Abstract

The physical nature of particles, such as size, shape, and composition govern their angular light scattering, which is described by the volume scattering function (VSF). Despite the fact that the VSF is one of the most important inherent optical properties, it has rarely been measured in aquatic environments since no commercial instrument exists to measure the full VSF in the field. The commonly used LISST (Laser In Situ Scattering and Transmissometry) particle sizer (Sequoia Scientific, http://www.sequoiasci.com) measures near-forward angular scattering of a laser source (λ = 670 nm) at 32 logarithmically-spaced photodetectors arranged between 0.08 and 15 degrees and inverts the data to obtain particle size distribution (PSD). In order to calibrate the LISST to provide the near-forward VSF of unknown particle suspensions, we analyzed the scattering of light by polystyrene bead suspensions of known size distributions and composition, and empirically compared it with the results of Mie theory. This (1) allowed us to obtain a set of instrument specific scaling factors needed to retrieve the magnitude of the VSF and (2) provided validation that the shape of the VSF was appropriately obtained.

© 2006 Optical Society of America

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References

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  1. C.D. Mobley, Light and Water (Academic Press, San Diego, 1994).
  2. D.J. Bogucki, J.A. Domaradzki, R.E. Ecke and C.R. Truman, "Light scattering on oceanic turbulence," Appl. Opt. 43, 5662-5668 (2004).
    [CrossRef] [PubMed]
  3. X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
    [CrossRef]
  4. E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).
  5. C.F Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, 1983).
  6. M.I. Mishchenko, L.D. Travis, and A.A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002).
  7. C.D. Mobley, L.K. Sundman, and E. Boss, "Phase function effects on oceanic light fields," Appl. Opt. 41, 1035-1050 (2002).
    [CrossRef] [PubMed]
  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(4), 563-571 (2003).
    [CrossRef]
  9. T.J. Petzold, "Volume scattering functions for selected ocean waters," Contract No. N62269-71-C-0676, UCSD, SIO Ref. 72-78 (1972).
  10. WETLabs Inc. (http://www.wetlabs.com), PO Box 518, Philomath, OR 97370.
  11. G.R. Fournier and J.L. Forand, "Analytical phase function for ocean water," in Ocean Optics XII, J.S. Jaffe, ed., Proc. SPIE 2258, 194-201 (1994).
    [CrossRef]
  12. Sequoia Scientific Inc. (http://www.sequoiasci.com), 2700 Richards Road, Suite 107, Bellevue, WA 98005.
  13. P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
    [CrossRef]
  14. Y.C. Agrawal and C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168(1-4), 89-114 (2000).
    [CrossRef]
  15. Y.C. Agrawal and P. Traykovski, "Particles in the bottom boundary layer: concentration and size dynamics through events," J. Geophys. Res. 106(C5), 9533-9542 (2001).
    [CrossRef]
  16. Y.C. Agrawal, "The optical volume scattering function: Temporal and vertical variability in the water column off the New Jersey coast," Limnol. Oceanogr. 50(6), 1787-1794 (2005).
    [CrossRef]
  17. Duke Scientific Corporation (http://www.dukesci.com), 2463 Faber Place, Palo Alto, CA 94303.
  18. X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
    [CrossRef]
  19. P.W. Holland and R.E. Welsch, "Robust regression using iteratively reweighted least-squares," Comm. Stat.: Theory Meth. A6, 813-827 (1977).
    [CrossRef]
  20. W.H. Slade, "LISST Calibration Information," (http://misclab.umeoce.maine.edu/code/lisstvsf.html).
  21. A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Neilsen, eds. (Academic, New York, 1974), pp. 1-24.
  22. K.J. Voss and E.S. Fry, "Measurement of the Mueller matrix for ocean water," Appl. Opt. 23, 4427-4439 (1984).
    [CrossRef] [PubMed]

2005

Y.C. Agrawal, "The optical volume scattering function: Temporal and vertical variability in the water column off the New Jersey coast," Limnol. Oceanogr. 50(6), 1787-1794 (2005).
[CrossRef]

