Abstract

Current mathematical scintillation theory describing laser propagation through the atmosphere has been developed for terrestrial environments. Scintillation expressions valid in all regimes of optical turbulence for propagation in the maritime environment, based on what we believe to be a newly developed marine atmospheric spectrum, have been developed for spherical waves. Path average values of the structure parameter, Cn2, were inferred from optical scintillation measurements of a diverged laser beam propagating in a marine environment, using scintillation expressions based on both terrestrial and marine refractive index spectra. In the moderate-to-strong fluctuation regime, the inferred marine Cn2 values were about 20% smaller than inferred terrestrial Cn2 values, but a minimal difference was observed in the weak fluctuation regime. Measurements of angle-of-arrival fluctuations were used to infer Cn2 values in the moderate-to-strong fluctuation regime, resulting in values of the structure parameter that were at least an order of magnitude larger than the two scintillation-inferred Cn2 values.

© 2007 Optical Society of America

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    [CrossRef]
  2. C. W. Fairall, K. L. Davidson, and G. E. Schacher, "Meteorological models for optical properties in the marine atmospheric boundary layer," Opt. Eng. (Bellingham) 21, 847-857 (1982).
  3. O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
    [CrossRef]
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  20. O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
    [CrossRef]

2007

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

2006

K. R. Weiss-Wrana, "Turbulence statistics in littoral area," Proc. SPIE 6364, 63640F (2006).
[CrossRef]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

F. S. Vetelino, B. Clare, K. Corbett, C. Young, K. Grant, and L. Andrews, "Characterizing the propagation path in moderate to strong optical turbulence," Appl. Opt. 45, 3534-3543 (2006).
[CrossRef] [PubMed]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

2005

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

2004

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

2000

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

1999

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

1998

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

1992

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

1982

C. W. Fairall, K. L. Davidson, and G. E. Schacher, "Meteorological models for optical properties in the marine atmospheric boundary layer," Opt. Eng. (Bellingham) 21, 847-857 (1982).

1978

R. J. Hill, "Spectra of fluctuations in refractivity, temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges," Radio Sci. 13, 953-961 (1978).
[CrossRef]

1975

Al-Habash, M. A.

Allard, L.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Andrews, L.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

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

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press, 1998).

Bendall, C.

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

Bendall, I.

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

Berglund, F.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

Bolander, G.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Burris, H. R.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Champagne, F. H.

Clare, B.

Corbett, K.

Davidson, K.

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

Davidson, K. L.

C. W. Fairall, K. L. Davidson, and G. E. Schacher, "Meteorological models for optical properties in the marine atmospheric boundary layer," Opt. Eng. (Bellingham) 21, 847-857 (1982).

Davis, M. A.

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Dreyer, G. F.

Fairall, C. W.

C. W. Fairall, K. L. Davidson, and G. E. Schacher, "Meteorological models for optical properties in the marine atmospheric boundary layer," Opt. Eng. (Bellingham) 21, 847-857 (1982).

Flannerg, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannerg, Numerical Recipes in C: The Art of Scientific Computing (1988-1992), Chap. 10.4. http://www.library.cornell.edu/nr/bookcpdf/c10-4.pdf.

Frederickson, P.

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

Friehe, C. A.

Gibson, C. H.

Gilbreath, G. C.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Grant, K.

Grayshan, K.

K. Grayshan, F. Strömqvist Vetelino, and C. Y. Young, "A marine atmospheric spectrum for laser propagation," Waves Random Complex Media (to be published).

Gustavsson, F.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Gustavsson, O.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Hill, R. J.

R. J. Hill, "Spectra of fluctuations in refractivity, temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges," Radio Sci. 13, 953-961 (1978).
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

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

Karlsson, K.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

Kullander, F.

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

La Rue, J. C.

Larsson, T.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

Mahon, R.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Moore, C. I.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Murphy, J.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Oh, E.

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Petersson, M.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

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

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press, 1998).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannerg, Numerical Recipes in C: The Art of Scientific Computing (1988-1992), Chap. 10.4. http://www.library.cornell.edu/nr/bookcpdf/c10-4.pdf.

Rabinovich, W.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Rabinovich, W. S.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Reed, A. E.

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Schacher, G. E.

C. W. Fairall, K. L. Davidson, and G. E. Schacher, "Meteorological models for optical properties in the marine atmospheric boundary layer," Opt. Eng. (Bellingham) 21, 847-857 (1982).

Scharp, W.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Scharpf, W. J.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Sjoqvist, L.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Sjöqvist, L.

