Abstract

Light in the sea may be produced by the sun or stars, by chemical or biological processes, or by man-made sources. Serving as the primary source of energy for the oceans and supporting their ecology, light also enables the native inhabitants of the water world, as well as humans and their devices, to see. In this paper, new data drawn from investigations spanning nearly two decades are used to illustrate an integrated account of the optical nature of ocean water, the distribution of flux diverging from localized underwater light sources, the propagation of highly collimated beams of light, the penetration of daylight into the sea, and the utilization of solar energy for many purposes including heating, photosynthesis, vision, and photography.

© 1963 Optical Society of America

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References

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  1. See E. F. DuPré and L. H. Dawson, “Transmission of Light in Water: An Annotated Bibliography,” U. S. Naval Research Laboratory Bibliography No. 20, April, 1961 for abstracts of 650 publications by over 400 authors in more than 150 Swiss, German, French, Italian, English, and U. S. journals and other sources from 1818 to 1959.
  2. S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Division 16, NDRC (Columbia University Press, 1946), Vol. II, Chap. 5, p. 212.
  3. See J. G. Moore, Phil. Trans. Roy. Soc. (London) A240, 163 (1946–48) for a method of using such data to determine depth and attenuation coefficients of shallow water.
  4. See G. A. Stamm and R. A. Hengel, J. Opt. Soc. Am. 51, 1090 (1961) for data on the spectral irradiance incident on the underside of an aircraft flying above the ocean.
    [Crossref]
  5. J. E. Tyler, Limnology and Oceanography 4, 102 (1959).
    [Crossref]
  6. S. Q. Duntley, Natl. Acad. Sci.—Natl. Research Council Publ. 473, 79 (1956).
  7. L. F. Drummeter and G. L. Knestrick, U. S. Naval Research Laboratory Rept. No. 5642 (1961).
  8. N. G. Jerlov, Kgl. Vetenskap. Vitterh. Handl. F.6, Ser. B, BD8. N:o 11 (1961).
  9. N. G. Jerlov, Reports of the Swedish Deep Sea Expedition of 1947–48 (1951), Vol.  III, p. 49, Table 27.
  10. Multiple thermoclines often form in the upper portion of the sea; the maximum optical attenuation is associated with the maximum vertical temperature gradient and frequently falls on a secondary thermocline. Internal waves shift the scattering layer vertically. See E. C. La Fond, E. G. Barnham, and W. H. Armstrong, U. S. Navy Electronics Laboratory Rept. 1052 (July1961), p. 15. Also see J. Joseph, Deut. Hydrograph. Z., Nr. 5 (1961).
  11. Scattering is also contributed by fine particles, by molecules of water, and by various solutes, but these contributions are usually quite minor and often difficult to detect. Even in very clear, blue ocean water scattering by water molecules produces only 7% of the total scattering coefficient and is dominant only at scattering angles near 90°, where it provides more than 2/3 of the scattered intensity (see reference 8); although the magnitude of this small component of scattering varies inversely as the fourth power of wavelength (λ−4), it is so heavily masked by nonselective scattering due to large particles that total scattering in the sea is virtually independent of wavelength. The prominent blue color of clear ocean water, apart from sky reflection, is due almost entirely to selective absorption by water molecules.
  12. L. H. Dawson and E. O. Hulburt, J. Opt. Soc. Am. 31, 554 (1941).
    [Crossref]
  13. J. E. Tyler, Limnology and Oceanography 6, 451 (1961).
    [Crossref]
  14. H. F. Aughey and F. J. Baum, J. Opt. Soc. Am. 44, 833 (1954).
    [Crossref]
  15. M. V. Koslyaninov, Trudy Inst. Okeanol. Acad. Nauk S.S.S.R. 25, 134 (1957).
  16. W. H. Richardson and R. W. Preisendorfer, Scripps Inst. Oceanog., Ref. 60-43 (1960).
  17. S. Glasstone and M. C. Edlund, Elements of Nuclear Reactor Theory (D. Van Nostrand and Company, Inc., Princeton, New Jersey, 1952), p. 107.
  18. R. W. Preisendorfer (private communication).
  19. S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).
  20. S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).
  21. L. V. Whitney, J. Marine Research 4, 122 (1941).
  22. L. V. Whitney, J. Opt. Soc. Am. 31, 714 (1941).
    [Crossref]
  23. J. E. Tyler, Bull. Scripps Inst. Oceanog. 7, 363 (1960).
  24. R. W. Preisendorfer, J. Marine Research 18, 1 (1959).
  25. N. G. Jerlov and M. Fukuda, Tellus 12, 348 (1960).
    [Crossref]
  26. T. Sasaki, Bull. Japan. Soc. Sci. Fisheries 28, 489 (1962).
    [Crossref]
  27. R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-59, (1958).
  28. R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-60, (1958).
  29. R. W. Austin, Scripps Inst. Oceanog. Ref. 59-9, (1959).
  30. Along any underwater path of sight a remarkable proportion of the objects ordinarily encountered can be seen at limiting ranges between 4 and 5 times the distance 1/[α(z)−K(z,θ,ϕ) cosθ], regardless of their size or the background against which they appear, provided ample daylight prevails [see Eqs. (14) and (15)].
  31. S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
    [Crossref]
  32. S. Q. Duntley, J. Opt. Soc. Am. 37, 994(A) (1947) and U. S. Patent No. 2,661,650.
  33. S. Q. Duntley, Proc. Armed Forces–Natl. Research Council Vision Committee 23, 123 (1949); Proc. Armed Forces–Natl. Research Council Vision Committee 27, 57 (1950); Proc. Armed Forces–Natl. Research Council Vision Committee 28, 60 (1951).
  34. S. Q. Duntley and R. W. Preisendorfer, MIT Rept. N5ori 07864 (1952).
  35. R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-42 (1957).
  36. R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-41, (1957).
  37. S. Q. Duntley, Natl. Acad. Sci./Natl. Research Council Publ. 473, 85 (1956).

