Abstract

A fast graphics processing unit implementation of the finite-difference time-domain model was used to determine the computational effort required to accurately characterize the mean scattering functions of randomly orientated aspherical particles. The influence of the number of randomized rotational positions on the accuracy of the mean scattering phase function curve was appraised. In general, multiplying the number of orientations by 100 gives increased accuracy of factor 10. Dependent on particle shape, certain regions of the phase function were insensitive to particle orientation. In addition, an error in a key previous publication on scattering by aspherical particles was identified.

© 2013 Optical Society of America

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References

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2012

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2012).
[CrossRef]

2011

J. Hedley, “Modelling the optical properties of suspended particulate matter of coral reef environments using the finite difference time domain (FDTD) method,” Geo. Mar. Lett. 32, 173–182 (2011).
[CrossRef]

2009

T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. 114, C09015 (2009).
[CrossRef]

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

2004

2000

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]

1999

1998

H. Mühlenweg and E. Dan Hirleman, “Laser diffraction spectroscopy: influence of particle shape and a shape adaptation technique,” Part. Part. Syst. Charact. 15, 163–169 (1998).
[CrossRef]

1990

A. Adjas, J.-P. Masse, and L. Montaggioni, “Fine-grained carbonates in nearly closed reef environments: Mataiva and Takapoto atolls, Central Pacific Ocean,” Sed. Geol. 67, 115–132 (1990).
[CrossRef]

1985

E. Akkermans and R. Maynard, “Weak localisation of waves,” J. Phys. Lett. 46, 1045–1053 (1985).
[CrossRef]

Adjas, A.

A. Adjas, J.-P. Masse, and L. Montaggioni, “Fine-grained carbonates in nearly closed reef environments: Mataiva and Takapoto atolls, Central Pacific Ocean,” Sed. Geol. 67, 115–132 (1990).
[CrossRef]

Agrawal, Y. C.

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]

Akkermans, E.

E. Akkermans and R. Maynard, “Weak localisation of waves,” J. Phys. Lett. 46, 1045–1053 (1985).
[CrossRef]

Allen, A. G.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Bohren, C. F.

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

Chen, Z.

Dan Hirleman, E.

H. Mühlenweg and E. Dan Hirleman, “Laser diffraction spectroscopy: influence of particle shape and a shape adaptation technique,” Part. Part. Syst. Charact. 15, 163–169 (1998).
[CrossRef]

Dubovik, O.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2012).
[CrossRef]

Fu, Q.

Hedley, J.

J. Hedley, “Modelling the optical properties of suspended particulate matter of coral reef environments using the finite difference time domain (FDTD) method,” Geo. Mar. Lett. 32, 173–182 (2011).
[CrossRef]

Horwell, C. J.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Huffman, D. R.

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

Kattawar, G. W.

King, M. D.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2012).
[CrossRef]

Kostadinov, T. S.

T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. 114, C09015 (2009).
[CrossRef]

Maritorena, S.

T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. 114, C09015 (2009).
[CrossRef]

Martin, R. S.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Masse, J.-P.

A. Adjas, J.-P. Masse, and L. Montaggioni, “Fine-grained carbonates in nearly closed reef environments: Mataiva and Takapoto atolls, Central Pacific Ocean,” Sed. Geol. 67, 115–132 (1990).
[CrossRef]

Mather, T. A.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Maynard, R.

E. Akkermans and R. Maynard, “Weak localisation of waves,” J. Phys. Lett. 46, 1045–1053 (1985).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Mobley, C. D.

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

Montaggioni, L.

A. Adjas, J.-P. Masse, and L. Montaggioni, “Fine-grained carbonates in nearly closed reef environments: Mataiva and Takapoto atolls, Central Pacific Ocean,” Sed. Geol. 67, 115–132 (1990).
[CrossRef]

Mühlenweg, H.

