Abstract

We evaluate the theoretical performance of a point-source integrating-cavity absorption meter (PSICAM) with Monte Carlo simulations and a sensitivity analysis. We quantify the scattering errors, verifying that they are negligible for most ocean optics applications. Although the PSICAM detector response is highly sensitive to the value of the wall reflectivity, the absorption of an unknown fluid can be accurately determined with a PSICAM if appropriate reference solution(s) are chosen. We also quantify the error that results if the source is not perfectly isotropic, finding that moderate amounts of source anisotropy can be tolerated provided that the detector is properly located with respect to the source.

© 2000 Optical Society of America

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References

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  1. C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
    [CrossRef]
  2. C. Moore, “In situ biochemical, oceanic, optical meters,” Sea Technol. 35, 10–16 (1994).
  3. M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
    [CrossRef]
  4. H. R. Gordon, 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]
  5. R. A. Leathers, C. S. Roesler, N. J. McCormick, “Ocean inherent optical property determination from in-water light measurements,” Appl. Opt. 38, 5096–5103 (1999).
    [CrossRef]
  6. P. Elterman, “Integrating cavity spectroscopy,” Appl. Opt. 9, 2140–2142 (1970).
    [CrossRef] [PubMed]
  7. E. S. Fry, G. Kattawar, “Measurement of the absorption coefficient of ocean water using isotropic illumination,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 142–148 (1988).
    [CrossRef]
  8. E. S. Fry, G. Kattawar, R. M. Pope, “Integrating cavity absorption meter,” Appl. Opt. 31, 2055–2065 (1992).
    [CrossRef] [PubMed]
  9. J. T. O. Kirk, “Modeling the performance of an integrating-cavity absorption meter: theory and calculations for a spherical cavity,” Appl. Opt. 34, 4397–4408 (1995).
    [CrossRef] [PubMed]
  10. J. T. O. Kirk, “Point-source integrating-cavity absorption meter: theoretical principles and numerical modeling,” Appl. Opt. 36, 6123–6128 (1997).
    [CrossRef] [PubMed]
  11. T. J. Petzold, “Volume scattering functions for selected ocean waters,” (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
  12. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).
  13. L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  14. C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters (Academic, New York, 1994).

1999 (2)

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

R. A. Leathers, C. S. Roesler, N. J. McCormick, “Ocean inherent optical property determination from in-water light measurements,” Appl. Opt. 38, 5096–5103 (1999).
[CrossRef]

1998 (2)

H. R. Gordon, 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]

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

C. Moore, “In situ biochemical, oceanic, optical meters,” Sea Technol. 35, 10–16 (1994).

1992 (1)

1970 (1)

1941 (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Bevington, P. R.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

Boynton, G. C.

Donaghay, P. L.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Elterman, P.

Fry, E. S.

E. S. Fry, G. Kattawar, R. M. Pope, “Integrating cavity absorption meter,” Appl. Opt. 31, 2055–2065 (1992).
[CrossRef] [PubMed]

E. S. Fry, G. Kattawar, “Measurement of the absorption coefficient of ocean water using isotropic illumination,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 142–148 (1988).
[CrossRef]

Gordon, H. R.

Greenstein, J. L.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Henyey, L. C.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Kattawar, G.

E. S. Fry, G. Kattawar, R. M. Pope, “Integrating cavity absorption meter,” Appl. Opt. 31, 2055–2065 (1992).
[CrossRef] [PubMed]

E. S. Fry, G. Kattawar, “Measurement of the absorption coefficient of ocean water using isotropic illumination,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 142–148 (1988).
[CrossRef]

Kirk, J. T. O.

Leathers, R. A.

McCormick, N. J.

Mobley, C. D.

C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters (Academic, New York, 1994).

Moore, C.

C. Moore, “In situ biochemical, oceanic, optical meters,” Sea Technol. 35, 10–16 (1994).

Petzold, T. J.

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

Pope, R. M.

Robinson, D. K.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

Roesler, C. S.

R. A. Leathers, C. S. Roesler, N. J. McCormick, “Ocean inherent optical property determination from in-water light measurements,” Appl. Opt. 38, 5096–5103 (1999).
[CrossRef]

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
[CrossRef]

Sullivan, J. M.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Twardowski, M. S.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Zaneveld, J. R. V.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Appl. Opt. (6)

Astrophys. J. (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Oceanic Technol. 16, 691–707 (1999).
[CrossRef]

Limnol. Oceanogr. (1)

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43, 1649–1660 (1998).
[CrossRef]

Sea Technol. (1)

C. Moore, “In situ biochemical, oceanic, optical meters,” Sea Technol. 35, 10–16 (1994).

Other (4)

C. D. Mobley, Light and Water. Radiative Transfer in Natural Waters (Academic, New York, 1994).

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

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

E. S. Fry, G. Kattawar, “Measurement of the absorption coefficient of ocean water using isotropic illumination,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 142–148 (1988).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Percentage scattering errors in P 0 and 1/(1 - ρP s ) for isotropic and Petzold scattering when the probabilities of source-to-wall photon survival (P 0) and wall-to-wall photon survival (P s ) are computed with Eqs. (5) and (6) with a = 1.0 m-1 and r = r 0 = 0.05 m.

Fig. 2
Fig. 2

Percentage error in the PSICAM response predicted by Eqs. (2), (4), and (6) that is due to the presence of isotropic scattering for r = 0.05 m and ρ = 0.99.