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

Steinvall, O.

O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

Stell, M.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Stell, M. F.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Strömqvist Vetelino, F.

K. Grayshan, F. Strömqvist Vetelino, and C. Y. Young, "A marine atmospheric spectrum for laser propagation," Waves Random Complex Media (to be published).

Suite, M.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Suite, M. R.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannerg, Numerical Recipes in C: The Art of Scientific Computing (1988-1992), Chap. 10.4. http://www.library.cornell.edu/nr/bookcpdf/c10-4.pdf.

Vetelino, F. S.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannerg, Numerical Recipes in C: The Art of Scientific Computing (1988-1992), Chap. 10.4. http://www.library.cornell.edu/nr/bookcpdf/c10-4.pdf.

Vilcheck, M. J.

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

Wasiczko, L.

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

Wasiczko, L. M.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

Weiss-Wrana, K. R.

K. R. Weiss-Wrana, "Turbulence statistics in littoral area," Proc. SPIE 6364, 63640F (2006).
[CrossRef]

Young, C.

Young, C. Y.

K. Grayshan, F. Strömqvist Vetelino, and C. Y. Young, "A marine atmospheric spectrum for laser propagation," Waves Random Complex Media (to be published).

Zeisse, C.

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

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O. Steinvall, G. Bolander, L. Sjoqvist, M. Petersson, O. Gustavsson, F. Berglund, L. Allard, K. Karlsson, T. Larsson, and F. Gustavsson, "Single- and double-path 10.6 μm laser link measurements over sea water," Opt. Eng. (Bellingham) 46, 036001 (2007).
[CrossRef]

Proc. SPIE

P. Frederickson, K. Davidson, C. Zeisse, and I. Bendall, "A comparison of near-surface bulk and scintillation Cn2 measurements during EOPACE," Proc. SPIE 3433, 77-88 (1998).
[CrossRef]

P. Frederickson, K. Davidson, C. Zeisse, and C. Bendall, "Near-surface scintillation in a coastal ocean region," Proc. SPIE 3763, 230-238 (1999).
[CrossRef]

M. F. Stell, C. I. Moore, H. R. Burris, M. R. Suite, M. J. Vilcheck, M. A. Davis, R. Mahon, E. Oh, W. S. Rabinovich, G. C. Gilbreath, W. J. Scharpf, and A. E. Reed, "Passive optical monitor for atmospheric turbulence and windspeed," Proc. SPIE 5160, 422-431 (2004).
[CrossRef]

C. I. Moore, H. R. Burris, M. F. Stell, L. Wasiczko, M. R. Suite, R. Mahon, W. S. Rabinovich, G. C. Gilbreath, and W. J. Scharpf, "Atmospheric turbulence studies of a 16 km maritime path," Proc. SPIE 5793, 78-88 (2005).
[CrossRef]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, J. Murphy, G. C. Gilbreath, W. Rabinovich, and W. Scharp, "Characterization of the marine atmosphere for free-space optical communication," Proc. SPIE 6215, 621501 (2006).
[CrossRef]

K. R. Weiss-Wrana, "Turbulence statistics in littoral area," Proc. SPIE 6364, 63640F (2006).
[CrossRef]

O. Steinvall, L. Sjöqvist, F. Kullander, F. Berglund, T. Larsson, and K. Karlsson,"Multi-wavelength laser system propagation experiments," Proc. SPIE 6397, 63970A (2006).
[CrossRef]

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L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

Other

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

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannerg, Numerical Recipes in C: The Art of Scientific Computing (1988-1992), Chap. 10.4. http://www.library.cornell.edu/nr/bookcpdf/c10-4.pdf.

Downhill Simplex Method, code for MATLAB: http://freehost26.websamba.com/zhanshan2002/matlab/simplex.html

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press, 1998).

K. Grayshan, F. Strömqvist Vetelino, and C. Y. Young, "A marine atmospheric spectrum for laser propagation," Waves Random Complex Media (to be published).

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Figures (5)

Fig. 1
Fig. 1

Terrestrial and marine refractive index power spectra scaled by the Kolmogorov spectrum as a function of κ l 0 .

Fig. 2
Fig. 2

Scintillation index of a spherical wave for a point receiver based on the modified and the marine spectra, respectively, as a function of β 0 , for a varying C n 2 parameter, an outer scale of 1 m , and an inner scale of 2 mm and 7 mm , respectively.

Fig. 3
Fig. 3

Experimental scintillation index measured in a marine environment at each receiver aperture ( D ) in (a) weak and (b) moderate-to-strong optical turbulence.

