Abstract

A single detector instrument concept that collects scattered light over the full range of backscattering angles is described. Its light collection aperture is designed so as to introduce a sinθ factor into the collection probability. Hence, the instrument is exactly a bb meter; it directly measures bb, not a proxy for it. For an infinitesimal aperture to the detector, the instrument would give bb exactly; for a finite aperture (e.g., 1.26cm2), it would typically give bb to an accuracy of a few tenths of 1%. The instrumentation itself is as simple as that of the well-known fixed-angle meters—it projects a beam of light into the medium and collects backscattered light with a single detector; the differences are the position of the detector and the shape/orientation of the entrance aperture to the detector.

© 2011 Optical Society of America

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  1. H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
    [CrossRef] [PubMed]
  2. M. Kim and W. D. Philpot, “Development of a laboratory spectral backscattering instrument: design and simulation,” Appl. Opt. 44, 6952–6961 (2005).
    [CrossRef] [PubMed]
  3. R. Maffione and D. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
    [CrossRef] [PubMed]
  4. C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050(2002).
    [CrossRef] [PubMed]
  5. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
    [CrossRef]
  6. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
    [CrossRef]
  7. G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974), pp. 25–49.
  8. M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571(2003).
    [CrossRef]
  9. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography Visibility Laboratory, 1972).
  10. J. E. Tyler and W. H. Richardson, “Nephelometer for the measurement of volume scattering function in situ,” J. Opt. Soc. Am. 48, 354–357 (1958).
    [CrossRef]
  11. T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.
  12. G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
    [CrossRef]
  13. G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for absorption and backscattering profiles in natural waters: improvement for clear waters,” Appl. Opt. 41, 2224–2227 (2002).
    [CrossRef] [PubMed]
  14. H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
    [CrossRef] [PubMed]
  15. H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
    [CrossRef]
  16. A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
    [CrossRef]
  17. T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.
  18. J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.
  19. H. Tan, T. Oishi, and R. Doerffer, “Analysis of measured spectral backward scattering coefficient,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 006.pdf.
  20. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
    [CrossRef] [PubMed]
  21. E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
    [CrossRef]
  22. N. G. Jerlov, “Particle distribution in the ocean,” in Deep Sea Expedition, H.Pettersson, ed. (Swedish Natural Science Research Council, 1953), pp. 71–98.
  23. 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]
  24. J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
    [CrossRef] [PubMed]
  25. M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
    [CrossRef]
  26. D. R. Dana and R. A. Maffione, “Determining the backward scattering coefficient with fixed-angle backscattering sensors-revisited,” presented at Ocean Optics XVI Santa Fe, New Mexico, November 18–22 2002, paper 212.pdf.
  27. R. G. Beutell and A. W. Brewer, “Instruments for the measurement of the visual range,” J. Sci. Instrum. 26, 357–359 (1949).
    [CrossRef]
  28. D. J. Gray (personal communication, 2011).
  29. D. J. Gray and A. Weidemann, “Volume scattering function effects on underwater imaging systems,” presented at Ocean Optics XIX, Tuscany, Italy, October 6–10 2008, paper 481.pdf.
  30. WET Labs, “ECO BB user’s guide (BB)” (WET Labs, Inc., 2010).
  31. E. S. Fry, J. Musser, G. W. Kattawar, and P.-W. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053–9065(2006).
    [CrossRef] [PubMed]
  32. Duke Scientific, 0.203 μm (Cat. No. 3200A, No. Lot 36926), 0.596 μm (Cat. No. 3600A, No. Lot 36446), and 3.005 μm (Cat. No. 4203A, No. Lot 36453).
  33. M. S. Twardowski, “An integrated inherent optical property sensor for AUVs” (WET Labs, Inc., 2006).

2011

D. J. Gray (personal communication, 2011).

2010

WET Labs, “ECO BB user’s guide (BB)” (WET Labs, Inc., 2010).

2009

2007

2006

E. S. Fry, J. Musser, G. W. Kattawar, and P.-W. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053–9065(2006).
[CrossRef] [PubMed]

M. S. Twardowski, “An integrated inherent optical property sensor for AUVs” (WET Labs, Inc., 2006).

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

2005

2003

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571(2003).
[CrossRef]

2002

2001

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

2000

1998

1997

1994

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

1990

1983

A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

1974

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

1972

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

1958

1953

N. G. Jerlov, “Particle distribution in the ocean,” in Deep Sea Expedition, H.Pettersson, ed. (Swedish Natural Science Research Council, 1953), pp. 71–98.