2004

D.J. Bogucki, J.A. Domaradzki, R.E. Ecke and C.R. Truman, "Light scattering on oceanic turbulence," Appl. Opt. 43, 5662-5668 (2004).
[CrossRef] [PubMed]

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

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(4), 563-571 (2003).
[CrossRef]

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

2002

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

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

2001

Y.C. Agrawal and P. Traykovski, "Particles in the bottom boundary layer: concentration and size dynamics through events," J. Geophys. Res. 106(C5), 9533-9542 (2001).
[CrossRef]

2000

Y.C. Agrawal and C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168(1-4), 89-114 (2000).
[CrossRef]

1999

P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
[CrossRef]

1984

1977

P.W. Holland and R.E. Welsch, "Robust regression using iteratively reweighted least-squares," Comm. Stat.: Theory Meth. A6, 813-827 (1977).
[CrossRef]

Agrawal, Y.C.

Y.C. Agrawal, "The optical volume scattering function: Temporal and vertical variability in the water column off the New Jersey coast," Limnol. Oceanogr. 50(6), 1787-1794 (2005).
[CrossRef]

Y.C. Agrawal and P. Traykovski, "Particles in the bottom boundary layer: concentration and size dynamics through events," J. Geophys. Res. 106(C5), 9533-9542 (2001).
[CrossRef]

Y.C. Agrawal and C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168(1-4), 89-114 (2000).
[CrossRef]

Baratange, F.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

Bogucki, D.J.

Boss, E.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

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

Brock, R.S.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Domaradzki, J.A.

Ecke, R.E.

Fry, E.S.

Holland, P.W.

P.W. Holland and R.E. Welsch, "Robust regression using iteratively reweighted least-squares," Comm. Stat.: Theory Meth. A6, 813-827 (1977).
[CrossRef]

Hu, X.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Irish, J.D.

P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
[CrossRef]

Jacobs, K.M.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Johnson, B.

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

Korotaev, G.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

Latter, R.

P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
[CrossRef]

Lee, M.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

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(4), 563-571 (2003).
[CrossRef]

Lewis, M.

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

Lewis, M.R.

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(4), 563-571 (2003).
[CrossRef]

Lu, J.Q.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Mobley, C.D.

Pegau, W.S.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

Pottsmith, C.

Y.C. Agrawal and C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168(1-4), 89-114 (2000).
[CrossRef]

Shybanov, E.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

Sundman, L.K.

Traykovski, P.

Y.C. Agrawal and P. Traykovski, "Particles in the bottom boundary layer: concentration and size dynamics through events," J. Geophys. Res. 106(C5), 9533-9542 (2001).
[CrossRef]

P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
[CrossRef]

Truman, C.R.

Twardowski, M.S.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

Voss, K.J.

Welsch, R.E.

P.W. Holland and R.E. Welsch, "Robust regression using iteratively reweighted least-squares," Comm. Stat.: Theory Meth. A6, 813-827 (1977).
[CrossRef]

Yang, P.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Zhang, X.

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

Appl. Opt.

Comm. Stat.: Theory Meth.

P.W. Holland and R.E. Welsch, "Robust regression using iteratively reweighted least-squares," Comm. Stat.: Theory Meth. A6, 813-827 (1977).
[CrossRef]

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(4), 563-571 (2003).
[CrossRef]

J. Geophys. Res.

E. Boss, W.S. Pegau, M. Lee, M.S. Twardowski, E. Shybanov, G. Korotaev and F. Baratange, "The particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution," J. Geophys. Res. 109(C01014), doi:10.1029/2002JC001514 (2004).

Y.C. Agrawal and P. Traykovski, "Particles in the bottom boundary layer: concentration and size dynamics through events," J. Geophys. Res. 106(C5), 9533-9542 (2001).
[CrossRef]

Limnol. Oceanogr.

