Abstract

In situ experimental data are presented on the off-axis radiance produced by a pulsed underwater laser operating at a wavelength of 520 nm. Path lengths in homogeneous seawater range up to 50 m with separations of up to more than 6 m from the path. Absorption and scattering lengths in the water are about 6 and 4 m, respectively. These results are compared with the predictions provided by popular models derived from radiative transfer theory. Limitations are clearly shown on the accuracy of the radiance predicted by these models. The inability of the models in the small-angle approximation to predict the magnitude and shape of the radiance distributions are quantitatively shown for several experimental conditions and configurations.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Dell-Imagine, “A study of multiple, scattering of optical radiation with applications to laser communications,” in Advances in Communication Systems, V. A. Balakrishnar, ed. (Academic, New York, 1966), Vol. II, p. 1.
  2. H. M. Heggestad, “Multiple scattering model for light transmission through optically thick clouds,” J. Opt. Soc. Am. 61, 1293–1300 (1971).
    [CrossRef]
  3. D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).
  4. D. Arnush, “Underwater light-beam propagation in the small-angle-scattering approximation,” J. Opt. Soc. Am. 62, 1109–1111 (1972).
    [CrossRef]
  5. R. L. Fante, “Propagation of electromagnetic wavs through turbulent plasma using transport, theory,” IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).
    [CrossRef]
  6. A. Ishimaru and S. T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,” Radio Sci. 10, 637–644 (1975).
    [CrossRef]
  7. S. T. Hong and A. Ishimaru, “Two frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,” Radio Sci. 11(6), 551–559 (1976).
    [CrossRef]
  8. L. B. Stotts, “The radiance produced by laser radiation traversing a particulate multiple-scattering medium,” J. Opt. Soc. Am. 67, 815–819 (1977).
    [CrossRef]
  9. A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
    [CrossRef]
  10. D. L. Fried, “Propagation of the mutual coherence function for an infinite plane wave through a turbid medium,” Opt. Lett. 1, 104–106 (1977).
    [CrossRef] [PubMed]
  11. R. F. Lutomirski, “Atmospheric degradation of electro-optical system performance,” Appl. Opt. 17, 3915–3921 (1978).
    [CrossRef] [PubMed]
  12. G. N. Plass and G. W. Kattawar, “Monte Carlo calculations of light scattering from clouds,” Appl. Opt. 7, 415–419 (1968).
    [CrossRef] [PubMed]
  13. E. A. Bucher, “Computer simulation of light pulse propagation for communication through thick clouds,” Appl. Opt. 12, 2391–2400 (1973).
    [CrossRef] [PubMed]
  14. E. A. Bucher, “Propagation models for optical ommunications through fog and clouds,” Proc. Nat. Electron. Conf. 29, 180–185 (1974).
  15. E. A. Bucher and R. M. Lerner, “Experiments on light pulse communication through atmospheric clouds,” Appl. Opt. 12, 2401–2414 (1973).
    [CrossRef] [PubMed]
  16. R. Fante, “Electromagnetic Beam Propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1445 (1980).
    [CrossRef]
  17. W. H. Paik, M. Tebyani, D. J. Epstein, R. S. Kennedy, and J. H. Shapiro, “Propagation experiments in low-visibility atmospheres,” Appl. Opt. 17, 899–905 (1978).
    [CrossRef] [PubMed]
  18. J. S. Ryan and A. I. Carswell, “Laser beam broadening and depolarization in dense fogs,” J. Opt. Soc. Am. 68, 900–908 (1978).
    [CrossRef]
  19. G. C. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, and R. A. Krautwald, “B/G pulse propagation through maritime fogs,” Appl. Opt. 18, 429–448 (1979).
    [CrossRef] [PubMed]
  20. S. Q. Duntley, “Underwater lighting by submerged lasers,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1971), Ref. 71-1.
  21. R. G. Discroll, J. N. Martin, and S. Karp, “OPSATCOM Field Measurements,” Technical Document 490, Naval Electronics Laboratory Center, 1June1976.
  22. R. W. Austin, “Ocean Optical Properties—520 nanometers Santa Catalina Island, Lat: 33° 27.2′N, Long: 118° 28.0′W,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976). Technical Memorandum ML-76-005t Rev.23June1976.
  23. R. W. Austin and T. J. Petzold, “An instrument for the measurement of spectral attenuation coefficient and narrow angle volume scattering function of ocean waters,” Proc. SPIE 64, 50 (1975).
    [CrossRef]
  24. N. G. Jerlov, Marine Optics (American Elsevier, New York, 1976).
  25. S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1960) (reprinted by Dover, New York, 1960).
  26. V. Kourganoff, Basic Methods in Transfer Problems (Dover, New York, 1963).
  27. R. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965).
  28. G. R. Allgaier, “Spreading of light beams passing through substantial air-water paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 64, 23 (1975).
  29. L. B. Stotts, “Limitations of approximate fourier techniques in solving radiative-transfer problems,” J. Opt. Soc. Am. 69, 1719 (1979).
    [CrossRef]
  30. W. G. Tam and A. Zardecki, “Laser beam propagation in particulate media,” J. Opt. Soc. Am. 69, 68 (1977).