1962 (1)

T. Sasaki, Bull. Japan. Soc. Sci. Fisheries 28, 489 (1962).
[Crossref]

1961 (4)

See E. F. DuPré and L. H. Dawson, “Transmission of Light in Water: An Annotated Bibliography,” U. S. Naval Research Laboratory Bibliography No. 20, April, 1961 for abstracts of 650 publications by over 400 authors in more than 150 Swiss, German, French, Italian, English, and U. S. journals and other sources from 1818 to 1959.

See G. A. Stamm and R. A. Hengel, J. Opt. Soc. Am. 51, 1090 (1961) for data on the spectral irradiance incident on the underside of an aircraft flying above the ocean.
[Crossref]

N. G. Jerlov, Kgl. Vetenskap. Vitterh. Handl. F.6, Ser. B, BD8. N:o 11 (1961).

J. E. Tyler, Limnology and Oceanography 6, 451 (1961).
[Crossref]

1960 (3)

W. H. Richardson and R. W. Preisendorfer, Scripps Inst. Oceanog., Ref. 60-43 (1960).

J. E. Tyler, Bull. Scripps Inst. Oceanog. 7, 363 (1960).

N. G. Jerlov and M. Fukuda, Tellus 12, 348 (1960).
[Crossref]

1959 (3)

R. W. Preisendorfer, J. Marine Research 18, 1 (1959).

J. E. Tyler, Limnology and Oceanography 4, 102 (1959).
[Crossref]

R. W. Austin, Scripps Inst. Oceanog. Ref. 59-9, (1959).

1958 (2)

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-59, (1958).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-60, (1958).

1957 (4)

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
[Crossref]

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-42 (1957).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-41, (1957).

M. V. Koslyaninov, Trudy Inst. Okeanol. Acad. Nauk S.S.S.R. 25, 134 (1957).

1956 (2)

S. Q. Duntley, Natl. Acad. Sci.—Natl. Research Council Publ. 473, 79 (1956).

S. Q. Duntley, Natl. Acad. Sci./Natl. Research Council Publ. 473, 85 (1956).

1954 (1)

1952 (1)

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).

1951 (1)

N. G. Jerlov, Reports of the Swedish Deep Sea Expedition of 1947–48 (1951), Vol.  III, p. 49, Table 27.

1949 (1)

S. Q. Duntley, Proc. Armed Forces–Natl. Research Council Vision Committee 23, 123 (1949); Proc. Armed Forces–Natl. Research Council Vision Committee 27, 57 (1950); Proc. Armed Forces–Natl. Research Council Vision Committee 28, 60 (1951).

1947 (1)

S. Q. Duntley, J. Opt. Soc. Am. 37, 994(A) (1947) and U. S. Patent No. 2,661,650.

1941 (3)

Armstrong, W. H.

Multiple thermoclines often form in the upper portion of the sea; the maximum optical attenuation is associated with the maximum vertical temperature gradient and frequently falls on a secondary thermocline. Internal waves shift the scattering layer vertically. See E. C. La Fond, E. G. Barnham, and W. H. Armstrong, U. S. Navy Electronics Laboratory Rept. 1052 (July1961), p. 15. Also see J. Joseph, Deut. Hydrograph. Z., Nr. 5 (1961).

Aughey, H. F.

Austin, R. W.

R. W. Austin, Scripps Inst. Oceanog. Ref. 59-9, (1959).

Barnham, E. G.

Multiple thermoclines often form in the upper portion of the sea; the maximum optical attenuation is associated with the maximum vertical temperature gradient and frequently falls on a secondary thermocline. Internal waves shift the scattering layer vertically. See E. C. La Fond, E. G. Barnham, and W. H. Armstrong, U. S. Navy Electronics Laboratory Rept. 1052 (July1961), p. 15. Also see J. Joseph, Deut. Hydrograph. Z., Nr. 5 (1961).

Baum, F. J.

Boileau, A. R.

Culver, W. H.

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).

Dawson, L. H.

See E. F. DuPré and L. H. Dawson, “Transmission of Light in Water: An Annotated Bibliography,” U. S. Naval Research Laboratory Bibliography No. 20, April, 1961 for abstracts of 650 publications by over 400 authors in more than 150 Swiss, German, French, Italian, English, and U. S. journals and other sources from 1818 to 1959.

L. H. Dawson and E. O. Hulburt, J. Opt. Soc. Am. 31, 554 (1941).
[Crossref]

Drummeter, L. F.

L. F. Drummeter and G. L. Knestrick, U. S. Naval Research Laboratory Rept. No. 5642 (1961).

Duntley, S. Q.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
[Crossref]

S. Q. Duntley, Natl. Acad. Sci./Natl. Research Council Publ. 473, 85 (1956).

S. Q. Duntley, Natl. Acad. Sci.—Natl. Research Council Publ. 473, 79 (1956).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).

S. Q. Duntley, Proc. Armed Forces–Natl. Research Council Vision Committee 23, 123 (1949); Proc. Armed Forces–Natl. Research Council Vision Committee 27, 57 (1950); Proc. Armed Forces–Natl. Research Council Vision Committee 28, 60 (1951).

S. Q. Duntley, J. Opt. Soc. Am. 37, 994(A) (1947) and U. S. Patent No. 2,661,650.

S. Q. Duntley and R. W. Preisendorfer, MIT Rept. N5ori 07864 (1952).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Division 16, NDRC (Columbia University Press, 1946), Vol. II, Chap. 5, p. 212.

DuPré, E. F.

