Abstract

Measuring the absolute absorption of suspensions of absorbing particles with unknown scattering characteristics is not possible in conventional spectrophotometers or in integrating spheres that have the sample located outside the sphere. A method for the calibration and use of an integrating sphere with a centrally located sample to measure absolute absorption coefficients of scattering suspensions is presented. Under the tested conditions the integrating sphere used in this study was insensitive to changes in the scattering coefficient of the sample but had a nonlinear response to increasing absorption of the sample, which could be corrected with an empirically derived function. This response was analyzed by using a Monte Carlo simulation, and results indicated that amplification of the absorption signal was primarily due to photons reflected from the sphere surface and the baffle reentering the cuvette. The calibration procedure described here may be generally applicable to spheres of different configuration. An example of the use of the sphere for determining the absorption and scattering coefficients of marine phytoplankton samples is presented.

© 1993 Optical Society of America

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References

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  1. J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, 1983).
  2. W. L. Butler, “Absorption of light by turbid materials,” J. Opt. Soc. Am. 52, 292–299 (1962).
    [CrossRef]
  3. W. L. Butler, “Absorption spectroscopy in vivo: theory and application,” Annu Rev. Plant Physiol. 15, 451–470 (1964).
    [CrossRef]
  4. A. Bricaud, A. Morel, L. Prieur, “Optical efficiency factors of some phytoplankton,” Limnol. Oceanogr. 28, 816–832 (1983).
    [CrossRef]
  5. K. Shibata, “Spectrophotometry of translucent biological materials: opal glass transmission method,” Methods Biochem. Anal. 7, 77–109 (1959).
    [CrossRef]
  6. N. B. Nelson, B. B. Prézelin, “Chromatic light effects and physiological modeling of absorption properties of Heterocapsa pygmaea (=Glenodinium sp.),” Mar. Ecol. Prog. Ser. 63, 37–46 (1990).
    [CrossRef]
  7. A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
    [CrossRef] [PubMed]
  8. A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton: a simplified theoretical approach,” Deep-Sea Res. 34, 1093–1105 (1987).
    [CrossRef]
  9. A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
    [CrossRef] [PubMed]
  10. H. Haardt, H. Maske, “Specific in vivo absorption coefficient of chlorophyll a at 675 nm,” Limnol. Oceanogr. 32, 608–619 (1987).
    [CrossRef]
  11. D. G. Goebel, “Generalized integrating-sphere theory,” Appl. Opt. 6, 125–128 (1967).
    [CrossRef] [PubMed]
  12. SLM Instruments, DW-2000 UV-VIS Spectrophotometer: Operator's Manual (SLM-Aminco, Urbana, Ill., 1987).
  13. K. F. Carr, “Integrating sphere flux calculations,” in 1990 Catalog (Labsphere, Inc., North Sutton N.H., 1990), pp. 84–86.
  14. J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust, J. Mar. Freshwater Res. 32, 517–532 (1981).
    [CrossRef]
  15. T. T. Bannister, “Estimation of absorption coefficients of scattering suspensions using opal glass,” Limnol. Oceanogr. 33, 607–615 (1988).
    [CrossRef]
  16. K. M. Crocker, University of California, Santa Barbara, Santa Barbara, Calif. 93106 (personal communication, 1992).
  17. N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
    [CrossRef]
  18. T. L. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref.72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  19. B. G. Mitchell, “Algorithms for determining the absorption coefficient of aquatic particulates using the quantitative filter technique (QFT),” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt Instrum. Eng.1302, 137–148 (1990).
  20. K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
    [CrossRef]

1993

N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
[CrossRef]

1991

1990

N. B. Nelson, B. B. Prézelin, “Chromatic light effects and physiological modeling of absorption properties of Heterocapsa pygmaea (=Glenodinium sp.),” Mar. Ecol. Prog. Ser. 63, 37–46 (1990).
[CrossRef]

1988

T. T. Bannister, “Estimation of absorption coefficients of scattering suspensions using opal glass,” Limnol. Oceanogr. 33, 607–615 (1988).
[CrossRef]

1987

A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton: a simplified theoretical approach,” Deep-Sea Res. 34, 1093–1105 (1987).
[CrossRef]

H. Haardt, H. Maske, “Specific in vivo absorption coefficient of chlorophyll a at 675 nm,” Limnol. Oceanogr. 32, 608–619 (1987).
[CrossRef]

1986

1983

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

1981

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust, J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

1978

K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
[CrossRef]

1967

1964

W. L. Butler, “Absorption spectroscopy in vivo: theory and application,” Annu Rev. Plant Physiol. 15, 451–470 (1964).
[CrossRef]

1962

1959

K. Shibata, “Spectrophotometry of translucent biological materials: opal glass transmission method,” Methods Biochem. Anal. 7, 77–109 (1959).
[CrossRef]

Bannister, T. T.