1980 (1)

R. Fante, “Electromagnetic Beam Propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1445 (1980).
[CrossRef]

1979 (2)

1978 (3)

1977 (4)

1976 (1)

S. T. Hong and A. Ishimaru, “Two frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,” Radio Sci. 11(6), 551–559 (1976).
[CrossRef]

1975 (3)

R. W. Austin and T. J. Petzold, “An instrument for the measurement of spectral attenuation coefficient and narrow angle volume scattering function of ocean waters,” Proc. SPIE 64, 50 (1975).
[CrossRef]

G. R. Allgaier, “Spreading of light beams passing through substantial air-water paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 64, 23 (1975).

A. Ishimaru and S. T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,” Radio Sci. 10, 637–644 (1975).
[CrossRef]

1974 (1)

E. A. Bucher, “Propagation models for optical ommunications through fog and clouds,” Proc. Nat. Electron. Conf. 29, 180–185 (1974).

1973 (3)

1972 (1)

1971 (1)

1968 (1)

Allgaier, G. R.

G. R. Allgaier, “Spreading of light beams passing through substantial air-water paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 64, 23 (1975).

Arnush, D.

Austin, R. W.

R. W. Austin and T. J. Petzold, “An instrument for the measurement of spectral attenuation coefficient and narrow angle volume scattering function of ocean waters,” Proc. SPIE 64, 50 (1975).
[CrossRef]

R. W. Austin, “Ocean Optical Properties—520 nanometers Santa Catalina Island, Lat: 33° 27.2′N, Long: 118° 28.0′W,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976). Technical Memorandum ML-76-005t Rev.23June1976.

Bravo-Zhivotovskiy, D. M.

D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).

Bucher, E. A.

Carswell, A. I.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1960) (reprinted by Dover, New York, 1960).

Dell-Imagine, R. A.

R. A. Dell-Imagine, “A study of multiple, scattering of optical radiation with applications to laser communications,” in Advances in Communication Systems, V. A. Balakrishnar, ed. (Academic, New York, 1966), Vol. II, p. 1.

Discroll, R. G.

R. G. Discroll, J. N. Martin, and S. Karp, “OPSATCOM Field Measurements,” Technical Document 490, Naval Electronics Laboratory Center, 1June1976.

Dolin, L. S.

D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).

Duntley, S. Q.

S. Q. Duntley, “Underwater lighting by submerged lasers,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1971), Ref. 71-1.

Epstein, D. J.

Fante, R.

R. Fante, “Electromagnetic Beam Propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1445 (1980).
[CrossRef]

Fante, R. L.

R. L. Fante, “Propagation of electromagnetic wavs through turbulent plasma using transport, theory,” IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).
[CrossRef]

Fried, D. L.

Geller, M.

Heggestad, H. M.

Hong, S. T.

S. T. Hong and A. Ishimaru, “Two frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,” Radio Sci. 11(6), 551–559 (1976).
[CrossRef]

A. Ishimaru and S. T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,” Radio Sci. 10, 637–644 (1975).
[CrossRef]

Ishimaru, A.

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
[CrossRef]

S. T. Hong and A. Ishimaru, “Two frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,” Radio Sci. 11(6), 551–559 (1976).
[CrossRef]

A. Ishimaru and S. T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,” Radio Sci. 10, 637–644 (1975).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics (American Elsevier, New York, 1976).

Karp, S.

R. G. Discroll, J. N. Martin, and S. Karp, “OPSATCOM Field Measurements,” Technical Document 490, Naval Electronics Laboratory Center, 1June1976.

Kattawar, G. W.

Kennedy, R. S.

Kourganoff, V.

V. Kourganoff, Basic Methods in Transfer Problems (Dover, New York, 1963).

Krautwald, R. A.

Lerner, R. M.

Luchmin, A. G.

D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).

Lutomirski, R. F.

Martin, J. N.

R. G. Discroll, J. N. Martin, and S. Karp, “OPSATCOM Field Measurements,” Technical Document 490, Naval Electronics Laboratory Center, 1June1976.

Mooradian, G. C.

Paik, W. H.

Petzold, T. J.

R. W. Austin and T. J. Petzold, “An instrument for the measurement of spectral attenuation coefficient and narrow angle volume scattering function of ocean waters,” Proc. SPIE 64, 50 (1975).
[CrossRef]

Plass, G. N.