See E. F. DuPré and L. H. Dawson, “Transmission of Light in Water: An Annotated Bibliography,” U. S. Naval Research Laboratory Bibliography No. 20, April, 1961 for abstracts of 650 publications by over 400 authors in more than 150 Swiss, German, French, Italian, English, and U. S. journals and other sources from 1818 to 1959.

Edlund, M. C.

S. Glasstone and M. C. Edlund, Elements of Nuclear Reactor Theory (D. Van Nostrand and Company, Inc., Princeton, New Jersey, 1952), p. 107.

Fukuda, M.

N. G. Jerlov and M. Fukuda, Tellus 12, 348 (1960).
[Crossref]

Glasstone, S.

S. Glasstone and M. C. Edlund, Elements of Nuclear Reactor Theory (D. Van Nostrand and Company, Inc., Princeton, New Jersey, 1952), p. 107.

Hengel, R. A.

Hulburt, E. O.

Jerlov, N. G.

N. G. Jerlov, Kgl. Vetenskap. Vitterh. Handl. F.6, Ser. B, BD8. N:o 11 (1961).

N. G. Jerlov and M. Fukuda, Tellus 12, 348 (1960).
[Crossref]

N. G. Jerlov, Reports of the Swedish Deep Sea Expedition of 1947–48 (1951), Vol.  III, p. 49, Table 27.

Knestrick, G. L.

L. F. Drummeter and G. L. Knestrick, U. S. Naval Research Laboratory Rept. No. 5642 (1961).

Koslyaninov, M. V.

M. V. Koslyaninov, Trudy Inst. Okeanol. Acad. Nauk S.S.S.R. 25, 134 (1957).

La Fond, E. C.

Multiple thermoclines often form in the upper portion of the sea; the maximum optical attenuation is associated with the maximum vertical temperature gradient and frequently falls on a secondary thermocline. Internal waves shift the scattering layer vertically. See E. C. La Fond, E. G. Barnham, and W. H. Armstrong, U. S. Navy Electronics Laboratory Rept. 1052 (July1961), p. 15. Also see J. Joseph, Deut. Hydrograph. Z., Nr. 5 (1961).

Moore, J. G.

See J. G. Moore, Phil. Trans. Roy. Soc. (London) A240, 163 (1946–48) for a method of using such data to determine depth and attenuation coefficients of shallow water.

Preisendorfer, R. W.

W. H. Richardson and R. W. Preisendorfer, Scripps Inst. Oceanog., Ref. 60-43 (1960).

R. W. Preisendorfer, J. Marine Research 18, 1 (1959).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-59, (1958).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-60, (1958).

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
[Crossref]

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-42 (1957).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-41, (1957).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).

R. W. Preisendorfer (private communication).

S. Q. Duntley and R. W. Preisendorfer, MIT Rept. N5ori 07864 (1952).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).

Richardson, W. H.

W. H. Richardson and R. W. Preisendorfer, Scripps Inst. Oceanog., Ref. 60-43 (1960).

Richey, F.

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. 42, 877(A) (1952).

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).

Sasaki, T.

T. Sasaki, Bull. Japan. Soc. Sci. Fisheries 28, 489 (1962).
[Crossref]

Stamm, G. A.

Tyler, J. E.

J. E. Tyler, Limnology and Oceanography 6, 451 (1961).
[Crossref]

J. E. Tyler, Bull. Scripps Inst. Oceanog. 7, 363 (1960).

J. E. Tyler, Limnology and Oceanography 4, 102 (1959).
[Crossref]

Whitney, L. V.

L. V. Whitney, J. Marine Research 4, 122 (1941).

L. V. Whitney, J. Opt. Soc. Am. 31, 714 (1941).
[Crossref]

Bull. Japan. Soc. Sci. Fisheries (1)

T. Sasaki, Bull. Japan. Soc. Sci. Fisheries 28, 489 (1962).
[Crossref]

Bull. Scripps Inst. Oceanog. (1)

J. E. Tyler, Bull. Scripps Inst. Oceanog. 7, 363 (1960).

J. Marine Research (2)

R. W. Preisendorfer, J. Marine Research 18, 1 (1959).

L. V. Whitney, J. Marine Research 4, 122 (1941).

J. Opt. Soc. Am. (7)

Kgl. Vetenskap. Vitterh. Handl. F.6, Ser. B, BD8. N:o 11 (1)

N. G. Jerlov, Kgl. Vetenskap. Vitterh. Handl. F.6, Ser. B, BD8. N:o 11 (1961).

Limnology and Oceanography (2)

J. E. Tyler, Limnology and Oceanography 4, 102 (1959).
[Crossref]

J. E. Tyler, Limnology and Oceanography 6, 451 (1961).
[Crossref]

Natl. Acad. Sci./Natl. Research Council Publ. (1)

S. Q. Duntley, Natl. Acad. Sci./Natl. Research Council Publ. 473, 85 (1956).

Natl. Acad. Sci.—Natl. Research Council Publ. (1)

S. Q. Duntley, Natl. Acad. Sci.—Natl. Research Council Publ. 473, 79 (1956).

Phil. Trans. Roy. Soc. (London) (1)

See J. G. Moore, Phil. Trans. Roy. Soc. (London) A240, 163 (1946–48) for a method of using such data to determine depth and attenuation coefficients of shallow water.

Proc. Armed Forces–Natl. Research Council Vision Committee (1)

S. Q. Duntley, Proc. Armed Forces–Natl. Research Council Vision Committee 23, 123 (1949); Proc. Armed Forces–Natl. Research Council Vision Committee 27, 57 (1950); Proc. Armed Forces–Natl. Research Council Vision Committee 28, 60 (1951).

Reports of the Swedish Deep Sea Expedition of 1947–48 (1)

N. G. Jerlov, Reports of the Swedish Deep Sea Expedition of 1947–48 (1951), Vol.  III, p. 49, Table 27.

Scripps Inst. Oceanog. Ref. (5)

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-42 (1957).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-41, (1957).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-59, (1958).