1949

R. G. Beutell and A. W. Brewer, “Instruments for the measurement of the visual range,” J. Sci. Instrum. 26, 357–359 (1949).
[CrossRef]

Barnard, Andrew H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Berthon, J.-F.

Beutell, R. G.

R. G. Beutell and A. W. Brewer, “Instruments for the measurement of the visual range,” J. Sci. Instrum. 26, 357–359 (1949).
[CrossRef]

Boss, E.

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050(2002).
[CrossRef] [PubMed]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Boynton, G. C.

Brewer, A. W.

R. G. Beutell and A. W. Brewer, “Instruments for the measurement of the visual range,” J. Sci. Instrum. 26, 357–359 (1949).
[CrossRef]

Bricaud, A.

A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Chami, M.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

Dana, D.

Dana, D. R.

D. R. Dana and R. A. Maffione, “Determining the backward scattering coefficient with fixed-angle backscattering sensors-revisited,” presented at Ocean Optics XVI Santa Fe, New Mexico, November 18–22 2002, paper 212.pdf.

Doerffer, R.

H. Tan, T. Oishi, and R. Doerffer, “Analysis of measured spectral backward scattering coefficient,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 006.pdf.

T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Fournier, G. R.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Freeman, S. A.

Fry, E. S.

Gordon, H. R.

Gray, D. J.

D. J. Gray and A. Weidemann, “Volume scattering function effects on underwater imaging systems,” presented at Ocean Optics XIX, Tuscany, Italy, October 6–10 2008, paper 481.pdf.

D. J. Gray (personal communication, 2011).

Heuermann, R.

T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

Hosaka, T.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

Jerlov, N. G.

N. G. Jerlov, “Particle distribution in the ocean,” in Deep Sea Expedition, H.Pettersson, ed. (Swedish Natural Science Research Council, 1953), pp. 71–98.

Kattawar, G. W.

Khomenko, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

Kim, M.

Korotaev, G.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

Kullenberg, G.

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

Lee, M. E.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571(2003).
[CrossRef]

Lee, M. E.-G.

Lewis, M. R.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
[CrossRef] [PubMed]

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571(2003).
[CrossRef]

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Maffione, R.

Maffione, R. A.

D. R. Dana and R. A. Maffione, “Determining the backward scattering coefficient with fixed-angle backscattering sensors-revisited,” presented at Ocean Optics XVI Santa Fe, New Mexico, November 18–22 2002, paper 212.pdf.

Marken, E.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

McLean, S. D.

Mobley, C. D.

Morel, A.

A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Musser, J.

Oishi, T.

T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.

H. Tan, T. Oishi, and R. Doerffer, “Analysis of measured spectral backward scattering coefficient,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 006.pdf.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

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]

Pegau, W. S.

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Petzold, T. J.

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

Philpot, W. D.

Prieur, L.

A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Richardson, W. H.

Shybanov, E.

Stamnes, J. J.

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

Sullivan, J. M.

Sundman, L. K.

Suzuki, J.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

Tan, H.

H. Tan, T. Oishi, and R. Doerffer, “Analysis of measured spectral backward scattering coefficient,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 006.pdf.

T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

Tanaka, A.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

Twardowski, M. S.

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
[CrossRef] [PubMed]

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009).
[CrossRef] [PubMed]

M. S. Twardowski, “An integrated inherent optical property sensor for AUVs” (WET Labs, Inc., 2006).

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Tyler, J. E.

Ura, K.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

Voss, K. J.

Weidemann, A.

D. J. Gray and A. Weidemann, “Volume scattering function effects on underwater imaging systems,” presented at Ocean Optics XIX, Tuscany, Italy, October 6–10 2008, paper 481.pdf.

Zaneveld, J. Ronald V.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

Zhai, P.-W.

Zibordi, G.

Appl. Opt.