Preisendorfer, R.

R. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965).

Ryan, J. S.

Sarelyev, V. A.

D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).

Shapiro, J. H.

Stephens, D. H.

Stotts, L. B.

Tam, W. G.

Tebyani, M.

Zardecki, A.

Appl. Opt. (6)

IEEE Trans. Antennas Propag. (1)

R. L. Fante, “Propagation of electromagnetic wavs through turbulent plasma using transport, theory,” IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).
[CrossRef]

J. Opt. Soc. Am. (6)

Opt. Lett. (1)

Proc. IEEE (2)

R. Fante, “Electromagnetic Beam Propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1445 (1980).
[CrossRef]

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
[CrossRef]

Proc. Nat. Electron. Conf. (1)

E. A. Bucher, “Propagation models for optical ommunications through fog and clouds,” Proc. Nat. Electron. Conf. 29, 180–185 (1974).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. R. Allgaier, “Spreading of light beams passing through substantial air-water paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 64, 23 (1975).

Proc. SPIE (1)

R. W. Austin and T. J. Petzold, “An instrument for the measurement of spectral attenuation coefficient and narrow angle volume scattering function of ocean waters,” Proc. SPIE 64, 50 (1975).
[CrossRef]

Radio Sci. (2)

A. Ishimaru and S. T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,” Radio Sci. 10, 637–644 (1975).
[CrossRef]

S. T. Hong and A. Ishimaru, “Two frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,” Radio Sci. 11(6), 551–559 (1976).
[CrossRef]

Other (9)

R. A. Dell-Imagine, “A study of multiple, scattering of optical radiation with applications to laser communications,” in Advances in Communication Systems, V. A. Balakrishnar, ed. (Academic, New York, 1966), Vol. II, p. 1.

D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchmin, and V. A. Sarelyev, “Structure of a narrow light beam in sea water,” Atmos. Oceanic Phys.5, (2), 160–167 (1969) (translated by P. A. Kaehn).

N. G. Jerlov, Marine Optics (American Elsevier, New York, 1976).

S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1960) (reprinted by Dover, New York, 1960).

V. Kourganoff, Basic Methods in Transfer Problems (Dover, New York, 1963).

R. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965).

S. Q. Duntley, “Underwater lighting by submerged lasers,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1971), Ref. 71-1.

R. G. Discroll, J. N. Martin, and S. Karp, “OPSATCOM Field Measurements,” Technical Document 490, Naval Electronics Laboratory Center, 1June1976.

R. W. Austin, “Ocean Optical Properties—520 nanometers Santa Catalina Island, Lat: 33° 27.2′N, Long: 118° 28.0′W,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976). Technical Memorandum ML-76-005t Rev.23June1976.

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 (15)

Fig. 1
Fig. 1

Experimental configuration.

Fig. 2
Fig. 2

Positioning carriage subassembly.

Fig. 3
Fig. 3

Submerged instrument platform.

Fig. 4
Fig. 4

Underwater radiance receiver.

Fig. 5
Fig. 5

Ocean optical properties—520 nm, July 23, 1975, 1024 PDT.

Fig. 6
Fig. 6

Volume scattering function 520, July 23, 1975, 2106 PDT.

Fig. 7
Fig. 7

Source depth, 22.9 m.

Fig. 8
Fig. 8

Source depth, 38.1 m.

Fig. 9
Fig. 9

Source depth, 45.7 m.

Fig. 10
Fig. 10

Spatial and angular coordinate system.

Fig. 11
Fig. 11

Comparison of Eq. (13) with measured data for r = 2.48 m, π and z = 24 m.

Fig. 12
Fig. 12

Comparison of Eq. (13) with measured data for r = 6.9 m, π and z = 25 m.

Fig. 13
Fig. 13

Comparison of theory and experiment at r = 3.9 m, 0 and z = 42.8 m.

Fig. 14
Fig. 14

Comparison of theory and experiment at r = 3.5 m, π and z = 47.6m.

Fig. 15
Fig. 15

Comparison of theory at r = 6.47 m, π and z = 48.2 m.

