Abstract

The backward-scattering coefficient b b is an important optical property that plays a central role in studies of ocean-color remote sensing, suspended particle distributions, water clarity, and underwater visibility. We investigate the fixed-angle backscattering sensor approach for the application of measuring b b. Analysis shows that the sensor response to volume scattering can be expressed as the integral of the volume scattering function (VSF) over the backward angles (90–180°) weighted by the sensor-response function. We present a procedure for determining the sensor-response function that contains all the information necessary to calibrate the sensor fully to measure the VSF at a nominal backscattering angle. It is shown that, for fixed-angle backscattering sensors, b b is most accurately estimated when the sensor-response function covers the middle range of backscattering angles, roughly 110–160°, where the shape of the VSF has the least variability. Backscattering at and near the end angles, namely, 90° and 180°, are least correlated with b b. We describe a variety of spectral backscattering sensors that we have developed, and we present their sensor-response functions.

© 1997 Optical Society of America

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References

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  1. W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
    [CrossRef]
  2. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  3. G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N. G. Jerloy, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 25–49.
  4. T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°,” Appl. Opt. 29, 4658–4665 (1990).
    [CrossRef] [PubMed]
  5. N. Højerslev, “A history of early optical oceanographic instrument design in Scandinavia,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford University Press, New York, 1994), Chap. 7, pp. 118–147.
  6. H. Pettersson, “A transparency-meter for sea-water,” Medd. Oceanogr. Inst. Gothenburg, Ser. B 4, (1934).
  7. J. E. Tyler, W. H. Richardson, “Nephelometer for the measurement of volume scattering function in situ,” J. Opt. Soc. Am. 48, 354–357 (1958).
    [CrossRef]
  8. C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).
  9. R. A. Maffione, D. R. Dana, R. C. Honey, “Instrument for underwater measurement of optical backscatter,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 173–184, (1991).
    [CrossRef]
  10. J. H. Smart, A. B. Fraser, M. J. Jose, “Variability in optical properties across the Gulf of Alaska,” Proc. Oceans (Honolulu, Haw.)91, 657–666 (1991).
  11. R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Oregon, 1995 (Optical Society of America, Washington, D.C.).
  12. R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.
  13. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relations between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  14. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  15. N. G. Jerlov, Marine Optics, 2nd ed. (Elsevier, New York, 1976), p. 231.
  16. G. Mie, “Beiträge zur optik trüber median, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–442 (1908).
    [CrossRef]
  17. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 470.
  18. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

1995 (1)

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

1990 (1)

1977 (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

1975 (1)

1958 (1)

1934 (1)

H. Pettersson, “A transparency-meter for sea-water,” Medd. Oceanogr. Inst. Gothenburg, Ser. B 4, (1934).

1908 (1)

G. Mie, “Beiträge zur optik trüber median, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–442 (1908).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

Brown, O. B.

Cleveland, J. S.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Damron, S.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

Dana, D. R.

R. A. Maffione, D. R. Dana, R. C. Honey, “Instrument for underwater measurement of optical backscatter,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 173–184, (1991).
[CrossRef]

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Oregon, 1995 (Optical Society of America, Washington, D.C.).

R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.

Doss, W.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Frysinger, G. S.

R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.

Gordon, H. R.

Hancock, D.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

Hilbers, R.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

Højerslev, N.

N. Højerslev, “A history of early optical oceanographic instrument design in Scandinavia,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford University Press, New York, 1994), Chap. 7, pp. 118–147.

Honey, R.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

Honey, R. C.

R. A. Maffione, D. R. Dana, R. C. Honey, “Instrument for underwater measurement of optical backscatter,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 173–184, (1991).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

Jacobs, M. M.

Jerlov, N. G.

N. G. Jerlov, Marine Optics, 2nd ed. (Elsevier, New York, 1976), p. 231.

Kennedy, C. D.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Kullenberg, G.

G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N. G. Jerloy, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 25–49.

Maffione, R. A.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Oregon, 1995 (Optical Society of America, Washington, D.C.).

R. A. Maffione, D. R. Dana, R. C. Honey, “Instrument for underwater measurement of optical backscatter,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 173–184, (1991).
[CrossRef]

R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.

Mie, G.

G. Mie, “Beiträge zur optik trüber median, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–442 (1908).
[CrossRef]

Moore, C. A.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

Morel, A.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Mueller, J. L.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Oishi, T.

Pegau, W. S.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Pettersson, H.

H. Pettersson, “A transparency-meter for sea-water,” Medd. Oceanogr. Inst. Gothenburg, Ser. B 4, (1934).

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Prieur, L.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Richardson, W. H.

Stone, R.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Trees, C. C.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Tyler, J. E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 470.

Voss, J. M.

R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Oregon, 1995 (Optical Society of America, Washington, D.C.).

Weidemann, A. D.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Wells, W. H.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Zaneveld, J. R. V.

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Beiträge zur optik trüber median, speziell kolloidaler metallösungen,” Ann. Phys. 25, 377–442 (1908).
[CrossRef]

Appl. Opt. (2)

J. Geophys. Res. (1)

W. S. Pegau, J. S. Cleveland, W. Doss, C. D. Kennedy, R. A. Maffione, J. L. Mueller, R. Stone, C. C. Trees, A. D. Weidemann, W. H. Wells, J. R. V. Zaneveld, “A comparison of methods for the measurement of the absorption coefficient in natural waters,” J. Geophys. Res. 100, 13,201–13,220 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

Limnol. Oceanogr. (1)

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Medd. Oceanogr. Inst. Gothenburg, Ser. B (1)

H. Pettersson, “A transparency-meter for sea-water,” Medd. Oceanogr. Inst. Gothenburg, Ser. B 4, (1934).

Other (11)

N. G. Jerlov, Marine Optics, 2nd ed. (Elsevier, New York, 1976), p. 231.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 470.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

N. Højerslev, “A history of early optical oceanographic instrument design in Scandinavia,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford University Press, New York, 1994), Chap. 7, pp. 118–147.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N. G. Jerloy, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 25–49.