H. Mühlenweg and E. Dan Hirleman, “Laser diffraction spectroscopy: influence of particle shape and a shape adaptation technique,” Part. Part. Syst. Charact. 15, 163–169 (1998).
[CrossRef]

Oppenheimer, C.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Pottsmith, H. C.

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]

Power, M.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Pyle, D. M.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Siegel, D. A.

T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. 114, C09015 (2009).
[CrossRef]

Sun, W.

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Tsanev, V. I.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Ward, E. P. W.

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

Wiscombe, W. J.

Yang, P.

Appl. Opt.

Geo. Mar. Lett.

J. Hedley, “Modelling the optical properties of suspended particulate matter of coral reef environments using the finite difference time domain (FDTD) method,” Geo. Mar. Lett. 32, 173–182 (2011).
[CrossRef]

J. Geophys. Res.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2012).
[CrossRef]

T. S. Kostadinov, D. A. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color observations,” J. Geophys. Res. 114, C09015 (2009).
[CrossRef]

R. S. Martin, T. A. Mather, D. M. Pyle, M. Power, V. I. Tsanev, C. Oppenheimer, A. G. Allen, C. J. Horwell, and E. P. W. Ward, “Size distributions of fine silicate and other particles in Masaya’s volcanic plume,” J. Geophys. Res. 114, D09217 (2009).
[CrossRef]

J. Phys. Lett.

E. Akkermans and R. Maynard, “Weak localisation of waves,” J. Phys. Lett. 46, 1045–1053 (1985).
[CrossRef]

Mar. Geol.

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]

Part. Part. Syst. Charact.

H. Mühlenweg and E. Dan Hirleman, “Laser diffraction spectroscopy: influence of particle shape and a shape adaptation technique,” Part. Part. Syst. Charact. 15, 163–169 (1998).
[CrossRef]

Sed. Geol.

A. Adjas, J.-P. Masse, and L. Montaggioni, “Fine-grained carbonates in nearly closed reef environments: Mataiva and Takapoto atolls, Central Pacific Ocean,” Sed. Geol. 67, 115–132 (1990).
[CrossRef]

Other

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

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

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

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Figures (4)

Fig. 1.
Fig. 1.

Mean phase function for the five platonic solids with 1000 repeats for circumscribed dimension [left, (a–e)] and volume [right, (f–j)] equivalent to a sphere 1 μm radius and refractive index 1.3085+i1.09×108 at a wavelength of 633 nm. Sphere Mie calculation also shown.

Fig. 2.
Fig. 2.

Phase functions for each individual randomized orientation superposed for 1000 orientations for (a) tetrahedron and (b) dodecahedron of radius 1 μm.

Fig. 3.
Fig. 3.

Coefficient of variation of the mean phase function P11(θ) from 20 sets of model runs with 10, 50, 100, 500, and 1000 randomized rotations of a tetrahedron (a) and a dodecahedron (b) of radius 1 μm, refractive index 1.3085+i1.09×108, wavelength of 633 nm. Each line represents a separate analysis and its closeness to the x axis is an estimate of model convergence achieved by the given number of random rotations.

Fig. 4.
Fig. 4.

Coefficient of variation of |S1|2 (b, d) and |S2|2 (a, c) from 20 sets of model runs with 10, 50, 100, 500, and 1000 randomized rotations of a tetrahedron (a, b) and a dodecahedron (c, d) of radius 1 μm, refractive index 1.3085+i1.09×108, wavelength of 633 nm. Each line represents a separate analysis and its closeness to the x axis is an estimate of model convergence achieved by the given number of random rotations.

Tables (1)

Tables Icon

Table 1. Radii and Grid Size Used for FDTD Modeling of the Platonic Solidsa

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

[EsEs]=eik(rz)ikr[S2S3S4S1][EiEi],
S11=12(|S1|2+|S2|2+|S3|2+|S4|2).
P11(θ)=4πk2×CscaS11(θ),

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