Abstract

We have built a simple, undersea radiometer that measures ten integral moments of the radiance as functions of depth in natural waters. From these data it is possible to calculate nine spherical moments of the scattering function, provided that this function varies slowly in the horizontal planes (i.e., the water is fairly stratified). This technique inverts the equations of radiative transfer, which avoids some of the limitations of conventional instruments. We took the instrument on a voyage in the coastal waters of San Diego and were able to measure the absorption coefficient in real time and in situ; we have been able to recover scattering functions with the help of nearly concurrent attenuation measurements.

© 1992 Optical Society of America

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References

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  1. J. R. V. Zaneveld, “New developments of the theory of radiative transfer in oceans,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), Chap. 6, pp. 121–134.
  2. J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson & Ross, Stroudsburg, Pa., 1977), pp. 233–252.
  3. R. C. Smith, R. W. Austin, J. E. Tyler, “Oceanographic radiance distribution camera system,” Appl. Opt. 9, 2015–2022 (1970).
    [CrossRef] [PubMed]
  4. K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
  5. K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34, 1618–1626 (1989).
    [CrossRef]
  6. W. H. Wells, “Techniques for measuring radiance in sea and air,” Appl. Opt. 22, 2313–2321 (1983).
    [CrossRef] [PubMed]
  7. G. C. Pomraning, “An asymptotically correct approximation to the multi dimensional transport equation,” Nucl. Sci. Eng 22, 328–337 (1965).
  8. W. H. Wells, J. J. Sidorowich, “Computational techniques for radiative transfer by spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 33, 347–363 (1985).
    [CrossRef]
  9. W. B. Doss, W. H. Wells, “Radiometer for light in the sea,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 363–372 (1990).
  10. B. G. Mitchell, D. A. Kiefer, “Chlorophyll a specific absorption and fluorescence excitation spectra for light-limited phytoplankton,” Deep Sea Res. 35, 639–663 (1988).
    [CrossRef]
  11. H. Hodara, “Experimental results of small angle scattering,” AGARD Lect. Ser. 61, 3.4-1–3.14-17 (1973).
  12. R. E. Morrison, “Experimental studies on the optical properties of seawater,” J. Geophys. Res. 75, 612–628 (1970).
    [CrossRef]

1989 (2)

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34, 1618–1626 (1989).
[CrossRef]

1988 (1)

B. G. Mitchell, D. A. Kiefer, “Chlorophyll a specific absorption and fluorescence excitation spectra for light-limited phytoplankton,” Deep Sea Res. 35, 639–663 (1988).
[CrossRef]

1985 (1)

W. H. Wells, J. J. Sidorowich, “Computational techniques for radiative transfer by spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 33, 347–363 (1985).
[CrossRef]

1983 (1)

1973 (1)

H. Hodara, “Experimental results of small angle scattering,” AGARD Lect. Ser. 61, 3.4-1–3.14-17 (1973).

1970 (2)

R. E. Morrison, “Experimental studies on the optical properties of seawater,” J. Geophys. Res. 75, 612–628 (1970).
[CrossRef]

R. C. Smith, R. W. Austin, J. E. Tyler, “Oceanographic radiance distribution camera system,” Appl. Opt. 9, 2015–2022 (1970).
[CrossRef] [PubMed]

1965 (1)

G. C. Pomraning, “An asymptotically correct approximation to the multi dimensional transport equation,” Nucl. Sci. Eng 22, 328–337 (1965).

Austin, R. W.

Doss, W. B.

W. B. Doss, W. H. Wells, “Radiometer for light in the sea,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 363–372 (1990).

Hodara, H.

H. Hodara, “Experimental results of small angle scattering,” AGARD Lect. Ser. 61, 3.4-1–3.14-17 (1973).

Kiefer, D. A.

B. G. Mitchell, D. A. Kiefer, “Chlorophyll a specific absorption and fluorescence excitation spectra for light-limited phytoplankton,” Deep Sea Res. 35, 639–663 (1988).
[CrossRef]

Mitchell, B. G.

B. G. Mitchell, D. A. Kiefer, “Chlorophyll a specific absorption and fluorescence excitation spectra for light-limited phytoplankton,” Deep Sea Res. 35, 639–663 (1988).
[CrossRef]

Morrison, R. E.

R. E. Morrison, “Experimental studies on the optical properties of seawater,” J. Geophys. Res. 75, 612–628 (1970).
[CrossRef]

Pomraning, G. C.