R. W. Preisendorfer, Scripps Inst. Oceanog. Ref. 58-60, (1958).

R. W. Austin, Scripps Inst. Oceanog. Ref. 59-9, (1959).

Scripps Inst. Oceanog., Ref. (1)

W. H. Richardson and R. W. Preisendorfer, Scripps Inst. Oceanog., Ref. 60-43 (1960).

Tellus (1)

N. G. Jerlov and M. Fukuda, Tellus 12, 348 (1960).
[Crossref]

Trudy Inst. Okeanol. Acad. Nauk S.S.S.R. (1)

M. V. Koslyaninov, Trudy Inst. Okeanol. Acad. Nauk S.S.S.R. 25, 134 (1957).

U. S. Naval Research Laboratory Bibliography No. 20 (1)

See E. F. DuPré and L. H. Dawson, “Transmission of Light in Water: An Annotated Bibliography,” U. S. Naval Research Laboratory Bibliography No. 20, April, 1961 for abstracts of 650 publications by over 400 authors in more than 150 Swiss, German, French, Italian, English, and U. S. journals and other sources from 1818 to 1959.

Other (9)

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Division 16, NDRC (Columbia University Press, 1946), Vol. II, Chap. 5, p. 212.

S. Glasstone and M. C. Edlund, Elements of Nuclear Reactor Theory (D. Van Nostrand and Company, Inc., Princeton, New Jersey, 1952), p. 107.

R. W. Preisendorfer (private communication).

Multiple thermoclines often form in the upper portion of the sea; the maximum optical attenuation is associated with the maximum vertical temperature gradient and frequently falls on a secondary thermocline. Internal waves shift the scattering layer vertically. See E. C. La Fond, E. G. Barnham, and W. H. Armstrong, U. S. Navy Electronics Laboratory Rept. 1052 (July1961), p. 15. Also see J. Joseph, Deut. Hydrograph. Z., Nr. 5 (1961).

Scattering is also contributed by fine particles, by molecules of water, and by various solutes, but these contributions are usually quite minor and often difficult to detect. Even in very clear, blue ocean water scattering by water molecules produces only 7% of the total scattering coefficient and is dominant only at scattering angles near 90°, where it provides more than 2/3 of the scattered intensity (see reference 8); although the magnitude of this small component of scattering varies inversely as the fourth power of wavelength (λ−4), it is so heavily masked by nonselective scattering due to large particles that total scattering in the sea is virtually independent of wavelength. The prominent blue color of clear ocean water, apart from sky reflection, is due almost entirely to selective absorption by water molecules.

L. F. Drummeter and G. L. Knestrick, U. S. Naval Research Laboratory Rept. No. 5642 (1961).

S. Q. Duntley and R. W. Preisendorfer, MIT Rept. N5ori 07864 (1952).

Along any underwater path of sight a remarkable proportion of the objects ordinarily encountered can be seen at limiting ranges between 4 and 5 times the distance 1/[α(z)−K(z,θ,ϕ) cosθ], regardless of their size or the background against which they appear, provided ample daylight prevails [see Eqs. (14) and (15)].

S. Q. Duntley, W. H. Culver, F. Richey, and R. W. Preisendorfer, J. Opt. Soc. Am. (to be published).

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Figures (32)

Fig. 1
Fig. 1

Spectroradiometric curves of light from the nadir reaching a spectrograph mounted in a glass-bottomed boat over shoals off Dania, Florida (March 1944). Spectral resolution: 7.7 mμ; spatial resolution: 2.0×10−6 sr.

Fig. 2
Fig. 2

Spectroradiometric curves of light from the nadir reaching a spectrograph in an airplane 4300 ft above the same ocean locations as in Fig. 1. Spectral resolution: 7.0 mμ; spatial resolution: 3.2×10−6 sr.

Fig. 3
Fig. 3

CIE chromaticity diagram showing loci of the colors of ocean shoals as seen from an altitude of 4300 ft (shorter curve) and from a glass-bottomed boat (longer, upper curve). The points were calculated from the spectral radiance data in Figs. 1 and 2. The circled point represents CIE source C.

Fig. 4
Fig. 4

Schematic diagram of the highly collimated underwater light source represented by a cross-hatched block in Figs. 5, 6, 7, 13, 20, and 21. This source was used in obtaining part or all of the data presented in Figs. 9, 10, 12, 17, 18, 20, and 22. Interchangeable 2, 10, 25, and 100 w zirconium concentrated-arc lamps in a water-tight air-filled enclosure produce nominal total beam spreads of 0.010°, 0.046°, 0.085°, and 0.174°, respectively, when used with a Wratten No. 61 green filter and a specially constructed air-to-water collimator lens having an effective first focal length of 495 mm. This lens, designed for the author by Justin J. Rennilson, is a cemented doublet 55 mm in diameter having radii r1=269.75 mm, r2=r3=102.60 mm, r4=−325.0 mm and axial thicknesses t1=3.0±0.2 mm, t2=6.5±0.2 mm. The first element is of Hayward LF-2 glass (ND=1.5800±0.0010; ν=41.0) and the second is of Hayward BSC-1 (ND=1.5110±0.0010; ν=63.5). The free aperture is 50.0 mm. The first back focal length of the doublet with its last surface in water is 493.88 mm. The air–glass surface was treated for increased light transmission. The achromatization is such that with the 2-W concentrated-arc lamp the extreme ray divergence is 0.0031°, 0.0039°, and 0.0109° at 480, 520, and 589 mμ, respectively, when the lamp is used in fresh water having a temperature of 20°C. A Wratten No. 61 green filter was used during all of the experiments with this lamp, but it does not appear in Fig. 4 because it was always incorporated in the photometer or the camera. An external circular stop (not shown) can be mounted in the water close to the lens whenever a smaller beam diameter is desired.