T. T. Bannister, “Estimation of absorption coefficients of scattering suspensions using opal glass,” Limnol. Oceanogr. 33, 607–615 (1988).
[CrossRef]

Bidigare, R. R.

N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
[CrossRef]

Bricaud, A.

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

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

Butler, W. L.

W. L. Butler, “Absorption spectroscopy in vivo: theory and application,” Annu Rev. Plant Physiol. 15, 451–470 (1964).
[CrossRef]

W. L. Butler, “Absorption of light by turbid materials,” J. Opt. Soc. Am. 52, 292–299 (1962).
[CrossRef]

Carr, K. F.

K. F. Carr, “Integrating sphere flux calculations,” in 1990 Catalog (Labsphere, Inc., North Sutton N.H., 1990), pp. 84–86.

Crocker, K. M.

K. M. Crocker, University of California, Santa Barbara, Santa Barbara, Calif. 93106 (personal communication, 1992).

Daniel, K. J.

K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
[CrossRef]

Goebel, D. G.

Haardt, H.

H. Haardt, H. Maske, “Specific in vivo absorption coefficient of chlorophyll a at 675 nm,” Limnol. Oceanogr. 32, 608–619 (1987).
[CrossRef]

Incropera, F. P.

K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust, J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, 1983).

Maske, H.

H. Haardt, H. Maske, “Specific in vivo absorption coefficient of chlorophyll a at 675 nm,” Limnol. Oceanogr. 32, 608–619 (1987).
[CrossRef]

Mitchell, B. G.

B. G. Mitchell, “Algorithms for determining the absorption coefficient of aquatic particulates using the quantitative filter technique (QFT),” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt Instrum. Eng.1302, 137–148 (1990).

Morel, A.

A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton: a simplified theoretical approach,” Deep-Sea Res. 34, 1093–1105 (1987).
[CrossRef]

A. Bricaud, A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25, 571–580 (1986).
[CrossRef] [PubMed]

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

Nelson, N. B.

N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
[CrossRef]

N. B. Nelson, B. B. Prézelin, “Chromatic light effects and physiological modeling of absorption properties of Heterocapsa pygmaea (=Glenodinium sp.),” Mar. Ecol. Prog. Ser. 63, 37–46 (1990).
[CrossRef]

Petzold, T. L.

T. L. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref.72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

Prézelin, B. B.

N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
[CrossRef]

N. B. Nelson, B. B. Prézelin, “Chromatic light effects and physiological modeling of absorption properties of Heterocapsa pygmaea (=Glenodinium sp.),” Mar. Ecol. Prog. Ser. 63, 37–46 (1990).
[CrossRef]

Prieur, L.

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

Privoznik, K. G.

K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
[CrossRef]

Roos, A.

Shibata, K.

K. Shibata, “Spectrophotometry of translucent biological materials: opal glass transmission method,” Methods Biochem. Anal. 7, 77–109 (1959).
[CrossRef]

Annu Rev. Plant Physiol.

W. L. Butler, “Absorption spectroscopy in vivo: theory and application,” Annu Rev. Plant Physiol. 15, 451–470 (1964).
[CrossRef]

Appl. Opt.

Aust, J. Mar. Freshwater Res.

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust, J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

Deep-Sea Res.

A. Morel, “Chlorophyll-specific scattering coefficient of phytoplankton: a simplified theoretical approach,” Deep-Sea Res. 34, 1093–1105 (1987).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

K. G. Privoznik, K. J. Daniel, F. P. Incropera, “Absorption, extinction, and phase function measurements for algal suspensions of Chlorella pyrenoidosa,” J. Quant. Spectrosc. Radiat. Transfer 20, 345–352 (1978).
[CrossRef]

Limnol. Oceanogr.

H. Haardt, H. Maske, “Specific in vivo absorption coefficient of chlorophyll a at 675 nm,” Limnol. Oceanogr. 32, 608–619 (1987).
[CrossRef]

T. T. Bannister, “Estimation of absorption coefficients of scattering suspensions using opal glass,” Limnol. Oceanogr. 33, 607–615 (1988).
[CrossRef]

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

Mar. Ecol. Prog. Ser.

N. B. Nelson, B. B. Prézelin, “Chromatic light effects and physiological modeling of absorption properties of Heterocapsa pygmaea (=Glenodinium sp.),” Mar. Ecol. Prog. Ser. 63, 37–46 (1990).
[CrossRef]

N. B. Nelson, B. B. Prézelin, R. R. Bidigare, “Phytoplankton light absorption and the package effect in California coastal waters,” Mar. Ecol. Prog. Ser. 94, 217–277 (1993).
[CrossRef]

Methods Biochem. Anal.

