Abstract

The universal scatter function for natural water produces beam spread patterns in multiple forward scatter which remain compact in time and angular subtense, even neglecting absorption.

© 1982 Optical Society of America

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References

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  1. H. M. Heggestad, J. Opt. Soc. Am. 61, 1293 (1971).
    [CrossRef]
  2. S. Karp, IEEE Trans. Commun. COM-24, 66 (1976).
    [CrossRef]
  3. L. B. Stotts, J. Opt. Soc. Am. 67, 815, 1695 (1977).
    [CrossRef]
  4. C. Alcock, S. Hachett, Astrophys. J. 222, 456 (1978).
    [CrossRef]
  5. R. W. Preisendorfer, Sears Found. J. Mar. Res.18, (1959); also reprinted in J. E. Tyler, Ed., Light in the Sea (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).
  6. S. Q. Duntley, J. Opt. Soc. Am. 53, 214 (1963).
    [CrossRef]
  7. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968), Chap. 20.
  8. Ref. 7, Chap. 10.
  9. E. A. Bucher, Appl. Opt. 12, 2391 (1973).
    [CrossRef] [PubMed]
  10. T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” in Light in the Sea, J. E. Tyler, Ed. (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).
  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 8.
  12. V. F. Weisskopf in The Science and Engineering of Nuclear Power, C. Goodman, Ed. (Addison-Wesley, Reading, Mass., 1947), pp. 87–89.

1978

C. Alcock, S. Hachett, Astrophys. J. 222, 456 (1978).
[CrossRef]

1977

L. B. Stotts, J. Opt. Soc. Am. 67, 815, 1695 (1977).
[CrossRef]

1976

S. Karp, IEEE Trans. Commun. COM-24, 66 (1976).
[CrossRef]

1973

1971

1963

Alcock, C.

C. Alcock, S. Hachett, Astrophys. J. 222, 456 (1978).
[CrossRef]

Bucher, E. A.

Duntley, S. Q.

Hachett, S.

C. Alcock, S. Hachett, Astrophys. J. 222, 456 (1978).
[CrossRef]

Heggestad, H. M.

Jerlov, N. G.

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968), Chap. 20.

Karp, S.

S. Karp, IEEE Trans. Commun. COM-24, 66 (1976).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” in Light in the Sea, J. E. Tyler, Ed. (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).

Preisendorfer, R. W.

R. W. Preisendorfer, Sears Found. J. Mar. Res.18, (1959); also reprinted in J. E. Tyler, Ed., Light in the Sea (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).

Stotts, L. B.

L. B. Stotts, J. Opt. Soc. Am. 67, 815, 1695 (1977).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 8.

Weisskopf, V. F.

V. F. Weisskopf in The Science and Engineering of Nuclear Power, C. Goodman, Ed. (Addison-Wesley, Reading, Mass., 1947), pp. 87–89.

Appl. Opt.

Astrophys. J.

C. Alcock, S. Hachett, Astrophys. J. 222, 456 (1978).
[CrossRef]

IEEE Trans. Commun.

S. Karp, IEEE Trans. Commun. COM-24, 66 (1976).
[CrossRef]

J. Opt. Soc. Am.

Other

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968), Chap. 20.

Ref. 7, Chap. 10.

R. W. Preisendorfer, Sears Found. J. Mar. Res.18, (1959); also reprinted in J. E. Tyler, Ed., Light in the Sea (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” in Light in the Sea, J. E. Tyler, Ed. (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1977).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 8.

V. F. Weisskopf in The Science and Engineering of Nuclear Power, C. Goodman, Ed. (Addison-Wesley, Reading, Mass., 1947), pp. 87–89.

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Figures (18)

Fig. 1
Fig. 1

Universal scattering law in water.

Fig. 2
Fig. 2

Universal laws of weakening of MFS.

Fig. 3
Fig. 3

Multiple forward scatter mode geometry with planar rule.

Fig. 4
Fig. 4

Radius of circle containing fixed fraction of multiple forward scatter photons as function of distance to measurement surface.

Fig. 5
Fig. 5

Universal law of radial spreading, spheres.

Fig. 6
Fig. 6

Cumulative intensity distributions at fixed depth.

Fig. 7
Fig. 7

Time dispersion at 50-m radius spherical surface for fixed fractions of MFS photons.

Fig. 8
Fig. 8

Time dispersion at 100-m radius spherical surface.

Fig. 9
Fig. 9

Time dispersion at 200-m radius spherical surface.

Fig. 10
Fig. 10

Time dispersion at 50-m depth plane for fixed MFS photon fractions.

Fig. 11
Fig. 11

Time dispersion at 100-m depth.

Fig. 12
Fig. 12

Time dispersion at 200-m depth.

Fig. 13
Fig. 13

Time within which 90% of MFS photons arrive as a function of distance to measurement surface.

Fig. 14
Fig. 14

Angular dispersion of photons observed near the boundaries of successive spatial quantities of MFS photons arrives at an observation surface.

Fig. 15
Fig. 15

Modified two-stream picture of radiative transfer.

Fig. 16
Fig. 16

Arrival time dispersion as a function of radius from original beam path.

Fig. 17
Fig. 17

Time compactness at various radii at fixed spherical surfaces.

Fig. 18
Fig. 18

Dispersion in time at 100 m (plane).

Equations (11)

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g ( t ) = f ( t ) exp ( - a c w t ) ,
I = I 0 exp [ - ( a + b ) x ] ,
p ( θ ) = h ( sinh 2 θ 0 / 2 + sin 2 θ / 2 ) 1 + m ,
1 2 0 π p ( θ ) sin ( θ ) d θ = 1 .
L s c a = 1 / b .
L d = L s c a / ( 1 - cos θ ¯ ) ,
cos θ ¯ = ½ 0 π p ( θ ) cos θ sin θ d θ .
s 0 · s j > 0 for j = 1 , 2 , , n .
s j · r j > 0             j > 0.
J = f ( w , t , ω , medium , boundaries , etc . ) .
T 90 ~ ( ρ % ) 1.55

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