Abstract

Irradiance fluctuations of an infrared laser beam from a shore-to-ship data link ranging from 5.1 to 17.8 km are compared to lognormal (LN), gamma–gamma (GG) with aperture averaging, and gamma-Laguerre (GL) distributions. From our data analysis, the LN and GG probability density function (PDF) models were generally in good agreement in near-weak to moderate fluctuations. This was also true in moderate to strong fluctuations when the spatial coherence radius was smaller than the detector aperture size, with the exception of the 2.54 cm power-in-bucket (PIB) where the LN PDF model fit best. For moderate to strong fluctuations, the GG PDF model tended to outperform the LN PDF model when the spatial coherence radius was greater than the detector aperture size. Additionally, the GL PDF model had the best or next to best overall fit in all cases with the exception of the 2.54 cm PIB where the scintillation index was highest. The GL PDF model also appears to be robust for off-of-beam center laser beam applications.

© 2013 Optical Society of America

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2012 (1)

2011 (3)

2010 (2)

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

2009 (3)

2007 (2)

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

F. Stromqvist Vetelino, C. Young, L. Andrews, and J. Recolons, “Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence,” Appl. Opt. 46, 2099–2108 (2007).
[CrossRef]

2006 (1)

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

2001 (2)

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. Ruilier and F. Cassaing, “Coupling of large telescopes and single-mode waveguides: application to stellar interferometry,” J. Opt. Soc. Am. A 18, 143–149 (2001).
[CrossRef]

1999 (1)

R. Barakat, “First-order intensity and log-intensity probability density functions of light scattered by the turbulent atmosphere in terms of lower-order moments,” J. Opt. Soc. Am. 16, 2269–2274 (1999).
[CrossRef]

1987 (1)

1975 (1)

J. W. Strohbehn, T.-I. Wang, and J. P. Speck, “On the probability density distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Airola, M. B.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Aitchison, J.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge, 1957).

Al-Habash, M. A.

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]

Allard, L.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Andrews, L.

Andrews, L. C.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[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]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Avramov-Zamurovic, S.

O. Korotkova, S. Avramov-Zamurovic, R. Malek-Madani, and C. Nelson, “Probability density function of the intensity of a laser beam propagating in the maritime environment,” Opt. Express 19, 20322–20331 (2011).
[CrossRef]

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

Barakat, R.

R. Barakat, “First-order intensity and log-intensity probability density functions of light scattered by the turbulent atmosphere in terms of lower-order moments,” J. Opt. Soc. Am. 16, 2269–2274 (1999).
[CrossRef]

Berglund, F.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Bolander, G.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Brown, J. A. C.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge, 1957).

Burris, H. R.

Cassaing, F.

Cherry, P. C.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Churnside, J. H.

Clare, B. A.

Cowley, W. G.

Das, S.

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

Davidson, F.

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Davidson, F. M.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Dwivedi, A.

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

Epple, B.

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

Ferraro, M.

Fitch, M. J.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Foshee, J. J.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Grant, K. J.

Gustafsson, O.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Gustavsson, F.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Hammons, A. R.

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

Henniger, H.

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

Hill, R. J.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Jones, S. D.

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

Juarez, J.

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Juarez, J. C.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Karlsson, K.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Kolodzy, P. J.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Korotkova, O.

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

O. Korotkova, S. Avramov-Zamurovic, R. Malek-Madani, and C. Nelson, “Probability density function of the intensity of a laser beam propagating in the maritime environment,” Opt. Express 19, 20322–20331 (2011).
[CrossRef]

Larsson, T.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Lyke, S. D.

Mackintosh, J. L.

Mahon, R.

Malek-Madani, R.

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

O. Korotkova, S. Avramov-Zamurovic, R. Malek-Madani, and C. Nelson, “Probability density function of the intensity of a laser beam propagating in the maritime environment,” Opt. Express 19, 20322–20331 (2011).
[CrossRef]

McIntire, W. K.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Mclaren, J. R. W.

Moore, C. I.

Mudge, K. A.

Nelson, C.

O. Korotkova, S. Avramov-Zamurovic, R. Malek-Madani, and C. Nelson, “Probability density function of the intensity of a laser beam propagating in the maritime environment,” Opt. Express 19, 20322–20331 (2011).
[CrossRef]

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Nichols, R. A.

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

Northcott, M.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Petersson, M.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Phillips, R. L.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[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]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Pike, H. A.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Rabinovich, W.

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

Rabinovich, W. S.

Recolons, J.