Fig. 3
Fig. 3

Percentage error in the PSICAM response predicted by Eqs. (2), (4), and (6) that is due to the presence of seawater scattering for r = 0.05 m and ρ = 0.99.

Fig. 4
Fig. 4

Seminormalized sensitivity coefficient (T)(∂a/∂T) (m-1) versus a (m-1).

Fig. 5
Fig. 5

Sensitivity coefficient ∂a/∂ρ (m-1) versus a (m-1) for r = 0.05 m.

Fig. 6
Fig. 6

Sensitivity coefficient ∂a/∂r (m-2) versus a (m-1) when ρ is known for r = 0.05 m and ρ = 0.99.

Fig. 7
Fig. 7

Sensitivity coefficient ∂a/∂a ref when ρ is known for r = 0.05 m and ρ = 0.99.

Fig. 8
Fig. 8

Sensitivity coefficient ∂a/∂a A for r = 0.05 m and ρ = 0.99.

Fig. 9
Fig. 9

Seminormalized sensitivity coefficient (T AB )(∂a/∂T AB ) versus a (m-1) for r = 0.05 m and ρ = 0.99.

Fig. 10
Fig. 10

Percentage error in the PSICAM detector response as a function of detector location for anisotropic light sources. The detector position is given by angle θ d with respect to the forward direction of the source. The source angular distribution is the Henyey–Greenstein function with asymmetry factors g = 0, 0.2, and 0.5. The results shown are for a = 0.3 m-1, b = 0.7 m-1, r = 0.05 m, and ρ = 0.99.

Tables (2)

Tables Icon

Table 1 Sensitivity Coefficients for the Determination of a with Eqs. (6) and (10) when ρ is Knowna

Tables Icon

Table 2 Sensitivity Coefficients for the Determination of a with Eqs. (6)–(10) when ρ is Unknowna

Equations (40)

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TAB=F0AF0B=NCANCB.
NC=P0+P0ρPs+P0ρ2Ps2+=P0n=0ρPsn=P0/1-ρPs.
TAB=P0A1-ρPsBP0B1-ρPsA.
P0a, r=exp-ar,
P0a, r0=exp-ar0,
Psa, r=12a2r21-exp-2ar2ar+1.
Psa, r=1-43ar+ar2-815ar3+ 2-2arn1n+1!-1n+2!+
TAB=exp-r0aA-aB1-ρPsaB, r1-ρPsaA, r,
ρ=TAB exp-aBr0-exp-aAr0TAB exp-aBr0PsaA, r-exp-aAr0PsaB, r.
T=exp-r0a-aref1-ρPsaref, r1-ρPsa, r.
TaaT=-2a2r2-ρ1-2ar+1exp-2ar2a3r3-ρ2a2r2+3ar+2exp-2ar-2+ar,
aρ=-T/ρT/a.
ar=-T/rT/a, aaref=-T/arefT/a.
Δa=aT2ΔT2+aρ2Δρ2+ar2Δr2+aaref2Δaref21/2.
Δa=0.710.004862+160.0022+3.2×0.00012+2.10.00521/2 m-1=1.2×10-5+1.0×10-3+1.0×10-7+1.1×10-41/2 m-1=0.034 m-1.
Δa=0.710.004862+0+0+1×0.00521/2 m-1=0.0061 m-1.
Δa=T aT2ΔTT2+aaref2Δaref2+TABaTAB2ΔTABTAB2+aaA2ΔaA21/2.
Δa=0.350.012+1.20.0052+0.56×0.012+4.20.00521/2 m-1=1.2×10-5+3.6×10-5+3.1×10-5+4.4×10-41/2 m-1=0.023 m-1.
NC=ρP0Ps1-ρPs,
s=-1/cln1-,
Φ=2π.
μs=1-2.
β˜g; μs14π1-g21+g2-2gμs3/2,
Cμs=12μs11-g21+g2-2gμs3/2=1-g22g11-g-11+g2-2gμs1/2.
μs=2g+1-2g-2+22g+g2-2g3-2g2+2g32-g-1+2g2.
Cμs=,
αβγ=αγ/1-γ2-β/1-γ2αβγ/1-γ2α/1-γ2β-1-γ20γ×αsβsγs, γ2<1,
αβγ=signγαsβsγs, γ2=1,
αs=sinΘcosΦ, βs=sinΘsinΦ, γs=cosΘ.
T4Ta, aref, r, ρ.
aT4a, aref, r, ρ=1T4a,
aarefa, aref, r, ρ=-T4arefT4a, BR.
T6Ta, aref, r, aA, aB, TAB.
Tra, aref, r, aA, aB, ρ=T6r=T4r+T4ρρr,
ara, aref, r, aA, aB, ρ=-T6/r/T6/a=-T4r+T4ρρrT4/(a,
aaAa, aref, r, aA, aB, ρ=-T6/aA/T4/a=-T4/ρρ/aA/T4/a,
aaBa, aref, r, aA, aB, ρ=-T6/aB/T4/a=-T4/ρρ/aB/T4/a,
aTABa, aref, r, aA, aB, ρ=-T6/TAB/T4/a=-T4/ρρ/TAB/T4/a,
T5=Ta, aref, r, aA, TAB,
aarefa, aref, r, aA, ρ=-T5arefT4a=T4aref+T4ρρarefT4a,

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