Y.C. Agrawal, "The optical volume scattering function: Temporal and vertical variability in the water column off the New Jersey coast," Limnol. Oceanogr. 50(6), 1787-1794 (2005).
[CrossRef]

X. Zhang, M. Lewis, M. Lee, B. Johnson and G. Korotaev, "The volume scattering function of natural bubble populations," Limnol. Oceanogr. 47, 1273-1282 (2002).
[CrossRef]

Mar. Geol.

P. Traykovski, R. Latter, and J.D. Irish, "A laboratory evaluation of the LISST instrument using natural sediments," Mar. Geol. 159, 355-367 (1999).
[CrossRef]

Y.C. Agrawal and C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168(1-4), 89-114 (2000).
[CrossRef]

Phys. Med. Biol.

X. Ma, J.Q. Lu, R.S. Brock, K.M. Jacobs, P. Yang, and X. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Other

C.D. Mobley, Light and Water (Academic Press, San Diego, 1994).

W.H. Slade, "LISST Calibration Information," (http://misclab.umeoce.maine.edu/code/lisstvsf.html).

A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Neilsen, eds. (Academic, New York, 1974), pp. 1-24.

Duke Scientific Corporation (http://www.dukesci.com), 2463 Faber Place, Palo Alto, CA 94303.

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

M.I. Mishchenko, L.D. Travis, and A.A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002).

T.J. Petzold, "Volume scattering functions for selected ocean waters," Contract No. N62269-71-C-0676, UCSD, SIO Ref. 72-78 (1972).

WETLabs Inc. (http://www.wetlabs.com), PO Box 518, Philomath, OR 97370.

G.R. Fournier and J.L. Forand, "Analytical phase function for ocean water," in Ocean Optics XII, J.S. Jaffe, ed., Proc. SPIE 2258, 194-201 (1994).
[CrossRef]

Sequoia Scientific Inc. (http://www.sequoiasci.com), 2700 Richards Road, Suite 107, Bellevue, WA 98005.

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Figures (7)

Fig. 1.
Fig. 1.

Incident flux, Φ i (λ) is scattered within a differential length, Δz, into a solid angle, ΔΩ. In the figure shown, the scattering is assumed to be azimuthally symmetric about the axis of the incident beam.

Fig. 2.
Fig. 2.

The LISST has four main optical elements: laser diode source (a), sample volume (d), receiving lens (f), and concentric photodetector rings (g). The laser diode and companion focusing optics (b) provides a collimated beam of incident light (λ= 670 nm, in air) to the sample volume. The sample volume is separated from the internal optics and electronics by two pressure windows (c and e).

Fig. 3.
Fig. 3.

Plot (a) shows theoretical near-forward VSF of three microsphere standards, derived using Mie theory. The VSF is normalized to beam attenuation. In (b), the raw attentuation-corrected counts, scati /τ for representative 2 and 100 μm calibrations runs are shown along with a pure water zscat. Note that for the smaller beads, near-forward detector output is essentially zero, leading to the possibility of negative values of pscati .

Fig. 4.
Fig. 4.

Plots (a)-(c) show Mie-derived VSF plotted against LISST-measured scatter for three example detector rings. Each data point corresponds to a single run from Table 2; data are marked blue, green, and red, for 2, 20, and 100 μm runs, respectively. Error bars are ±3δ〈β Miei and ±δpscati . Data are plotted along with the robust fit regression line. In (d) the derived regression coefficients χi are shown for each ring, along with error bars ± the standard error for the coefficient estimates. Plot (e) shows the mean relative absolute error in the χi model-data fit for each ring. Plot (f) shows the mean relative uncertainty in VSF estimated for all validation data (10 and 50 μm beads) compared to Mie theory.

Fig. 5.
Fig. 5.