Riggins, J.

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

Roggemann, M. C.

Rottier, J. R.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Ruilier, C.

Sluz, J.

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Sluz, J. E.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Sova, R.

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Sova, R. M.

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Speck, J. P.

J. W. Strohbehn, T.-I. Wang, and J. P. Speck, “On the probability density distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Stadler, B.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Steinvali, O.

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[CrossRef]

Stell, M.

Stotts, L. B.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, T.-I. Wang, and J. P. Speck, “On the probability density distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Stromqvist Vetelino, F.

Suite, M.

Suite, M. R.

Terry, D.

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Thomas, J. C.

Thomas, L. M.

Voelz, D. G.

Wang, T.-I.

J. W. Strohbehn, T.-I. Wang, and J. P. Speck, “On the probability density distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Weerackody, V.

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

Young, C.

Young, D.

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

Young, D. W.

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

Appl. Opt. (5)

IEEE Commun. Mag. (1)

J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R. A. Nichols, “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag. 44(11), 46–51 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

R. Barakat, “First-order intensity and log-intensity probability density functions of light scattered by the turbulent atmosphere in terms of lower-order moments,” J. Opt. Soc. Am. 16, 2269–2274 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

O. Steinvali, G. Bolander, M. Petersson, O. Gustafsson, 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. 46, 036001 (2007).
[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]

Opt. Express (1)

Proc. IEEE (1)

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97, 1109–1127 (2009).
[CrossRef]

Proc. SPIE (3)

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” Proc. SPIE 7685, 76850H (2010).
[CrossRef]

J. E. Sluz, J. Riggins, J. C. Juarez, R. M. Sova, D. W. Young, and C. Nelson, “Characterization of data transmission through a maritime free-space optical channel with a custom bit error rate tester,” Proc. SPIE 7700, 77000D (2010).
[CrossRef]

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, and F. Davidson, “Probability density function computations for power-in-bucket and power-in-fiber measurements of an infrared laser beam propagating in the maritime environment,” Proc. SPIE 8038, 80380G (2011).
[CrossRef]

Radio Sci. (1)

J. W. Strohbehn, T.-I. Wang, and J. P. Speck, “On the probability density distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Other (6)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

S. Das, H. Henniger, B. Epple, C. I. Moore, W. Rabinovich, R. Sova, and D. Young, Requirements and Challenges for Tactical Free-Space Lasercomm (Milcom, 2008).

J. Juarez, J. Sluz, C. Nelson, F. Davidson, D. Young, and R. Sova, “Lasercomm demonstration in maritime environment for tactical applications,” in Applications of Lasers for Sensing and Free Space Communications, OSA Technical Digest Series (Optical Society of America, 2010), paper LSMA2.

J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge, 1957).

J. C. Juarez, J. E. Sluz, C. Nelson, M. B. Airola, M. J. Fitch, D. W. Young, D. Terry, F. M. Davidson, J. R. Rottier, and R. M. Sova, “Free-space optical channel characterization in the maritime environment,” presented at the SPIE Defense, Security, and Sensing Conference, April, 2010.

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Figures (11)

Fig. 1.
Fig. 1.

Shore-to-ship, bi-directional 1550 nm optical link from the tower located at Cedar Island and research vessel traveling along the Atlantic Coast. (a) tower location, (b) picture of boat, and (c) picture of 17m tower, 1—boat starting point, 2—boat ending point [7,22].

Fig. 2.
Fig. 2.

Experimental setup of instrumentation [7]. Devices relevant for the paper’s analysis are highlighted. (a) 2.54 cm power-in-fiber adaptive optics (PIF AO) aperture, A; 0.64 and 2.54 cm PIB apertures, B and C, respectively; (b) 1.2m×1.2m white screen for IR imaging of the overall optical beam. The cut-outs on the screen fit the detector apertures.

Fig. 3.
Fig. 3.

IR spatial profiles of the propagating beam [7]. Location of detectors is as in (a).

Fig. 4.
Fig. 4.

PDF models and histogram for Case I using a 2.54 cm PIF communication terminal with an IR laser at λ=1550nm. (a) 5.1 km, computed scintillation index, σB2=0.066, ρ04.1cm, σR21.0. (b) 10.7 km, computed scintillation index, σB2=0.123, ρ03.2cm, σR23.7. (c) 17.8 km, computed scintillation index, σB2=0.63, ρ02.6cm, σR29.4.

Fig. 5.
Fig. 5.

