Abstract

Small-angle (≲10−3 rad) scattering of light by ocean water is quantitatively analyzed. The two mechanisms that give rise to such scatterings are suspended biological particles having an index of refraction close to that of water and refractive effects due to large-scale (compared to the laser beam diameter) index of refraction variations. Results of recent experiments performed at the Stanford Research Institute are compared with the present analysis, and reasonable agreement is obtained. Also, the modulation transfer function (MTF) for the scattering mechanisms is derived. It is found that for values of the transverse distances ρ less than the size of the large-scale index of refraction fluctuations but larger than the size of the suspended biological particles, the MTF due to the two mechanisms has a different functional dependence on transverse distance. Thus, an experimental determination of the dependence of the MTF on ρ will be useful in determining if a dominant scattering mechanism is at play. Also, we conclude that for long propagation paths (≳10 m), suspended particles can degrade the transverse coherence properties of the laser beam much more than do large-scale refractive index variations.

© 1971 Optical Society of America

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References

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  1. S. Q. Duntley, J. Opt. Soc. Amer. 43, 214 (1963).
  2. R. Honey, G. Sorenson, paper presented at the AGARDNATO Conference on Electromagnetic Properties of the Sea, CNRS, Paris, June 1970.
  3. The region near 0.5 μ in the electromagnetic spectrum is the only place where water is a relatively poor absorber. In the ultraviolet, water absorbs strongly due to the excitations of its electronic levels, while in the infrared and far infrared strong absorption takes place in the broad continuum of its vibrational and rotational states. In the microwave region of the spectrum, seawater will absorb strongly since ionic conductivity is important there. It is extremely unlikely that any gaps other than those in the visible region exist (except for long radio waves).
  4. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  5. L. Lieberman, J. Acoust. Soc. Amer. 23, 563 (1951).
    [CrossRef]

1963 (1)

S. Q. Duntley, J. Opt. Soc. Amer. 43, 214 (1963).

1951 (1)

L. Lieberman, J. Acoust. Soc. Amer. 23, 563 (1951).
[CrossRef]

Duntley, S. Q.

S. Q. Duntley, J. Opt. Soc. Amer. 43, 214 (1963).

Honey, R.

R. Honey, G. Sorenson, paper presented at the AGARDNATO Conference on Electromagnetic Properties of the Sea, CNRS, Paris, June 1970.

Lieberman, L.

L. Lieberman, J. Acoust. Soc. Amer. 23, 563 (1951).
[CrossRef]

Sorenson, G.

R. Honey, G. Sorenson, paper presented at the AGARDNATO Conference on Electromagnetic Properties of the Sea, CNRS, Paris, June 1970.

Tatarskii, V. I.

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

J. Acoust. Soc. Amer. (1)

L. Lieberman, J. Acoust. Soc. Amer. 23, 563 (1951).
[CrossRef]

J. Opt. Soc. Amer. (1)

S. Q. Duntley, J. Opt. Soc. Amer. 43, 214 (1963).

Other (3)

R. Honey, G. Sorenson, paper presented at the AGARDNATO Conference on Electromagnetic Properties of the Sea, CNRS, Paris, June 1970.

The region near 0.5 μ in the electromagnetic spectrum is the only place where water is a relatively poor absorber. In the ultraviolet, water absorbs strongly due to the excitations of its electronic levels, while in the infrared and far infrared strong absorption takes place in the broad continuum of its vibrational and rotational states. In the microwave region of the spectrum, seawater will absorb strongly since ionic conductivity is important there. It is extremely unlikely that any gaps other than those in the visible region exist (except for long radio waves).

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

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Figures (1)

Fig. 1
Fig. 1

Modulation transfer function due to large-scale (a = 50 cm, Δn2 = 10−8) index of refraction fluctuations (solid curve) and due to suspended particles (L1 = 5m) (dashed curve). The value of Δn2 used here is characteristic of rather strong turbulence conditions.

Equations (30)

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P ( L ) = P 0 e - α L ,
p = c exp [ - ( k y 2 / 2 k y 2 ¯ ) ] exp [ - ( k z 2 / 2 k z 2 ¯ ) ] ,
k y 2 ¯ = N i ( k y 2 ¯ ) s i ,
N i = L / L i ,
θ 2 ¯ k y 2 ¯ + k z 2 ¯ / k 2 ,
p 1 ( θ , φ ) = d σ 1 d Ω · 1 ( d σ 1 d Ω ) d Ω
L i = σ 1 - 1 .
n ( r ) = n 0 { 1 + [ f δ n ( r ) / n 0 ] }
δ n ( r ) ¯ = 0 , δ n ( r ) δ n ( r + R ) ¯ = μ 2 B ( R ) ,
d σ 1 / d Ω = 2 π k 4 Φ n [ 2 k sin ( θ / 2 ) ] ,
Φ n ( K ) = f 2 μ 2 n 0 2 d 3 R ( 2 π ) 3 B ( R ) e i K · R .
d σ 0 / d Ω = ( μ 2 f 2 D 3 k 4 / n 0 2 8 π 3 / 2 ) exp [ - ( D 2 k 2 θ 2 / 4 ) ] ,
θ 1 2 ¯ = 4 / ( K D ) 2 .
L 1 = σ 1 - 1 = 2 n 0 2 / π 1 2 μ 2 f 2 k 2 D .
θ 2 ¯ = ( L / L 1 ) θ 1 2 ¯ = ( 2 π 1 2 μ 2 f 2 / n 0 2 D ) L .
( Δ θ ) 2 ¯ = ( L / a ) ( Δ n ) 2 ¯ .
Δ n = ( Δ p ρ ) ( n 2 - 1 2 n ) ( n 2 + 2 3 ) ,
( Δ ρ / ρ ) T = - α Δ T ,
Δ n 2 ¯ = ( n 2 - 1 2 n ) 2 ( n 2 + 2 3 ) 2 [ α 2 Δ T 2 ¯ + Δ ( ρ S ) 2 ¯ ρ 2 ] .
Δ n 2 ¯ 0.6 × 10 - 8 Δ T 2 ¯ .
M ( ρ ) U ( r 1 ) U * ( r 2 ) ¯ ,
M ( ρ ) = U 0 2 exp [ - ( 2 L / L 1 ) ( 1 - e - ρ 2 / D 2 ) , ]
U 0 2 exp [ - ( 2 L ρ 2 / L 1 D 2 ) ] for ρ D
U 0 2 exp [ - ( 2 L / L 1 ) ] for ρ D ,
U ( r ) = U 0 e i k . r = U 0 exp [ i ( k x x + k y y + k z z ) ] ,
M ( ρ ) = U 0 2 exp { i [ k y ( y 1 - y 2 ) + k z ( z 1 - z 2 ) ] } ¯ = U 0 2 [ e i k y ( y 1 - y 2 ) ¯ ] [ e i k z ( z 1 - z 2 ) ¯ ]
M ( ρ ) = U 0 2 e - 1 2 ( y 1 - y 2 ) 2 k y 2 ¯ e - 1 2 ( z 1 - z 2 ) 2 k z 2 ¯ .
M ( ρ ) = U 0 2 e - ( ρ 2 k 2 θ 2 ¯ / 4 ) ,
M ( ρ ) = U 0 2 e - ( ρ 2 k 2 Δ n 2 ¯ L / 4 a ) ,
Δ x min L / k ρ max .

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