Abstract

We present in-water forward scattering phase functions covering the angle range 0.08 to 16° for 19 narrow-sized dispersions of randomly shaped sediment grains. These dispersions cover particle size range from 1 to 20 microns. These phase functions offer a realistic alternative to Mie theory. Qualitatively, (i) the magnitude of phase functions at the smallest angles for equal size spheres and randomly shaped particles are nearly equal; (ii) the oscillations predicted by Mie theory for spheres disappear for random shaped grains, and (iii) the tendency of phase functions of large spheres to merge at large angles is also seen with randomly shaped grains. The data are also provided in tabulated form.

© 2009 Optical Society of America

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References

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  1. Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
    [CrossRef]
  2. E. Boss, W. H. Slade, M. Behrenfeld, and G. Dall'Olmo, "Acceptance angle effects on the beam attenuation in the ocean" Opt. Express 17, 1535-155 (2009).
    [CrossRef] [PubMed]
  3. Y. C. Agrawal and H. C. Pottsmith, "Instruments for particle size and settling velocity observations in sediment transport," Mar. Geol. 168, 89-114 (2000).
    [CrossRef]
  4. E. D. Hirleman, "Optimal scaling of the inverse Fraunhofer Diffraction particle sizing problem: the linear system produced by Quadrature," Part. Charact. 4, 128-133 (1987).
    [CrossRef]
  5. W. H. Slade and E. S. Boss, "Calibrated near-forward volume scattering function obtained from the LISST particle sizer," Opt. Express 14, 3602-3614 (2006).
    [CrossRef] [PubMed]
  6. H. C. Van de Hulst, Light Scattering by Small Particles, (Dover, New York, 1981), pp. 470.
  7. R. Jones, "Fraunhofer diffraction by random irregular particles" Part. Charact. 4, 123-127 (1987).
    [CrossRef]
  8. Y. C. Agrawal, "The optical volume scattering function: temporal and vertical variability in the water column off the New Jersey coast," Limnol. Oceanogr. 50, 1787-1794 (2005).
    [CrossRef]

2009 (1)

2008 (1)

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

2006 (1)

2005 (1)

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

2000 (1)

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

1987 (2)

E. D. Hirleman, "Optimal scaling of the inverse Fraunhofer Diffraction particle sizing problem: the linear system produced by Quadrature," Part. Charact. 4, 128-133 (1987).
[CrossRef]

R. Jones, "Fraunhofer diffraction by random irregular particles" Part. Charact. 4, 123-127 (1987).
[CrossRef]

Agrawal, Y. C.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

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

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

Behrenfeld, M.

Boss, E.

Boss, E. S.

Dall'Olmo, G.

Hirleman, E. D.

E. D. Hirleman, "Optimal scaling of the inverse Fraunhofer Diffraction particle sizing problem: the linear system produced by Quadrature," Part. Charact. 4, 128-133 (1987).
[CrossRef]

Jones, R.

R. Jones, "Fraunhofer diffraction by random irregular particles" Part. Charact. 4, 123-127 (1987).
[CrossRef]

Mikkelsen, O. A.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

Pottsmith, H. C.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

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

Slade, W. H.

Whitmire, A.

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

J. Geophys. Res. (1)

Y. C. Agrawal, A. Whitmire, O. A. Mikkelsen and H. C. Pottsmith, "Light scattering by random shaped particles and consequences on measuring suspended sediments by Laser Diffraction" J. Geophys. Res. 113, (2008).
[CrossRef]

Limnol. Oceanogr. (1)

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

Mar. Geol. (1)

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

Opt. Express (2)

Part. Charact. (2)

R. Jones, "Fraunhofer diffraction by random irregular particles" Part. Charact. 4, 123-127 (1987).
[CrossRef]

E. D. Hirleman, "Optimal scaling of the inverse Fraunhofer Diffraction particle sizing problem: the linear system produced by Quadrature," Part. Charact. 4, 128-133 (1987).
[CrossRef]

Other (1)

H. C. Van de Hulst, Light Scattering by Small Particles, (Dover, New York, 1981), pp. 470.

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Figures (6)

Fig. 1.
Fig. 1.

LISST-ST schematic (left). Left to right: beam from a laser diode is collimated by lens L1, passes through the scattering volume and is focused by receive lens L2. Multi-angle scattered light is sensed by ring detectors (RD), while attenuated laser beam power is measured by photo-diode XM. The layers in order of decreasing density are marked A,B, C and the particles are inserted in top layer. (right) an image of grains, 25–32 micron dia., that were sorted for illustrating shape.

Fig. 2.
Fig. 2.

CSF’s of 3 distinct sized particles according to Mie theory; red: 61.7, green: 31.9 and blue: 16.5 μm.

Fig. 3.
Fig. 3.

Phase functions as measured (solid line), and replaced values at small angles (broken line). Three sizes are shown for clarity, size increases from lowest curve to top.

Fig. 4.
Fig. 4.

Measured phase functions for random grains (.-) vs. Mie calculations (solid) for spheres of refractive index 1.5 in water; diameters: 1.1 (black), 6.7 (red), and 18.1 μm (blue).

Fig. 5.
Fig. 5.

The characteristic scattering functions of randomly shaped grains as seen by the ring detectors, for all 19 size classes. Numbers on curves indicate size classes. Sizes above 12 are sequential below the curve labeled 12.

Fig. 6.
Fig. 6.

Phase functions; numbers on top and bottom curves indicate grain diameters in microns.

Tables (1)

Tables Icon

Table - I, Phase functions (units: sr-1) of randomly shaped grains from 1.09 to 21.39 micron sizes. Top row shows size, and first column on left shows angles in degrees.

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