H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters,” Appl. Opt. 36, 2636–2641 (1997).
[CrossRef] [PubMed]

R. Maffione and D. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
[CrossRef] [PubMed]

H. R. Gordon and G. C. Boynton, “Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies,” Appl. Opt. 37, 3886–3896 (1998).
[CrossRef]

G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects,” Appl. Opt. 39, 3012–3022 (2000).
[CrossRef]

E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40, 5503–5507 (2001).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41, 1035–1050(2002).
[CrossRef] [PubMed]

G. C. Boynton and H. R. Gordon, “Irradiance inversion algorithm for absorption and backscattering profiles in natural waters: improvement for clear waters,” Appl. Opt. 41, 2224–2227 (2002).
[CrossRef] [PubMed]

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]

M. Kim and W. D. Philpot, “Development of a laboratory spectral backscattering instrument: design and simulation,” Appl. Opt. 44, 6952–6961 (2005).
[CrossRef] [PubMed]

E. S. Fry, J. Musser, G. W. Kattawar, and P.-W. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053–9065(2006).
[CrossRef] [PubMed]

J.-F. Berthon, E. Shybanov, M. E.-G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203 (2007).
[CrossRef] [PubMed]

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
[CrossRef] [PubMed]

J. Atmos. Ocean. Technol.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571(2003).
[CrossRef]

J. Geophys. Res.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, Andrew H. Barnard, and J. Ronald V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142 (2001).
[CrossRef]

M. Chami, E. Marken, J. J. Stamnes, G. Khomenko, and G. Korotaev, “Variability of the relationship between the particulate backscattering coefficient and the volume scattering function measured at fixed angles,” J. Geophys. Res. 111, 1–10(2006).
[CrossRef]

J. Opt. Soc. Am.

J. Sci. Instrum.

R. G. Beutell and A. W. Brewer, “Instruments for the measurement of the visual range,” J. Sci. Instrum. 26, 357–359 (1949).
[CrossRef]

Limnol. Oceanogr.

A. Bricaud, A. Morel, and L. Prieur, “Optical efficiency factors of some phytoplankters,” Limnol. Oceanogr. 28, 816–832 (1983).
[CrossRef]

Opt. Express

Proc. SPIE

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Other

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

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

T. Oishi, H. Tan, R. Doerffer, and R. Heuermann, “Development of new spectral scattering function meter,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 004.pdf.

T. Oishi, H. Tan, T. Hosaka, A. Tanaka, and R. Heuermann, “Realization of new bb meter and its quality control,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 042.pdf.

J. Suzuki, T. Oishi, K. Ura, H. Tan, and T. Hosaka, “Numerical evaluation of new bb meter,” presented at Ocean Optics XVI, Santa Fe, New Mexico, November 18–22 2002, paper 041.pdf.

H. Tan, T. Oishi, and R. Doerffer, “Analysis of measured spectral backward scattering coefficient,” presented at Ocean Optics XVII, Fremantle, Australia, October 25–29 2004, paper 006.pdf.

D. J. Gray (personal communication, 2011).

D. J. Gray and A. Weidemann, “Volume scattering function effects on underwater imaging systems,” presented at Ocean Optics XIX, Tuscany, Italy, October 6–10 2008, paper 481.pdf.

WET Labs, “ECO BB user’s guide (BB)” (WET Labs, Inc., 2010).

N. G. Jerlov, “Particle distribution in the ocean,” in Deep Sea Expedition, H.Pettersson, ed. (Swedish Natural Science Research Council, 1953), pp. 71–98.

Duke Scientific, 0.203 μm (Cat. No. 3200A, No. Lot 36926), 0.596 μm (Cat. No. 3600A, No. Lot 36446), and 3.005 μm (Cat. No. 4203A, No. Lot 36453).

M. S. Twardowski, “An integrated inherent optical property sensor for AUVs” (WET Labs, Inc., 2006).

D. R. Dana and R. A. Maffione, “Determining the backward scattering coefficient with fixed-angle backscattering sensors-revisited,” presented at Ocean Optics XVI Santa Fe, New Mexico, November 18–22 2002, paper 212.pdf.

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Figures (13)

Fig. 1
Fig. 1

Conceptual sketch of instrument (cylindrical symmetry around z axis).

Fig. 2
Fig. 2

The functions θ 1 ( z ) , θ 2 ( z ) and the functions z 1 ( θ ) , z 2 ( θ ) are the same curves, respectively, i.e., for the latter, z is read off the horizontal axis as a function of θ on the vertical axis. The light gray and dark gray areas correspond to the domains of integration of the first and second integral in Eq. (9).