Fig. 5
Fig. 5

Illustrating the geometry of Eq. (1). The cross-hatched block represents the collimated underwater light source (projector) shown schematically in Fig. 4.

Fig. 6
Fig. 6

Polar diagram illustrating Rayleigh scattering by pure water. The ratio of the light scattered into the rear hemisphere to that scattered into the forward hemisphere is 1 to 1. The cross-hatched block represents the collimated underwater light source shown schematically in Fig. 4.

Fig. 7
Fig. 7

Polar diagram illustrating measured scattering by a typical sample of commercial distilled water. The ratio of the light scattered into the rear hemisphere to that scattered into the forward hemisphere is 1 to 6 for this water sample. Data are by Tyler (see reference 13). The scale of this polar plot is smaller than that used in Fig. 6.

Fig. 8
Fig. 8

Coaxial scattering meter for in situ measurement of the volume scattering function at small scattering angles. In this schematic drawing the vertical scale has been exaggerated five times over the horizontal scale in order to illustrate the principle of the device more clearly. The collimated underwater light source shown in Fig. 4 is used with the addition of an external opaque central stop which results in the formation of a thin-walled hollow cylinder of light. This traverses 26 in. of water to a high-quality glass window behind which, in air, is a photoelectric telephotometer with a 2° total field of view. The light source and the telephotometer are coaxial, but the latter is equipped with an external stop small enough to exclude the hollow cylinder of light so that only light scattered by the water is collected. The cylindrical scattering volume is indicated by cross-hatching. The upper limit of the scattering angle is determined by the field of the telephotometer and the lower limit is set by the size of its external stop, i.e., by the entrance pupil. A detailed geometrical analysis of the configuration depicted above shows that the scattering is measured at 0.47 deg±0.15°; this datum is used as the volume scattering function for 1/2° scattering angle in Figs. 9 and 10. Photometric calibration of the scattering meter is achieved by removing the external stop on the telephotometer.

Fig. 9
Fig. 9

Volume scattering function curves for pure water (Dawson and Hulburt, see reference 12), the Atlantic between Madeira and Gibraltar (Jerlov, see reference 8), and the Diamond Island Field Station, Lake Winnipesaukee, New Hampshire. The upper curve (lake) represents in situ measurements at 5° intervals between scattering angles 20° > ϑ > 160° by means of a conventional type, pivoted-arm scattering meter and a single datum at ϑ=0.5° obtained in situ with the coaxial scattering meter shown schematically in Fig. 8; the data are of 20 August 1961; and are for green light isolated by means of a Wratten No. 61 filter.

Fig. 10
Fig. 10

Comparison of the shape of the in situ volume scattering function data for Lake Winnipesaukee, New Hampshire, from Fig. 9 with the shape of a curve representing the in vivo scattering data obtained by Koslyaninov (see reference 15) using a shipboard laboratory apparatus and a sample of water taken from the East China Sea. The curves have been normalized at a scattering angle of 90° (circled point) for purposes of shape comparison. Koslyaninov used blue light isolated by means of an absorption filter having an effective wavelength of 494 mμ; he reported data at scattering angles of 1, 2.5, 4, 6, 10, 15, 30, 50, 70, 110, and 144 deg. The curves are similar in shape for scattering angles less than 60°.

Fig. 11
Fig. 11

Comparison of in situ scattering data by Tyler (see reference 13) in clear Pacific ocean water near Catalina with comparable data for a typical sample of commercial distilled water. Both curves were obtained with the same pivoted-arm scattering meter and are in the same relative units. The data are for green light isolated by means of a Wratten No. 61 filter.

Fig. 12
Fig. 12

Comparison of scattering data by seven investigators using dissimilar instruments in seven different parts of the world. All curves are superimposed at a scattering angle of 90°, as indicated by the circled point. Gross similarity in curve shape is apparent in the forward (0<ϑ<90°) scattering directions despite major differences in water clarity (2 m/ln<1/α<20 m/ln), spectral region, geographical location, instrumental design, and experimental technique. Most of the scattering in natural waters is caused by transparent organisms and particles large compared with the wavelength of light. The scattering is believed to result chiefly from refraction and reflection at the surfaces of these scatterers. As a consequence, scattering at small forward angles predominates and polarized light tends to preserve its polarization. To the extent that all scattering curves have identical shapes the scattering by natural waters can be specified in terms of some single number, such as the total volume scattering coefficient s or the volume scattering function at some selected angle.

Fig. 13
Fig. 13

Illustrating the irradiation of an object by multiply scattered light at arbitrary points inside and outside the light beam. The dotted curve associated with each cross-hatched volume element has the shape shown in Fig. 7 and represents a polar plot of the volume scattering function. The need for additional scattering data at small forward angles is obvious.

Fig. 14
Fig. 14

Apparent radiance of a uniform, spherical underwater lamp at various distances, illustrating the exponential nature of the attenuation of apparent lamp radiance with distance. Photographic photometry was employed using a Wratten No. 61 filter and Eastman Plus X 35-mm film (Emulsion No. 5061-64-16A) developed to unity gamma in D-76. Exposure time at f/1.5 varied from 1.75 msec at a lamp distance of 10.5 ft to 180 000 msec when the lamp was 80 ft from the camera. The source of light was a 1000-W incandescent “diving lamp” (No. MG25/1) manufactured by the General Electric Company. The 3-in. spherical lamp envelope was sprayed with a white gloss lacquer in order to produce a uniform translucent white covering which gave the lamp the same radiant intensity in all directions (to within ±7%) except toward the base, which was turned away from the camera. Two or more exposure times differing by 5- or 10-fold were used at each lamp distance. Open circles represent data from a single time of exposure; solid points indicate that identical values of apparent radiance were obtained from negatives made with two different exposure times. A solid straight line, representing an attenuation length 1/α=5.00 ft/ln, has been drawn near the points. Dashed lines corresponding to attenuation lengths of 4.72 ft/ln and 5.12 ft/ln, respectively, represent values measured by means of a light-beam transmissometer before and after the all-night experimental session. Cooling of the water during the night correlated with the observed increase of attenuation length, presumably due to plankton shrinkage. Data are of 26 August 1959 at Diamond Island Field Station.