G. C. Pomraning, “An asymptotically correct approximation to the multi dimensional transport equation,” Nucl. Sci. Eng 22, 328–337 (1965).

Sidorowich, J. J.

W. H. Wells, J. J. Sidorowich, “Computational techniques for radiative transfer by spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 33, 347–363 (1985).
[CrossRef]

Smith, R. C.

Tyler, J. E.

R. C. Smith, R. W. Austin, J. E. Tyler, “Oceanographic radiance distribution camera system,” Appl. Opt. 9, 2015–2022 (1970).
[CrossRef] [PubMed]

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson & Ross, Stroudsburg, Pa., 1977), pp. 233–252.

Voss, K. J.

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34, 1618–1626 (1989).
[CrossRef]

Wells, W. H.

W. H. Wells, J. J. Sidorowich, “Computational techniques for radiative transfer by spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 33, 347–363 (1985).
[CrossRef]

W. H. Wells, “Techniques for measuring radiance in sea and air,” Appl. Opt. 22, 2313–2321 (1983).
[CrossRef] [PubMed]

W. B. Doss, W. H. Wells, “Radiometer for light in the sea,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 363–372 (1990).

Zaneveld, J. R. V.

J. R. V. Zaneveld, “New developments of the theory of radiative transfer in oceans,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), Chap. 6, pp. 121–134.

AGARD Lect. Ser. (1)

H. Hodara, “Experimental results of small angle scattering,” AGARD Lect. Ser. 61, 3.4-1–3.14-17 (1973).

Appl. Opt. (2)

Deep Sea Res. (1)

B. G. Mitchell, D. A. Kiefer, “Chlorophyll a specific absorption and fluorescence excitation spectra for light-limited phytoplankton,” Deep Sea Res. 35, 639–663 (1988).
[CrossRef]

J. Geophys. Res. (1)

R. E. Morrison, “Experimental studies on the optical properties of seawater,” J. Geophys. Res. 75, 612–628 (1970).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

W. H. Wells, J. J. Sidorowich, “Computational techniques for radiative transfer by spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 33, 347–363 (1985).
[CrossRef]

Limnol. Oceanogr. (1)

K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34, 1618–1626 (1989).
[CrossRef]

Nucl. Sci. Eng (1)

G. C. Pomraning, “An asymptotically correct approximation to the multi dimensional transport equation,” Nucl. Sci. Eng 22, 328–337 (1965).

Opt. Eng. (1)

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).

Other (3)

J. R. V. Zaneveld, “New developments of the theory of radiative transfer in oceans,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), Chap. 6, pp. 121–134.

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson & Ross, Stroudsburg, Pa., 1977), pp. 233–252.

W. B. Doss, W. H. Wells, “Radiometer for light in the sea,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 363–372 (1990).

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Figures (6)

Fig. 1
Fig. 1

Angular responses of the reflectors.

Fig. 2
Fig. 2

Schematic of the compound radiometer.

Fig. 3
Fig. 3

Details of one of the ten elements.

Fig. 4
Fig. 4

Recovered scattering function.

Fig. 5
Fig. 5

Recovered scattering functions from various workers.

Fig. 6
Fig. 6

Geometric considerations.

Tables (1)

Tables Icon

Table I Comparison of Absorption Coefficient a (m−1) Measurements at 450 nm

Equations (10)

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n L ˙ n - 1 + ( n + 1 ) L ˙ n + 1 + ( 2 n + 1 ) A n L n = 0 ,
L n = L ( θ , ϕ ) P n ( cos θ ) d Ω , n = 0 , 1 , 2 ,
A n = c - S n , S n = 2 π β ( η ) P n ( cos η ) d η ,
S = 0 ,             S 0 = b = β d Ω
A = c ,             A 0 = c - b = a
A 0 = - L ˙ 1 / L 0 , A 1 = - ( L ˙ 0 + 2 L ˙ 2 ) / 3 L 1 , A 8 = - ( 8 L ˙ 7 + 9 L ˙ 9 ) / 17 L 8 .
β ( η ) = n = 0 2 n + 1 4 π ( c - A n ) P n ( cos η ) .
Λ j ( z ) = L ( θ , ϕ ) R j ( θ ) d Ω .
L n = Q n j Λ j .
( n + 1 ) ( d d r + n + 2 r ) L n + 1 + n ( d d r - n - 1 r ) L n - 1 + ( 2 n + 1 ) A n L n = 0 ,

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