Fig. 3
Fig. 3

Domains of integration for the integrals in Eq. (14).

Fig. 4
Fig. 4

Detection solid angle Ω ( z ) with R = 0.01 m and Z 0 = 0.001 m .

Fig. 5
Fig. 5

Coefficient of β ( θ ) in the integrand of Eq. (27).

Fig. 6
Fig. 6

Dependence on attenuation c of the percent deviation from b b that would be observed in a measurement of P ( c ) , Eq. (25).

Fig. 7
Fig. 7

Percent deviation from b b of a measurement of P ( c ) after multiplication by the attenuation correction factor ( 1 + 2.7 c R ) to obtain P A ( c ) .

Fig. 8
Fig. 8

Instrument implementation—cylindrical symmetry around laser beam (except for fibers).

Fig. 9
Fig. 9

“Placebo” experiment showing a slight signal increase as samples are added.

Fig. 10
Fig. 10

Measured data for aqueous suspensions of polymer microspheres with diameters d = 203 , 596, and 3005 nm . The least-squares fits of the data to the straight lines are also shown.

Fig. 11
Fig. 11

Attenuation effects on the measured signal.

Fig. 12
Fig. 12

Three possibilities for the window at the aperture to the detector.

Fig. 13
Fig. 13

Effective reduction in the observation solid angle as a function of z due to reflection at the quartz window in the aperture of Fig. 12b.

Tables (2)

Tables Icon

Table 1 Deviations from b b That Would Be Observed for Measurements Made with This Instrumentation in Natural Waters or Suspensions of Microspheres a

Tables Icon

Table 2 Numerical Evaluations of Eq. (25, 27), and the Various Terms in Eq. (28) Using MVSM Data for β ( θ ) Obtained during October 2009 in Chesapeake Bay [28, 29] a

Equations (33)