Fig. 15
Fig. 15

Angular distribution of apparent radiance produced by a uniform, spherical, underwater lamp at distances of 8.5, 18.5, 29, and 39 feet. The lamp was identical to the one described in connection with Fig. 14. The photometry was by means of an automatic scanning, photoelectric, telephotometer having a circular acceptance cone 0.25° in diameter and with its spectral response limited by a Wratten No. 61 filter. Attenuation length was 5.1 ft/ln. Data are of 3 August 1961 at the Diamond Island Field Station.

Fig. 16
Fig. 16

Total irradiance produced at various distances by a uniform, spherical underwater lamp at the Diamond Island Field Station. The solid curve was passed through the data points by means of a least-squares procedure. The lamp was identical with the one described in connection with Fig. 14. The photometry was by means of an underwater photoelectric irradiance meter facing directly toward the lamp. The spectral response of the irradiometer was limited by means of a Wratten No. 61 green filter. The attenuation length of the water was 5.0 ft/ln. Data are of 26 August 1959.

Fig. 17
Fig. 17

Apparent radiance produced by scattering from the beam of the highly collimated underwater lamp shown in Fig. 4. The photometry was by means of an automatic scanning, photoelectric telephotometer having a circular acceptance cone 0.25° in diameter and with its spectral response limited by a Wratten No. 61 filter. The beam from the lamp had a divergence of 0.01°; it was directed toward the telephotometer and filled the entrance pupil of that instrument at all times. Lamp distances of 11, 20, and 30 ft were used. Tests of the telephotometer showed that the data in Fig. 17 are free from stray-light effects. Attenuation length of the water was 6.7 ft/ln. The data are of 11 August 1961 at the Diamond Island Field Station.

Fig. 18
Fig. 18

Irradiance normal to the axis of the beam of light having a divergence of 1/6° produced by a collimated underwater lamp (Fig. 4) at distances up to 8 attenuation lengths is shown by the data points and the solid lines for beam diameters of 1/300, 2/300, and 8/300 of an attenuation length. The data are of 14 August 1961 at the Diamond Island Field Station; attenuation length 1/α=6.3 ft/ln. Dashed lines represent the monopath irradiance in each case computed from Eq. (7). Geometrical divergence reduces the axial monopath irradiance at all lamp distances beyond the points marked by triangles, which occur at 1.15 and 2.30 attenuation lengths for the two smaller lamps and at 9.20 attenuation lengths (not shown) for the largest lamp. Spreading of the beam by diffraction also reduces the monopath irradiance at all lamp distances, often dramatically. In a plot involving dimensionless lamp distance (such as Fig. 18), the dashed lines cannot be drawn to include the potentially major effect of diffraction because the wavelength of light is independent of the attenuation length, but they should be appropriately lowered when the figure is interpreted in terms of actual dimensions. The vertical separation between the dashed and the solid curves in each pair is a measure of the multipath irradiance. Caution: The data in this figure relate only to the axis of an aplanatic underwater projection system having a beam spread ψ=1/6°; they should not be scaled by the ratio D/ψ; they do not, for example, apply to the case of ψ=1/60° and lamp diameters D=1/3000, 2/3000, or 8/3000 attenuation length.

Fig. 19
Fig. 19

Ratio of monopath irradiance to multipath irradiance produced by a uniform spherical lamp (lower curve) and by the same source mounted within a blackened enclosure (box) which limited its emittance to a circular cone 20° in total angular diameter (upper curve). In producing these curves, monopath irradiance Hr0 was calculated by means of Eq. (3) and multipath irradiance Hr* was obtained by subtracting Hr0 from the total irradiance data given by Fig. 16 for the unrestricted spherical lamp and from corresponding data for the 20° case.

Fig. 20
Fig. 20

Irradiance outside a collimated beam of light. Beam divergence: 0.046°; beam diameter: 2-in. Filter: Wratten No. 61. Attenuation length 4.8 ft/ln; Diamond Island.

Fig. 21
Fig. 21

Techniques for observing (upper figure) and recording (lower figure) the effects of refractive inhomogeneities on the transmission of a highly collimated beam of light through natural water.

Fig. 22
Fig. 22

Photograph of the light distribution from the collimated underwater lamp (Fig. 4) after traversing 10 ft of water in the manner shown schematically in Fig. 21. Camera: Contax without lens. Exposure time: 1/50 sec. Film: Eastman Plus-X. Development: normal, D-76. Beam spread: 0.01°. Beam diameter: 2 in. Attenuation length: 5.6 ft/ln; Diamond Island; 22 August 1961. The diameter of the outer black circular border (caused by the opening in the camera body) measured 1.3 in. on the negative.

Fig. 23
Fig. 23

Depth profiles of underwater apparent radiance for several paths of sight (i.e., zenith angles) in the plane of the sun on a clear, calm, cloudless, sunny day (28 April 1957) at Pend Oreille, Idaho. The circles denote data by Tyler (see reference 23). The solar zenith angle was 33.4°. The submerged photoelectric radiance photometer measured blue light by means of an RCA 931A multiplier phototube equipped with a Wratten No. 45 filter; its field of view was circular and 6.6° in angular diameter. The water was nearly uniform in its optical properties; i.e., the attenuation length (as measured by means of a light beam transmissometer having a tungsten source, an RCA 931A phototube, and a Wratten No. 45 filter) was 2.52 m/ln just beneath the surface and increased very slightly at a steady rate to 2.62 m/ln at a depth of 61 m; that is to say, the change in attenuation length with depth was barely detectable. Additional families of radiance profiles in vertical planes at other azimuths can be constructed from Tyler’s tables, which also provide corresponding data for overcast conditions. All such sets of profiles are remarkably similar at great depth. Parallel profiles signify that the radiance distribution has its asymptotic form.