K. Shibata, “Spectrophotometry of translucent biological materials: opal glass transmission method,” Methods Biochem. Anal. 7, 77–109 (1959).
[CrossRef]

Other

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge U. Press, Cambridge, 1983).

K. M. Crocker, University of California, Santa Barbara, Santa Barbara, Calif. 93106 (personal communication, 1992).

SLM Instruments, DW-2000 UV-VIS Spectrophotometer: Operator's Manual (SLM-Aminco, Urbana, Ill., 1987).

K. F. Carr, “Integrating sphere flux calculations,” in 1990 Catalog (Labsphere, Inc., North Sutton N.H., 1990), pp. 84–86.

T. L. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref.72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).

B. G. Mitchell, “Algorithms for determining the absorption coefficient of aquatic particulates using the quantitative filter technique (QFT),” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt Instrum. Eng.1302, 137–148 (1990).

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Figures (7)

Fig. 1
Fig. 1

Schematic drawing of the DW-2000 spectrophotometer sample compartment in (a) the split-beam mode, and (b) with the integrating sphere installed. In the split-beam operation the sample and reference beams are of the same wavelength, and they pass alternately through the sample and reference cuvettes. With the integrating sphere, scanning sample and fixed-wavelength reference beams pass alternately through the single cuvette. A second (blank) scan is necessary to calculate the absorption of the sample.

Fig. 2
Fig. 2

Flow chart schematic of the Monte Carlo integrating sphere simulation. Round-cornered boxes indicate procedures, and square-cornered boxes represent possible locations of the photon. During the simulation the vector angles (θ in the XY plane and ϕ in the YZ plane) and the step length are used to determine the Cartesian coordinates of the photon (x, y, z) after each movement. For each simulated photon, the simulation records whether the photon was absorbed or transmitted, the total distance traveled through the cuvette, the number of interactions with the sphere surface, and the number of scattering events.

Fig. 3
Fig. 3

A, Response of the integrating sphere signal (OD at 663 nm) to changes in the absorbing sample volume. Arrows indicate the region where the sample is of sufficient volume to intercept the measuring beam partially. B, Changes in optical density caused by settling of a 5-mg suspension of MgCO3 in 90% acetone over a 5-min period, in the split-beam mode and in the integrating sphere. C, Response of the integrating sphere signal to changes in absorption of nonscattering solutions of chlorophyll a in 90% acetone. For clarity, only 20% of the total data points are shown.

Fig. 4
Fig. 4

OD at 663 nm measured in the split-beam mode (open circles) and in the integrating sphere (solid circles) for A, the variable concentration of MgCO3 suspended in 90% acetone and B, the variable concentration of MgCO3 suspended in a solution of 5 mg/L pure chlorophyll a in 90% acetone.

Fig. 5
Fig. 5

Results of the Monte Carlo simulation (zero scattering, variable absorption, 10,000 photons/run) of the integrating sphere. Input OD (representing true absorption) is shown on the X axis, and simulated output OD (representing absorption measured in the integrating sphere) is shown on the Y axis. The curves represent separate simulations using the actual integrating sphere configuration (solid diamonds) and with the baffle moved 9 mm closer to the cuvette (open diamonds) plotted over the empirical data (open circles, data from Fig. 3C).

Fig. 6
Fig. 6

Results of the Monte Carlo simulation (zero scattering, variable absorption, 10,000 photons/run) of the integrating sphere. A, Ratio of x (simulated integrating sphere absorption coefficient, in inverse meters to a (input absorption coefficient, in inverse meters, open circles) and the ratio of simulated mean path through the cuvette to geometric path through the cuvette (open diamonds). B, Fraction of total absorbed photons absorbed on the first pass through the cuvette (i.e., before any interaction with the sphere surface or the baffle).

Fig. 7
Fig. 7

Absorption spectra measured in the split-beam mode (x, in inverse meters) and in the integrating sphere (a, in inverse meters) for a seawater sample from a diatom bloom off the coast of southern California. Both spectra were corrected for concentration, and the integrating sphere spectrum was corrected for signal amplification by using Eq. (4). B, Estimated scattering spectrum of the sample (b, in inverse meters) calculated by using Eq. (3).

Equations (4)

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x ( λ ) = a ( λ ) + b ( λ ) ( 1 ) ,
= 2 π 0 θ a β ( θ ) sin θ d θ ,
b ( λ ) = x ( λ ) a ( λ ) 1 ,
OD d = 0.3477 ( ± 0.017 ) OD s + 0.8119 ( ± 0.034 ) OD s 2 ,

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