Three example calibration results for bead runs listed in Table 2. In the left plots, Mie-derived ring-averaged VSF is plotted against calibrated LISST ring-averaged VSF. Vertical error bars are ±3δ〈β Mie i . Horizontal bars express the LISST-derived ring averaged VSF as 16th and 84th percentile pscati values multiplied by χi-3δχi and χi+3δχi, respectively, where δχi are the standard errors for the coefficient estimates. The solid line is 1:1. In the right plots, calibrated LISST ring-averaged VSF (red filled rectangles) is plotted vs. angle, along with the Mie-derived ring-averaged VSF (empty rectangles) and the continuous VSF (solid line). Dashed vertical lines denote the ring edges. Rings with low signal compared with zscat are not shown.

Fig. 6.
Fig. 6.

The effects of including absorption in Mie simulations for 2 and 100 μm microsphere standards. Note that absorbing and non-absorbing cases for the 2 μm beads are indistinguishable in the plot.

Fig. 7.
Fig. 7.

Magnitude of polarization factor, |P(Ψ)| = |S 12(Ψ)/S 11(Ψ)| for the microsphere standards, derived from Mie theory.

Tables (2)

Tables Icon

Table 1. Particle size standards used in calibration experiments. μ D , δ D , and σ D are the mean diameter, uncertainty in mean diameter, and standard deviation of microsphere particle size distribution, respectively [17].

Tables Icon

Table 2. Microsphere runs considered in the present analysis. nLISST is the number of scans recorded (at 1 Hz) from the LISST for each run. cLISST (670) and δcLISST (670) are the median and relative error of beam attenuation at 670 nm obtained from the LISST during the run. The number concentration of particles, N 0 [m-3], is derived from the LISST attenuation measurements (N 0 = cLISST /c Mie ). The calibration coefficients for the detector rings are determined based on a selection of 2, 20, and 100 μm runs where δcLISST /cLISST < 0.1, marked (•). Runs marked (✓) were used to validate the calibration coefficients.

Equations (18)

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β ( λ , ψ , ϕ ) = lim ΔΩ 0 lim Δ z 0 [ Φ S ( λ , ψ , ϕ ) Φ i ( λ ) ΔΩΔ z ] .
b ( λ ) = 4 π β ( λ , ψ , ϕ ) d Ω = 2 π 0 π β ( λ , ψ ) sin ( ψ ) .
c s c a t i = ( s c a t i τ z s c a t i ) d c a l i ,
pscat i = cscat i ( ref ref 0 ) ( π ϕ Δz ( ψ i + 1 2 ψ i 2 ) ) 1 ,
ψ i = sin 1 ( sin ( 200 ( i 1 ) 32 ψ min ( air ) ) m w ) .
m p ( λ ) = 1.5725 + 0.0031080 λ 2 + 0.00034779 λ 4
N ( D ) = N 0 N ˜ ( D ) = N 0 ( σ D 2 π ) 1 exp [ ( D μ D ) 2 2 σ D 2 ] ,
c Mie = 0 N 0 N ˜ ( D ) C ext d D .
c Mie = c Mie N 0 = 0 N ˜ ( D ) C ext dD .
S 11 ( ψ ) = 1 2 S 1 ( ψ ) 2 + 1 2 S 2 ( ψ ) 2 ,
β ˜ ( ψ ) = S 11 ( ψ ) 2 π 0 π S 11 ( ψ ) sin ( ψ ) d ψ .
β Mie ( ψ ) = 0 N 0 N ˜ ( D ) β ˜ ( ψ ) C sca d D ,
β Mie ( ψ ) = β Mie ( ψ ) N 0 = 0 N ˜ ( D ) β ˜ ( ψ ) C sca d D .
β Mie i = ψ i ψ i + 1 β Mie ( ψ ) sin ψ d ψ ψ i ψ i + 1 sin ψ d ψ .
β Mie i = c LISST β Mie i c Mie
δ β Mie i β Mie i = δ c LISST c LISST + δ β Mie i β Mie i + δ c Mie c Mie ,
χ i = β Mie i pscat i .
median ( β Mie i χ i pscat i β Mie i ) .

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