Fig. 24
Fig. 24

The solid curves are radiance attenuation functions (i.e., slopes) of the depth profiles of apparent radiance in Fig. 23. The circled points are from Tyler’s attenuation function tables (see reference 23). The dashed curve is the attenuation function for scalar irradiance; i.e., the slope of the depth profile of scalar irradiance, a radiometric quantity proportional to the response of a spherical diffuse collector such as that at the top of the instrument pictured in Fig. 25. The transformation of the light field to its asymptotic form is illustrated by the convergence of the radiance attenuation functions to a common, steady value at sufficient depth.

Fig. 25
Fig. 25

Water-clarity meter for measuring depth profiles of scalar irradiance h(z) and attenuation coefficient α(z) at sea. The hollow, translucent, white sphere at the top of the instrument is the collector for the measurement of scalar irradiance. Attenuation is measured by means of a highly collimated beam of light, produced by a projector in the lower compartment, which travels upward to a photoelectric telephotometer in the upper chamber. Baffles are used to minimize the effect of daylight in near surface measurements. The use of multiplier phototubes enables this equipment to produce profiles of scalar irradiance at depths greater than 10 attenuation lengths. A pressure transducer is incorporated in the instrument to indicate its depth. Due to the spherical nature of the irradiance sensor, the orientation of the instrument is not important; it can, if desired, be oriented horizontally (see reference 29).

Fig. 26
Fig. 26

Underwater radiance distributions in the plane of the sun on a clear, sunny day at depths of 4.24, 16.6, 29.0, 41.3, 53.7, and 66.1 m, respectively. The circles denote data by Tyler (see reference 23) at Pend Oreille, Idaho, 28 April 1957. The solar zenith angle was 33.4° For additional experimental details see Fig. 23. At the shallowest depth measured (4.24 m), the peak of the radiance distribution is at a slightly greater zenith angle than refracted rays from the sun (24.4°); see Fig. 29. At progressively greater depths the distribution becomes less sharply peaked and the maximum moves toward zero zenith angle. The radiance distribution is nearly in its asymptotic form at 66.1 m, the greatest depth at which data were taken. Corresponding trends appear in similar plots of data obtained by Sasaki in ocean water near Japan (see reference 26) and in Gullmar fjord by Jerlov and Fukuda (see reference 25).

Fig. 27
Fig. 27

In this figure the underwater radiance distribution curves for depths 4.24, 16.6, 29.0, and 41.3 m from Fig. 26 have been superimposed at their respective maxima in order to compare their shapes. The radiance curves for depths 53.7 and 66.1 m are not shown since, within the limits of experimental error, their shapes are identical with the curve for 41.3 m depth. Thus, the shape of the underwater radiance distribution has nearly completed its transformation to the asymptotic form at 41.3 m depth. The maximum of the curve has not, however, reached zero zenith angle at this depth and is, in fact, changing at maximum rate; see Fig. 28.

Fig. 28
Fig. 28

Illustrating how the peaks of the underwater daylight radiance distributions shown in Fig. 26 shift toward zero zenith angle with increasing depth. At shallow depths in these data the peak occurs at a greater zenith angle than the direction (underwater) of rays from the sun. The extrapolated (dashed) portion of the curve suggests that a depth of more than 100 m is required to bring the peak to zero zenith angle; i.e., to complete the transformation of the light field to its asymptotic form.

Fig. 29
Fig. 29

Illustrating the effect of (vertical) object-to-camera distance on the apparent radiance (lower figure) and the photographic contrast (upper figure) of an object having both white and black areas submerged 35 m beneath the surface of deep, optically uniform water characterized by an attenuation length (1/α) of 3.2 m/ln, (α/K)=2.7, H(z,+)/H(z,−)=0.02, and asymptotic radiance distribution. The prevailing spectral irradiance on the surface of the water is assumed to be 1 W/m2, mμ.

Fig. 30
Fig. 30

Interrelated experiments from the September 1948 series at the Diamond Island Field Station: (Left) Semilogarithmic depth profile of scalar irradiance obtained by lowering a 6-in.-diameter, air-filled, hollow, translucent, opal glass sphere having a photovoltaic cell sealed in an opening at its bottom. The straightness of the curve indicates optical homogeneity of the water and a depth invariant attenuation coefficient k(z)=0.066 ln/ft. (Center) Semilogarithmic plot of the absolute apparent contrast of a horizontal, flat, white target lowered vertically beneath a telephotometer mounted in a small, hooded, glass-bottomed boat; calm water, clear sky, low sun. The long, straight portion of the curve illustrates Eq. (15) and its slope indicates that α(z)+K(z,π,0)=0.247 ln/ft. Because the sun was low the radiance distribution was approximately asymptotic, so that K(z,π,0)≈k(z)=0.066 ln/ft and, by subtraction α(z)=0.181 ln/ft or the attenuation length 1/α=5.5 ft/ln. (Right) Two semilogarithmic plots of apparent contrast vs target distance along 60°-downward-sloping paths of sight for black targets (lower portion) and white targets (upper portion) have been combined to demonstrate (1) that the apparent contrast is exponentially attenuated with target distance at the same space rate for both light targets and dark targets, (2) that this space rate is independent of azimuth, and (3) that Eq. (16) is valid. All four paths of sight have the same zenith angle, θ=150°, but the azimuth angles relative to the plane of the sun are ϕ=0 (circled points) and ϕ=45° (crosses), ϕ=95° (diamonds) and ϕ=135° (squares). The dashed straight lines are constructed parallel and, in accordance with Eq. (16), they have a slope 0.181+0.066 cos150°=0.214 ln/ft. These lines were passed through the uppermost datum point of each series without regard to the lower points; the lines are provided solely to facilitate judgment of the slope and linearity of the data. Photographic underwater telephotometry; green light, calm water, clear sky, low sun.