Fig. 4
Fig. 4

Comparison between the inferred marine and terrestrial C n 2 values in (a) weak and (b) moderate-to-strong optical turbulence, where marine and terrestrial refer to C n 2 values determined using the marine and the modified (terrestrial) spectra, respectively.

Fig. 5
Fig. 5

Comparison between the inferred marine and terrestrial C n 2 values, based on scintillation measurements, and C n 2 values inferred from AOA measurements.

Tables (1)

Tables Icon

Table 1 Scintillation Index for a Spherical Wave based on the Modified and Marine Atmospheric Spectra a

Equations (23)

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Φ n ( κ ) = 0.033 C n 2 [ 1 + 1.802 ( κ κ l ) 0.254 ( κ κ l ) 7 6 ] exp ( κ 2 κ l 2 ) ( κ 2 + κ 0 2 ) 11 6 ,
Φ n , M a ( κ ) = 0.033 C n 2 [ 1 0.061 ( κ κ H ) + 2.836 ( κ κ H ) 7 6 ] exp ( κ 2 κ H 2 ) ( κ 2 + κ 0 2 ) 11 6 ,
σ I 2 = I 2 I 2 1 ,
σ R 2 = 1.23 C n 2 k 7 6 L 11 6 ,
Φ n , e ( κ ) = 0.033 C n 2 κ 11 3 [ f ( κ l 0 ) g ( κ L 0 ) G x ( κ ) + G y ( κ ) ] ,
f ( κ l 0 ) = exp ( κ 2 κ l 2 ) [ 1 + 1.80 ( κ κ l ) 0.25 ( κ κ l ) 7 6 ] ,
f M a ( κ l 0 ) = exp ( κ 2 κ H 2 ) [ 1 0.061 ( κ κ H ) + 2.836 ( κ κ H ) 7 6 ] ,
g ( κ l 0 ) = 1 exp ( κ 2 κ 0 2 ) ,
G x ( κ ) = exp ( κ 2 κ x 2 ) ,
G y ( κ ) = κ 11 3 ( κ 2 + κ y 2 ) 11 6 ,
L k l x = 1 κ x { L k , L k ρ 0 2 1 L k ρ 0 , L k ρ 0 2 1 } ,
l y = 1 κ y { L k , L k ρ 0 2 1 ρ 0 , L k ρ 0 2 1 } ,
σ I 2 = exp ( σ ln I 2 ) 1 = exp ( σ ln x 2 + σ ln y 2 ) 1 ,
σ ln x 2 ( l 0 , L 0 ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ ) G x ( κ ) f ( κ l 0 ) g ( κ L 0 ) { 1 cos [ L κ 2 k ξ ( 1 ξ ) ] } d κ d ξ = σ ln x 2 ( l 0 ) σ ln x 2 ( L 0 ) ,
σ ln y 2 ( l 0 ) = 8 π 2 k 2 L 0 1 0 κ Φ n ( κ ) G y ( κ ) { 1 cos [ L κ 2 k ξ ( 1 ξ ) ] } d κ d ξ = 3.18 β 0 2 η y 5 6 ,
1 η x = c 1 + c 2 L k ρ 0 2 ,
η y = c 3 + c 4 L k ρ 0 2 = 8.99 ( β 0 2 σ S 2 ) ( 1 + 0.69 σ S 12 5 ) ,
σ I 2 ( L ) = 1 + 32 π 2 k 2 L 0 1 0 κ Φ n ( κ ) sin 2 [ L κ 2 2 k ξ ( 1 ξ ) ] × exp { 0 ξ D S [ L κ k τ ( 1 ξ ) ] d τ ξ 1 D S [ L κ k ξ ( 1 τ ) ] d τ } d κ d ξ ,
D S ( ρ ) = 1 2 D p l ( ρ ) = 4 π 2 k 2 L 0 κ Φ n ( κ ) [ 1 J 0 ( κ ρ ) ] d κ 2.196 C n 2 k 2 L l 0 1 3 ρ 2 .
σ I 2 ( L ) 1 + 6.75 ( σ R 2 Q H 7 6 ) 1 6 ,
f ( l 0 , L 0 , C n 2 ) = j = 1 3 [ σ I 2 ( l 0 , L 0 , C n 2 , D j ) σ I , exp 2 ( D j ) ] 2 ,
C n 2 = 1 9.12 ln ( 1 + σ I , exp 2 ) D 7 3 L 3 ,
σ β 2 = 1.093 C n 2 L D 1 3 , ( L k ) 1 2 D ,

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