Abstract

The Mueller matrix imaging method is a powerful tool for target detection. In this study, the effect of the air–sea interface on the detection of underwater objects is studied. A backward Monte Carlo code has been developed to study this effect. The main result is that the reflection of the diffuse sky light by the interface reduces the Mueller image contrast. If the air–sea interface is ruffled by wind, the distinction between different regions of the underwater target is smoothed out. The effect of the finite size of an active light source is also studied. The image contrast is found to be relatively insensitive to the size of the light source. The volume scattering function plays an important role on the underwater object detection. Generally, a smaller asymmetry parameter decreases the contrast of the polarimetry images.

© 2009 Optical Society of America

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References

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  2. S. R. Pal and A. I. Carswell, “Polarization anisotropy in lidar multiple scattering from atmospheric clouds,” Appl. Opt. 24, 3464-3471 (1985).
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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] [PubMed]
  31. E. P. Zege and L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19-31 (1996).
    [CrossRef]
  32. K. F. Evans, “The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429-446 (1998).
    [CrossRef]
  33. Concise Dictionary of Scientific Biography (Scribner, 1981), p. 643. Willebrord Snel von Royen used only one l in his last name.
  34. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035-1050(2002).
    [CrossRef] [PubMed]
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2008 (2)

Alberic Jaulin, Laurent Bigue, and Pierre Ambs, “High-speed degree-of-polarization imaging with a ferroelectric liquid-crystal modulator,” Opt. Eng. 47, 033201 (2008).
[CrossRef]

P. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method,” Appl. Opt. 47, 1037-1047 (2008).
[CrossRef] [PubMed]

2004 (4)

J. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt. 43, 283-292 (2004).
[CrossRef] [PubMed]

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824-2832 (2004).
[CrossRef] [PubMed]

D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Proceedings of laser radar techniques for atmospheric sensing,” Proc. SPIE 5575, 8-15 (2004).
[CrossRef]

G. Yao, “Differential optical polarization imaging in turbid media with different embedded objects,” Opt. Commun. 241, 255-261 (2004).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1999 (4)

1998 (3)

1997 (2)

1996 (2)

E. P. Zege and L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19-31 (1996).
[CrossRef]

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7, 17-22 (1996).
[CrossRef]

1993 (1)

1992 (3)

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-I. theory,” J. Quant. Spectrosc. Radiat. Transfer 47, 19-33 (1992).
[CrossRef]

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere II. Application,” J. Quant. Spectrosc. Radiat. Transfer 47, 35-42 (1992).
[CrossRef]

D. M. O'Brien, “Accelerated quasi Monte Carlo integration of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 48, 41-59 (1992).
[CrossRef]

1991 (1)

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

R. D. M. Garcia and C. E. Siewert, “A generalized spherical harmonics solution for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 36, 401-423 (1986).
[CrossRef]

1985 (1)

1984 (1)

1954 (1)

C. Cox and W. Munk, “Statistics of sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

1941 (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Alfano, R. R.

J. H. Ali, W. B. Wang, P. P. Ho, and R. R. Alfano, “Detection of corrosion beneath a paint layer by use of spectral polarization optical imaging,” Opt. Lett. 25, 1303-1305 (2000).
[CrossRef]

S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150-155 (1997).
[CrossRef] [PubMed]

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7, 17-22 (1996).
[CrossRef]

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Ali, J. H.

Ambs, Pierre

Alberic Jaulin, Laurent Bigue, and Pierre Ambs, “High-speed degree-of-polarization imaging with a ferroelectric liquid-crystal modulator,” Opt. Eng. 47, 033201 (2008).
[CrossRef]

Bigue, Laurent

Alberic Jaulin, Laurent Bigue, and Pierre Ambs, “High-speed degree-of-polarization imaging with a ferroelectric liquid-crystal modulator,” Opt. Eng. 47, 033201 (2008).
[CrossRef]

Boss, E.

Cameron, B. D.

Carswell, A. I.

Chaikovskaya, L. I.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Collet, C.

Cote, G. L.

Cox, C.

C. Cox and W. Munk, “Statistics of sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

De Martino, A.

Demos, S. G.

Drévillon, B.

Evans, K. F.

K. F. Evans, “The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429-446 (1998).
[CrossRef]

Fry, E. S.

Gan, X.

Garcia, R. D. M.

R. D. M. Garcia and C. E. Siewert, “A generalized spherical harmonics solution for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 36, 401-423 (1986).
[CrossRef]

Gayen, S. K.

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7, 17-22 (1996).
[CrossRef]

Gray, D. J.

Greenstein, J. L.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Gu, M.

Henyey, L. C.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Ho,

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Ho, P. P.

Hostetler, C. A.

D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Proceedings of laser radar techniques for atmospheric sensing,” Proc. SPIE 5575, 8-15 (2004).
[CrossRef]

Hunt, W. H.

D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Proceedings of laser radar techniques for atmospheric sensing,” Proc. SPIE 5575, 8-15 (2004).
[CrossRef]

Jaulin, Alberic

Alberic Jaulin, Laurent Bigue, and Pierre Ambs, “High-speed degree-of-polarization imaging with a ferroelectric liquid-crystal modulator,” Opt. Eng. 47, 033201 (2008).
[CrossRef]

Jayaweera, K.