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b b ( λ ) 2 π π / 2 π β ( λ , θ ) sin θ d θ ,
d P = 2 π A E 0 θ 1 θ 2 e c x β ( θ ) sin θ d θ d z ,
P = 2 π A E 0 0 d z θ 1 θ 2 e c x β ( θ ) sin θ d θ .
θ 1 ( z ) = π tan 1 ( R z Z 0 ) π cos 1 ( z Z 0 R 2 + ( z Z 0 ) 2 ) .
θ 2 ( z ) = π tan 1 ( R z + Z 0 ) π cos 1 ( z + Z 0 R 2 + ( z + Z 0 ) 2 ) .
θ 10 = θ 1 ( 0 ) = tan 1 ( R Z 0 ) , θ 20 = θ 2 ( 0 ) = π tan 1 ( R Z 0 ) .
z 1 ( θ ) = Z 0 R tan θ , z 2 ( θ ) = Z 0 R tan θ .
P = 2 π A E 0 0 d z π tan 1 ( R z Z 0 ) π tan 1 ( R z + Z 0 ) β ( θ ) sin θ d θ .
P = 2 π A E 0 θ 20 π β ( θ ) sin θ d θ z 2 ( θ ) z 1 ( θ ) d z + 2 π A E 0 θ 10 θ 20 β ( θ ) sin θ d θ 0 z 1 ( θ ) d z ,
P = ( 2 Z 0 A E 0 ) { 2 π θ 20 π β ( θ ) sin θ d θ + π θ 10 θ 20 β ( θ ) sin θ d θ π R Z 0 θ 10 θ 20 β ( θ ) cos θ d θ } .
P = P 2 Z 0 A E 0 ;
P = 2 π θ 20 π β ( θ ) sin θ d θ + π π / 2 θ 20 β ( θ ) sin θ d θ + π θ 10 π / 2 β ( θ ) sin θ d θ π R Z 0 θ 10 θ 20 β ( θ ) cos θ d θ .
P = 2 π θ 20 π β ( θ ) sin θ d θ + 2 π π / 2 θ 20 β ( θ ) sin θ d θ π π / 2 θ 20 β ( θ ) sin θ d θ + π θ 10 π / 2 β ( θ ) sin θ d θ π R Z 0 θ 10 θ 20 β ( θ ) cos θ d θ .
P = 2 π π / 2 π β ( θ ) sin θ d θ + π θ 10 π / 2 β ( θ ) sin θ d θ π π / 2 θ 20 β ( θ ) sin θ d θ π R Z 0 θ 10 θ 20 β ( θ ) cos θ d θ .
P = I + I I + I I I + I V = b b ( 1 + ρ 2 + ρ 3 + ρ 4 ) ,
ρ 2 = I I b b ; ρ 3 = I I I b b ; ρ 4 = I V b b .
S = K 0 ( 1 + ρ 2 + ρ 3 + ρ 4 ) b b = K b b ,
K 0 = K 1 + ρ 2 + ρ 3 + ρ 4 .
Ω ( z ) = 2 π θ 1 ( z ) θ 2 ( z ) sin θ d θ = 2 π π tan 1 ( R z Z 0 ) π tan 1 ( R z + Z 0 ) sin θ d θ = 2 π { Z 0 z R 2 + ( Z 0 z ) 2 + Z 0 + z R 2 + ( Z 0 + z ) 2 } .
x = z + R sin ( θ ) ,
P ( c ) = 2 π A E 0 0 d z θ 1 θ 2 e c ( z + R sin ( θ ) ) β ( θ ) sin θ d θ .
P ( c ) = 2 π A E 0 θ 20 π β ( θ ) sin θ d θ Z 0 R tan θ Z 0 R tan θ e c ( z + R sin θ ) d z + 2 π A E 0 θ 10 θ 20 β ( θ ) sin θ d θ 0 Z 0 R tan θ e c ( z + R sin θ ) d z .
P ( c ) = 2 π A E 0 c ( e c Z 0 e c Z 0 ) θ 20 π β ( θ ) sin θ e c R 1 cos θ sin θ d θ + 2 π A E 0 c θ 10 θ 20 β ( θ ) sin θ e c R sin θ d θ 2 π A E 0 c e c Z 0 θ 10 θ 20 β ( θ ) sin θ e c R 1 cos θ sin θ d θ .
2 π A E 0 c e c Z 0 π / 2 θ 20 β ( θ ) sin θ e c R 1 cos θ sin θ d θ .
P ( c ) = P ( c ) 2 Z 0 A E 0 = ( e c Z 0 e c Z 0 c Z 0 ) π π / 2 π β ( θ ) sin θ e c R 1 cos θ sin θ d θ + π { 1 c Z 0 θ 10 θ 20 β ( θ ) sin θ e c R sin θ d θ e c Z 0 c Z 0 θ 10 π / 2 β ( θ ) sin θ e c R 1 cos θ sin θ d θ e c Z 0 c Z 0 π / 2 θ 20 β ( θ ) sin θ e c R 1 cos θ sin θ d θ } .
e c Z 0 e c Z 0 2 c Z 0 ( 1 + 1 6 c 2 Z 0 2 + 1 120 c 4 Z 0 4 ) .
P 0 ( c ) = 2 π π / 2 π β ( θ ) sin θ e c R 1 cos θ sin θ d θ .
P 1 ( c ) = P 1 ( c ) 2 Z 0 A E 0 = { π θ 10 π / 2 β ( θ ) sin θ d θ π π / 2 θ 20 β ( θ ) sin θ d θ R π Z 0 θ 10 θ 20 β ( θ ) cos θ d θ } + c { R π π / 2 θ 20 β ( θ ) ( 1 cos θ ) d θ R π θ 10 π / 2 β ( θ ) ( 1 cos θ ) d θ Z 0 π 2 θ 10 θ 20 β ( θ ) sin θ d θ + R 2 Z 0 π θ 10 θ 20 β ( θ ) cos θ sin θ d θ R 2 2 Z 0 π θ 10 θ 20 β ( θ ) cos 2 θ sin θ d θ } + ε ,
P A ( c ) = ( 1 + 2.7 c R ) P ( c ) ,
P A ( c ) = [ 1 + 2.7 ( c ± δ c ) R ] P ( c ) = ( 1 + 2.7 c R ) P ( c ) ± 2.7 δ c R P ( c ) .
Δ = δ P A ( c ) P A ( c ) = ± 2.7 δ c R P ( c ) ( 1 + 2.7 c R ) P ( c ) = ± 2.7 R δ c ( 1 + 2.7 c R ) = ± [ 0.027 1 / c + 0.027 ] δ c c .
K 203 = 304.3 ± 1.7 , K 596 = 298.2 ± 2.9 , K 3005 = 308.5 ± 3.7 ,
K 0 = 303 ± 5.5 % ,

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