Tables (4)

Tables Icon

Table 1 Laser Specifications

Tables Icon

Table 2 Underwater Radiance Receiver

Tables Icon

Table 3 Summary of Daylight Measurements—July 23, 1975

Tables Icon

Table 4 Location of Apparent Source—(zy)(m)

Equations (35)

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

a = c - b .
a ¯ = 0.166 , std dev = 0.008 ; 5 % , b ¯ = 0.269 , std dev = 0.036 ; 13 % .
a ¯ = 0.162 , std dev = 0.012 ; 7 % , b ¯ = 0.251 , std dev = 0.050 ; 20 % .
a ¯ = 0.1428 m - 1 , b ¯ = 0.1892 m - 1 .
4 × 5 × 10 3 π ( 0.0226 × 46.9 ) 2 = 5.67 × 10 3 W M - 2 = 0.567 W cm - 2 .
3.02 × 10 - 6 0.567 = exp ( - 12.1 ) .
c = a + b = 12.1 / 46.9 = 0.259 m - 1
( μ d d τ + 1 ) N ( τ , r , μ , ϕ , t ) = N 0 ( τ , r , μ , ϕ , t ) - ω 0 × - 1 + 1 0 2 π p ( θ , ϕ , θ , ϕ ) N ( τ , r , μ , ϕ , t ) d μ d ϕ ,
( z + γ · r + c ) N ( z , r , γ ) c N 0 ( z , r , γ ) + ω 0 c × - + p ( γ - γ ) N ( z , r , γ ) d 2 γ
p ( θ ) = β 2 π θ exp ( - β θ ) ,
N ( z , r , γ ) = N 0 exp { - σ 2 γ 2 + Δ γ · r - r 2 / r 1 2 } ,
N 0 = P T exp [ - ( 1 - ω 0 ) τ ] π 2 ( γ T 2 + 2 ω 0 τ / γ 2 ) r 1 2 ,
σ 2 = 1 ( γ T 2 + 2 ω 0 τ / γ 2 ) + z 2 ( γ T 2 + ω 0 τ / γ 2 ) 2 r 1 2 ( γ T 2 + 2 ω 0 τ / γ 2 ) 2 ,
Δ = 2 z ( γ 0 2 + ω 0 τ / γ 2 ) r 1 2 ( γ T 2 + 2 ω 0 τ / γ 2 ) ,
r 1 2 = r 0 2 + z 2 γ T 2 + 2 ω 0 τ 3 γ 2 z 2 - ( γ T 2 + ω 0 τ / γ 2 ) 2 ( γ T 2 + 2 ω 0 τ / γ 2 ) z 2 ,
N ( z , r , γ ) = N 0 exp ( - σ 2 γ 2 + Δ γ · r - r 2 / r 1 2 )
N 0 = P T exp - ( 1 - ω 0 ) τ , π ( ω 0 τ γ 0 2 ) ( r 0 2 + 1 12 ω 0 τ z 2 γ 0 2 ) ,
σ 2 = 1 ω 0 τ γ 0 2 + z 2 4 ( r 0 2 + 1 12 ω 0 τ z 2 γ 0 2 ) ,
Δ = z ( r 0 2 + 1 12 ω 0 τ z 2 γ 0 2 ) ,
r 1 2 = r 0 2 + 1 12 ω 0 τ z 2 γ 0 2 ,
N z + γ · N r - ω 0 c γ 0 2 4 2 N + ( 1 - ω 0 ) c N c N 0 ,
N 0 ( τ , r , γ ) = δ ( τ ) exp ( - r 2 / r 0 2 - γ 2 / γ T 2 ) π 2 r 0 2 γ T 2 ,
N ( z , r , γ ) = N 0 exp ( - σ 2 γ 2 + Δ γ · r - r 2 / r 1 2 ) ,
N 0 = P T exp { - ( 1 - ω 0 ) τ } π 2 ( γ T 2 + ω 0 τ γ 0 2 ) r 1 2 ,
r 1 2 = r 0 2 + ω 0 τ γ 0 2 z 2 3 - ω 0 2 τ 2 γ 0 4 z 2 4 ( γ T 2 + ω 0 τ γ 0 2 ) ,
Δ = ω 0 τ γ 0 2 z r 1 2 ( γ T 2 + ω 0 τ γ 0 2 ) ,
σ 2 = 1 ( γ T 2 + ω 0 τ γ 0 2 ) + ω 0 2 τ 2 γ 0 4 z 4 4 ( γ T 2 + ω 0 τ γ 0 2 ) 2 r 1 2 ,
N ( z , r , γ ) = N 0 exp ( - σ 2 γ 2 + Δ γ · r - r 2 / r 1 2 ) ,
N 0 = 12 P T exp ( - ( 1 - ω 0 ) τ ) π 2 ( ω 0 τ γ 0 2 ) 2 z 2 ,
σ 2 = 1 ω 0 τ γ 0 2 + 3 ω 0 τ γ 0 2 = 4 ω 0 τ γ 0 2 ,
Δ = 12 ω 0 τ γ 0 2 z ,
r 1 2 = ω 0 τ γ 0 2 z 2 / 12.
γ 0 2 = 0 2 π β 0 exp { - β θ } 2 π θ d 2 θ = 2 β 2 .
γ 0 2 = ( 0.1414 ) 2 rad 2 ,
a = 0.1428 m - 1 , b = 0.1892 m - 1 .