PDF models and histogram for Case I using a 0.64 cm PIB aperture detector with an IR laser at λ=1550nm (a) 5.1 km, computed scintillation index, σB2=0.238, ρ04.1cm, σR21.0. (b) 10.7 km, computed scintillation index, σB2=0.129, ρ03.2cm, σR23.7. (c) 17.8 km, computed scintillation index, σB2=0.632, ρ02.6cm, σR29.4.

Fig. 6.
Fig. 6.

PDF models and histogram for Case I using a 2.54 cm PIB aperture detector with an IR laser at λ=1550nm. (a) 5.1 km, computed scintillation index, σB2=0.209, ρ04.1cm, σR21.0. (b) 10.7 km, computed scintillation index, σB2=0.097, ρ03.2cm, σR23.7. (c) 17.8 km, computed scintillation index, σB2=0.417, ρ02.6cm, σR29.4.

Fig. 7.
Fig. 7.

IR spatial profiles of the propagating beam [7]. Location of detectors is as in (a).

Fig. 8.
Fig. 8.

PDF models and histogram for Case II using a 2.54 cm PIF communication terminal with an IR laser at λ=1550nm. (a) 6.9 km, computed scintillation index, σB2=0.172, ρ02.4cm, σR23.6. (b) 8.5 km, computed scintillation index, σB2=0.279, ρ02.2cm, σR25.2. (c) 10.5 km, computed scintillation index, σB2=0.706, ρ02.1cm, σR27.7.

Fig. 9.
Fig. 9.

PDF models and histogram for Case II using 0.64 cm PIB aperture detector with an IR laser at λ=1550nm. (a) 6.9 km, computed scintillation index, σB2=0.184, ρ02.4cm, σR23.6. (b) 8.5 km, computed scintillation index, σB2=0.273, ρ02.2cm, σR25.2. (c) 10.5 km, computed scintillation index, σB2=0.790, ρ02.1cm, σR27.7.

Fig. 10.
Fig. 10.

PDF models and histogram for Case II using 2.54 cm PIB aperture detector with an IR laser at λ=1550nm. (a) 6.9 km, computed scintillation index, σB2=0.436, ρ02.4cm, σR23.6. (b) 8.5 km, computed scintillation index, σB2=0.750, ρ02.2cm, σR25.2. (c) 10.5 km, computed scintillation index, σB2=1.08, ρ02.1cm, σR27.7.

Fig. 11.
Fig. 11.

Comparison of PDF models and histogram [Figs. 4(b), 4(c) and 5(b), and 5(c) are overlapped] for Case I at 10.7 and 17.8 km using a 2.54 cm PIF and 0.64 cm PIB aperture detectors.

Equations (24)

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

P(aIb)=abW(I)dI.
WGL(I)=Wg(I)n=0UnLn(β1)(βIμ),I0,
Wg(I)=1Γ(β)(βμ)βIβ1exp(βIμ),
μ=I,β=I2/(I2I2).
Un=n!Γ(β)k=0n(β/μ)kIkk!(nk)!Γ(β+k),
Ln(β1)(x)=k=0n(n+β1n1)(x)kk!.
In=0InW(I)dI.
WGGA(I)=2(αβG)α+βG2Γ(α)Γ(βG)Iα+βG21KαβG(2αβGI),I>0,
α=1exp(σlnx2)1,βG=1exp(σlny2)1.
σlnx20.49σ12(ΩGΛ1ΩG+Λ1)2(1312Θ¯1+15Θ¯12)[ηx1+0.40ηx(2Θ¯1)(Λ1+ΩG)]76,
σlny21.27σ12ηy5/61+0.40ηy(Λ1+ΩG),ηy1,
ηx=(1312Θ¯1+15Θ¯12)67(σBσ1)1271+0.56σB125,
ηy=3(σ1σB)12/5(1+0.69σB12/5),
Λ1=(2LkW02)1+(2LkW02)2,
ΩG=16LkD2,
Θ¯1=1Θ,
Θ=[1+(2LkW02)2]1,
σB2=(I2I2)/I2,
σ12σRGB23.86{0.40[(1+2Θ)2+4Λ12]512cos[56tan1(1+2Θ2Λ1)]1116Λ15/6},
σRGB2σB2.
WLN(I)=1IσlnI2πexp[[ln(I)μlnI]22σlnI2],I>0,
σR2=1.23Cn2k76L116,
ρ0=[83(a+0.62Λ1)116]35(1.46Cn2k2L)35,l0ρ0L0,
a=1Θ831Θ,Θ0,

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