Fig. 31
Fig. 31

Comparison of apparent absolute contrast with apparent edge contrast of white targets for two horizontal underwater paths of sight having azimuths relative to the direction of the sun of 95° (crosses) and 135° (circles), respectively. The three lines are parallel and correspond to an attenuation length 1/α=5.65 ft/ln. The data are of 24 September 1948 at Diamond Island. Photographic telephotometry; green filter.

Fig. 32
Fig. 32

Superimposed semilogarithmic plots of monochromatic downwelling irradiance vs depth and monochromatic radiant power absorbed per unit of volume vs depth illustrate the (approximate) relation between these quantities expressed by Eq. (20). Monochromatic downwelling irradiance is the total monochromatic radiant power per unit of area received by the upper surface of a horizontal plane at arbitrary depth z. The product of this irradiance and its depth attentuation function (slope of its depth profile) is, within about 2%, equal to the monochromatic power absorbed per unit of volume. Thus, at a depth of 50 m in Fig. 32, H(50,−)=6.3×10−3 W/(m2, mμ.), K(50,−)=0.114 ln/m, and dP(50)/dv≈(6.3×10−3)(0.114)=7.2×10−4 W/(m3, mμ). Neither of the curves in this figure represent specific experimental data, but the irradiance profile is typical of the Pacific Ocean off California. The presence of a deep scattering layer is shown below 350 m.

Tables (3)

Tables Icon

Table I Attenuation length of distilled water at various wavelengths.ac

Tables Icon

Table II Attenuation length of the Atlantic Ocean for wavelength 465 mμ at various depths in the vicinity of Madeira and Gibraltar.a

Tables Icon

Table III Attenuation length of ocean water for wavelength 440 mμ at various locations.a

Equations (25)

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P r 0 = P 0 e - α r ,
s = 2 π 0 π σ ( ϑ ) sin ϑ d ϑ ,
N r = N 0 e - α r ,
H r 0 = J e - α r / r 2 .
H r * = J K e - K r / 4 π r ,
H r * = 2.5 ( 1 + 7 e - K r ) J K e - K r / 4 π r .
H r * = ( 2.5 - 1.5 log 10 2 π / β ) × [ 1 + 7 ( 2 π / β ) 1 / 2 e - K r ] J K e - K r / 4 π r ,
H r 0 = J e - α r / r 2 = H 0 e - α r ( D / ψ r ) 2 = H 0 e - α r / ( r / r ) 2
C r ( z , θ , ϕ ) / C 0 ( z t , θ , ϕ ) = T r ( z , θ , ϕ ) N b 0 ( z t , θ , ϕ ) / N b r ( z , θ , ϕ ) ,
d N ( z , θ , ϕ ) / d r = - K ( z , θ , ϕ ) cos θ N ( z , θ , ϕ ) ,
d N ( z , θ , ϕ ) / d r = N * ( z , θ , ϕ ) - α ( z ) N ( z , θ , ϕ ) ,
d N t ( z , θ , ϕ ) / d r = N * ( z , θ , ϕ ) - α ( z ) N t ( z , θ , ϕ ) .
N t r ( z , θ , ϕ ) = N t 0 ( z t , θ , ϕ ) exp [ - α ( z ) r ] + N ( z t , θ , ϕ ) exp [ + K ( z , θ , ϕ ) r cos θ ] × { 1 - exp [ - α ( z ) r + K ( z , θ , ϕ ) r cos θ ] } ,
exp { - 0 r [ α ( z ) - cos θ K ( z , θ , ϕ ) ] d r }
exp [ - α ( z ) r + cos θ K ( z , θ , ϕ ) r ] ;
N t r ( z , θ , ϕ ) - N b r ( z , θ , ϕ ) = [ N t 0 ( z t , θ , ϕ ) - N b 0 ( z t , θ , ϕ ) ] exp [ - α ( z ) r ] .
C 0 ( z t , θ , ϕ ) = [ N t 0 ( z t , θ , ϕ ) - N b 0 ( z t , θ , ϕ ) ] / N b 0 ( z t , θ , ϕ ) ,
C r ( z , θ , ϕ ) = [ N t r ( z , θ , ϕ ) - N b r ( z , θ , ϕ ) ] / N b r ( z , θ , ϕ ) .
C 0 ( z t , θ , ϕ ) / C r ( z , θ , ϕ ) = 1 - [ N ( z t , θ , ϕ ) / N b 0 ( z t , θ , ϕ ] × { 1 - exp [ α ( z ) r - K ( z , θ , ϕ ) r cos θ ] } .
C r ( z , θ , ϕ ) = C 0 ( z t , θ , ϕ ) × exp [ - α ( z ) r + K ( z , θ , ϕ ) r cos θ ] .
C r ( z , θ , ϕ ) / C 0 ( z t , θ , ϕ ) = exp [ - α + K cos θ ) ] r .
d N q ( z , 1 2 π , ϕ ) / d r = 0 = N * ( z , 1 2 π , ϕ ) - α ( z ) N q ( z , 1 2 π , ϕ ) .
α ( z ) = N * ( z , 1 2 π , ϕ ) / N ( z , 1 2 π , ϕ ) .
d P ( z ) d v = d d z { H ( z , - ) - H ( z , + ) } = d d z { H ( z , - ) [ 1 - H ( z , + ) H ( z , - ) ] } .
d P ( z ) / d v H ( z , - ) K ( z , - ) ,