Katsev, I. L.

Kattawar, G. W.

P. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method,” Appl. Opt. 47, 1037-1047 (2008).
[CrossRef] [PubMed]

G. W. Kattawar and D. J. Gray, “Mueller matrix imaging of targets in turbid media: effect of the volume scattering function,” Appl. Opt. 42, 7225-7230 (2003).
[CrossRef]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40, 400-412 (2001).
[CrossRef]

G. W. Kattawar and M. J. Raković, “Virtues of Mueller matrix imaging for underwater target detection,” Appl. Opt. 38, 6431-6438 (1999).
[CrossRef]

M. J. Raković, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399-3408 (1999).
[CrossRef]

M. J. Raković and G. W. Kattawar, “Theoretical analysis of polarization patterns from incoherent backscattering of light,” Appl. Opt. 37, 3333-3338 (1998).
[CrossRef]

B. D. Cameron, M. J. Raković, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cote, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485-487 (1998).
[CrossRef]

Kummerow, C.

L. Roberti and C. Kummerow, “Monte Carlo calculations of polarized microwave radiation emerging from cloud structures,” J. Geophys. Res. 104, 2093-2104 (1999).
[CrossRef]

Laude-Boulesteix, B.

Liu, G.

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Mehrubeoglu, M.

Mobley, C. D.

Munk, W.

C. Cox and W. Munk, “Statistics of sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

O'Brien, D. M.

D. M. O'Brien, “Accelerated quasi Monte Carlo integration of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 48, 41-59 (1992).
[CrossRef]

Pal, S. R.

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1977).

Polonsky, I. N.

Prikhach, A. S.

Rakovic, M. J.

Rastegar, S.

Roberti, L.

L. Roberti and C. Kummerow, “Monte Carlo calculations of polarized microwave radiation emerging from cloud structures,” J. Geophys. Res. 104, 2093-2104 (1999).
[CrossRef]

L. Roberti, “Monte Carlo radiative transfer in the microwave and in the visible: biasing techniques,” Appl. Opt. 36, 7929-7938 (1997).
[CrossRef]

Schilders, S. P.

Schwartz, L.

Siewert, C. E.

R. D. M. Garcia and C. E. Siewert, “A generalized spherical harmonics solution for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 36, 401-423 (1986).
[CrossRef]

Stamnes, K.

Sundman, L. K.

Takakura, Y.

Tsay, S.-C.

Tynes, H. H.

von Royen, Willebrord Snel

Concise Dictionary of Scientific Biography (Scribner, 1981), p. 643. Willebrord Snel von Royen used only one l in his last name.

Voss, K. J.

Wang, L.

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Wang, L. V.

Wang, W. B.

Weng, F.

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-I. theory,” J. Quant. Spectrosc. Radiat. Transfer 47, 19-33 (1992).
[CrossRef]

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere II. Application,” J. Quant. Spectrosc. Radiat. Transfer 47, 35-42 (1992).
[CrossRef]

Winker, D. M.

D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Proceedings of laser radar techniques for atmospheric sensing,” Proc. SPIE 5575, 8-15 (2004).
[CrossRef]

Wiscombe, W.

Yang, P.

Yao, G.

G. Yao, “Differential optical polarization imaging in turbid media with different embedded objects,” Opt. Commun. 241, 255-261 (2004).
[CrossRef]

Zallat, J.

Zege, E. P.

Zhai, P.

Zhang, G.

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Appl. Opt. (15)

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427-4439 (1984).
[CrossRef] [PubMed]

S. R. Pal and A. I. Carswell, “Polarization anisotropy in lidar multiple scattering from atmospheric clouds,” Appl. Opt. 24, 3464-3471 (1985).
[CrossRef] [PubMed]

K. Stamnes, S.-C. Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502-2509 (1988).
[CrossRef] [PubMed]

E. P. Zege, I. L. Katsev, and I. N. Polonsky, “Multicomponent approach to light propagation in clouds and mists,” Appl. Opt. 32, 2803-2812 (1993).
[CrossRef] [PubMed]

L. Roberti, “Monte Carlo radiative transfer in the microwave and in the visible: biasing techniques,” Appl. Opt. 36, 7929-7938 (1997).
[CrossRef]

S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150-155 (1997).
[CrossRef] [PubMed]

M. J. Raković and G. W. Kattawar, “Theoretical analysis of polarization patterns from incoherent backscattering of light,” Appl. Opt. 37, 3333-3338 (1998).
[CrossRef]

G. W. Kattawar and M. J. Raković, “Virtues of Mueller matrix imaging for underwater target detection,” Appl. Opt. 38, 6431-6438 (1999).
[CrossRef]

M. J. Raković, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399-3408 (1999).
[CrossRef]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40, 400-412 (2001).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035-1050(2002).
[CrossRef] [PubMed]

G. W. Kattawar and D. J. Gray, “Mueller matrix imaging of targets in turbid media: effect of the volume scattering function,” Appl. Opt. 42, 7225-7230 (2003).
[CrossRef]

J. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt. 43, 283-292 (2004).
[CrossRef] [PubMed]

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824-2832 (2004).
[CrossRef] [PubMed]

P. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method,” Appl. Opt. 47, 1037-1047 (2008).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70-83 (1941).
[CrossRef]

J. Atmos. Sci. (1)

K. F. Evans, “The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429-446 (1998).
[CrossRef]

J. Geophys. Res. (1)

L. Roberti and C. Kummerow, “Monte Carlo calculations of polarized microwave radiation emerging from cloud structures,” J. Geophys. Res. 104, 2093-2104 (1999).
[CrossRef]

J. Mar. Res. (1)

C. Cox and W. Munk, “Statistics of sea surface derived from sun glitter,” J. Mar. Res. 13, 198-227 (1954).

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (5)

R. D. M. Garcia and C. E. Siewert, “A generalized spherical harmonics solution for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 36, 401-423 (1986).
[CrossRef]

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-I. theory,” J. Quant. Spectrosc. Radiat. Transfer 47, 19-33 (1992).
[CrossRef]

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere II. Application,” J. Quant. Spectrosc. Radiat. Transfer 47, 35-42 (1992).
[CrossRef]

D. M. O'Brien, “Accelerated quasi Monte Carlo integration of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 48, 41-59 (1992).
[CrossRef]

E. P. Zege and L. I. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19-31 (1996).
[CrossRef]

Opt. Commun. (1)

G. Yao, “Differential optical polarization imaging in turbid media with different embedded objects,” Opt. Commun. 241, 255-261 (2004).
[CrossRef]

Opt. Eng. (1)

Alberic Jaulin, Laurent Bigue, and Pierre Ambs, “High-speed degree-of-polarization imaging with a ferroelectric liquid-crystal modulator,” Opt. Eng. 47, 033201 (2008).
[CrossRef]

Opt. Lett. (2)

Opt. Photonics News (1)

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photonics News 7, 17-22 (1996).
[CrossRef]

Proc. SPIE (1)

D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Proceedings of laser radar techniques for atmospheric sensing,” Proc. SPIE 5575, 8-15 (2004).
[CrossRef]

Science (1)

L. Wang, P. P. Ho, G. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering wall using an ultrafast Kerr gate,” Science 253, 769-771 (1991).
[CrossRef] [PubMed]

Other (4)

T.Gehrels, ed. Planets, Stars and Nebulae (University of Arizona, 1974).

Concise Dictionary of Scientific Biography (Scribner, 1981), p. 643. Willebrord Snel von Royen used only one l in his last name.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, 1977).

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Figures (10)

Fig. 1
Fig. 1

(a) Geometry of the underwater target detection system. (b) Target used in the simulation.

Fig. 2
Fig. 2

Three elements of the MSMM as the functions of the viewing angles. (a)  M 11 , (b) the reduced MSMM element M 22 , and (c) the reduced MSMM element M 44 . The detector is located 1 m above the air–sea interface. The target is located at 2 m below the air–sea interface. The lines of r uwo = 10 1 m are for the target with three annular regions and the lines of r uwo = 10 9 m are for a point target which serve as background references. The three annular regions of the disk are indicated by using vertical lines in the figure.

Fig. 3
Fig. 3

Same as Fig. 2, except that the detector is located just below the air–sea interface.

Fig. 4
Fig. 4

Same as Fig. 2, except that the target is located 4 m below the air–sea interface.

Fig. 5
Fig. 5

Same as Fig. 4, except that the detector is located just below the air–sea interface.

Fig. 6
Fig. 6

Water-leaving Mueller matrix elements for Fig. 2.

Fig. 7
Fig. 7

Water-leaving Mueller matrix elements for Fig. 4.

Fig. 8
Fig. 8

Same as Fig. 2, except that the radius of the active light source is 0.2 m , 0.4 m , 10 m , and infinity, respectively.

Fig. 9
Fig. 9

Effect of asymmetry parameters on the MSMM elements. g = 0.9185 and g = 0.95 are used. r uwo = 10 1 m . The radius of the active light source is 0.4 m . The other system parameters are the same as Fig. 2.

Fig. 10
Fig. 10

Same as Fig. 2, except that the air–sea interface is ruffled by a wind with a speed of 5 m / s . The radius of the active light source is 0.4 m . Also shown for a disk with a Lambertian surface and the same size as the tri-annular disk.

Equations (5)

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M 1 = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) , M 2 = ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) , M 3 = ( 1 0 0 0 0 0.61 0 0 0 0 0.58 0 0 0 0 0.51 ) .
P ˜ ( μ ) = ( 1 μ 2 1 μ 2 + 1 0 0 μ 2 1 μ 2 + 1 1 0 0 0 0 2 μ μ 2 + 1 0 0 0 0 2 μ μ 2 + 1 ) ,
p a ( μ ) = 3 16 π ( μ 2 + 1 ) .
p o ( μ ) = 1 4 π 1 g 2 ( 1 2 g μ + g 2 ) 3 / 2 ,
σ = 0.0351 v wind .

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