
Fig. 5

Sum of all Hilbert phases of the measured solar radiation IMFs ( Φ S ) for the following days: 2 February, 27 March, 28 March, and 3 April 2004. The solar radiation is superimposed at an arbitrary scale.

Fig. 6
Fig. 6

Difference plots for the morning of 10 November 2003. The dotted line is a linear regression, estimating the mean phase gradient. The leftmost graph shows a phase lock between C n 2 and relative humidity.

Fig. 7
Fig. 7

Plots of Hilbert phase differences between C n 2 and solar radiation for 27 and 28 March 2004. The solar radiation function is superimposed at an arbitrary scale on each graph. Note the flattening out of the phase difference function during the daylight hours.

Tables (2)

Tables Icon

Table 1 Mean and Range of Bulk Parameter Measurements and the Maximum Range of Specific Humidity ( Δ Q s )

Tables Icon

Table 2 Linear Regression Line Gradients of the Phase Differences

Equations (105)

Equations on this page are rendered with MathJax. Learn more.

C n 2
C n 2
C n 2
C n 2
C n 2
C n 2
C n 2
5 μ m
C n 2
n *
n * = A t * + B q * n * A t * = 1 + B q * A t *
t
q
n
n * A t * = 1 + ( ρ c p L ) B A ( B o ) = 1 + ( B K A ( B o ) ) ,
c p
B o t / q
T = 25 ° C
λ = 0.93 μ m
| B o |
n / A t
t
| B o |
q
n
C n 2
C n 2
C n 2
C n 2
( DP + )
0.96 μ m
1.0 μ m
C n 2
[ C χ ( r ) ]
C χ ( r )
C n 2
C n 2
C n 2
± 20 °
C n 2
C n 2
C n 2
C n 2
Ψ ( t ) = X ( t ) + i Y ( t ) ,
Y ( t ) = [ X ( t ) ] = 1 π P X ( τ ) ( t τ ) d τ ,
[ ]
Ψ ( t )
( 1 / [ π ( t τ ) ] )
π / 2
cos   t
Ψ ( t ) = a ( t ) exp i Φ ( t ) , where   a ( t ) = X 2 ( t ) + Y 2 ( t ) , Φ ( t ) = arctan ( Y ( t ) X ( t ) ) ,
Φ ( t )
ω ( t )
ω ( t ) = d Φ ( t ) d t .
Φ ( t )
ω ( t )
C n 2
ω ( t )
ω ( t )
[ Φ ( t ) ]
IMF Φ ( t )
IMF Φ ( t )
Φ C
Δ C T = Φ C Φ T , Δ C H = Φ C Φ H ,
Δ C HT ¯ = Φ C ( Φ H + Φ T ) 2 ,
C n 2
C n 2
C n 2
C n 2
( Φ C Φ S )
Δ C T
Δ C T
Δ C H
C n 2
C n 2
Δ C T < Δ C H
C n 2
C n 2
C n 2
3 μ m
A = 10 6 m 1 ( λ ) ( P / T 2 ) ,
B = 4.6150 × 10 6 [ m 2 ( λ ) m 1 ( λ ) ] .
m 1
m 2
m 1 ( λ ) = 23.7134 + 6839.397 130 ( 1 / λ ) 2 + 45.473 38.9 ( 1 / λ ) 2 ,
m 2 ( λ ) = 64.8731 + 0.58058 ( 1 / λ ) 2 0.0071150 ( 1 / λ ) 4 + 0.0008851 ( 1 / λ ) 6 ,
Δ Q s
R H ¯
Δ Q s
Δ C H T ¯
C n 2
C n 2
10 12 m 2 / 3
10 14 m 2 / 3
C n 2
n / ( A t )
λ = 0.93 μ m
C n 2
C n 2
10 15 m 2 / 3
C n 2
C n 2
( Φ S )
C n 2
C n 2

Metrics