C. A. Moore, R. Honey, D. Hancock, S. Damron, R. Hilbers, “Development and use of computerized optical sea-truth instrumentation for LIDEX-82,” (SRI International, Menlo Park, Calif., 1984).

R. A. Maffione, D. R. Dana, R. C. Honey, “Instrument for underwater measurement of optical backscatter,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. SPIE1537, 173–184, (1991).
[CrossRef]

J. H. Smart, A. B. Fraser, M. J. Jose, “Variability in optical properties across the Gulf of Alaska,” Proc. Oceans (Honolulu, Haw.)91, 657–666 (1991).

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Oregon, 1995 (Optical Society of America, Washington, D.C.).

R. A. Maffione, D. R. Dana, J. M. Voss, G. S. Frysinger, “Instrumented remotely operated vehicle for measuring inherent and apparent optical properties of the ocean,” in Underwater Light Measurements, H. C. Eilertsen, ed., Proc. SPIE2048, 124–137.

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Figures (12)

Fig. 1
Fig. 1

Schematic layout of the backscattering sensor developed at SRI International in the early 1980’s under an Advanced Research Projects Agency program called LIDEX.

Fig. 2
Fig. 2

Second-generation backscattering sensor developed at SRI in 1991. The major improvement was better collimating optics for application in the visible spectrum (400 to 700 nm) and for estimating b b .

Fig. 3
Fig. 3

Optical layout of the BB-4, BBC-4, and HydroScat-6. The HydroScat-6 does not include the condenser lens but instead uses a single, fast achromat.

Fig. 4
Fig. 4

Optical geometry for a generic fixed-angle backscattering sensor.

Fig. 5
Fig. 5

Optical geometry for analyzing the sensor response to a Lambertian target.

Fig. 6
Fig. 6

Weighting functions of three backscattering sensors with different optical geometries. The more narrow the weighting function, the more collimated the optics of the sensor.

Fig. 7
Fig. 7

W(z; c) for the BBC-4 and Petzold average phase function plotted as a function of the scattering angle.

Fig. 8
Fig. 8

W [ψ(z); c w ]β[ψ (z)] as computed from the two curves in Fig. 7.

Fig. 9
Fig. 9

W(z; c) for three values of c. An increase in c by a factor of 25 changed ψ* by only 7°.

Fig. 10
Fig. 10

Attenuation correction factor σ(c, c w ) computed for the 440-nm channel of the BBC-4. The attenuation coefficient of the filtered water, c w = 0.02 m-1 at 440 nm, was measured with the BBC-4 transmissometer.

Fig. 11
Fig. 11

VSF measurements by Petzold2 normalized by the factor 2π/b b . Each curve is an average of all the data reported by Petzold for that water type.

Fig. 12
Fig. 12

Computations of the VSF using Mie theory and assuming a Junge or hyperbolic particle-size distribution. Curves are normalized by the factor 2πβ(ψ)/b b = 1/χ. The thick solid curve is the average of all the VSF’s.

Equations (22)

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

β(ψ)=2Φ(ψ)/EΩV,
b=4πβψdΩ=2π0πβψ sin ψdψ,
bb=2ππ/2πβψ sin ψdψ.
ΔΦdVz=Φ0 exp-crsΔAz/Az.
z=ΔΦdVz/ΔAz=Φ0 exp-crs/Az.
ΔΦψ, z=βψEzΔΩzΔVz=βψΦ0 exp-crs/AzΔAz cos θd/rd2×ΔAzdz/cos θs=βψΦ0cos θd/cos θsexp-crs/rd2×ΔA2z/Azdz,
ΔΦβψ, z=ΔΦψ, zexp-crd=βψΦ0cos θd/cos θsexp-crs+rd/rd2×ΔA2z/Azdz=βψΦ0Wz; cdz,
Wz; c cos θd/cos θsexp-crs+rd/rd2×ΔA2z/Az
Ωβ=Φ0gβ0βψWz; cdz=Φ0gββψ*0 Wz; cdz.
ΔΦρz=Φ0gρρ/πcos2 θdexp-cwrs+rd/rd2×ΔA2z/Az=Φ0gρρ/πcos θs cos θdWz; cw.
Φρ=0ΔΦρzcos θs cos θddz=Φ0gρρ/π0 Wz; cwdz.
βψ*=ΦβgβρπgρΦρ0Wz; cw0Wz; c=Φβgβμ σc, cw,
μρ/πgρ/Φρ,
σc, cw 0Wz; cw0Wz; c.
ΔΦρzrd2 expcwrs+rd/cos θs cos θd=kΔA2z/AzkGz,
GzΔA2z/Az,
z*0zWz; cdz0Wz; cdz
βψ*=0βψzWz; cdz0Wz; cdz
Wz; cexp-crs+rdGz cos θdrd2 cos θs,
bb=2ππ/2πβψ sin ψdψ=2πβψ*π/2πsin ψdψ=2πβψ*.
χβψ*/βψχ,
bb=2πχβψχ.

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