Abstract

A T-matrix method for scattering by particles with small-scale surface roughness is presented. The method combines group theory with a perturbation expansion approach. Group theory is found to reduce CPU-time by 4–6 orders of magnitude. The perturbation expansion extends the range of size parameters by a factor of 5 compared to non-perturbative methods. An application to optically hard particles shows that small-scale surface roughness changes scattering in side- and backscattering directions, and it impacts the single-scattering albedo. This can have important implications for interpreting remote sensing observations, and for the climate impact of mineral aerosols.

© 2011 OSA

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  1. M. Kahnert, T. Nousiainen, and P. Mauno, “On the impact of small-scale surface roughness and non-sphericity on the optical properties of hematite aerosols,” J. Quant. Spectrosc. Radiat. Transfer (to be published).
  2. T. Rother, K. Schmidt, J. Wauer, V. Shcherbakov, and J.-F. Gaeyt, “Light scattering on Chebyshev particles of higher order,” Appl. Opt. 45, 6030–6037 (2006).
    [CrossRef] [PubMed]
  3. J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
    [CrossRef]
  4. M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
    [CrossRef]
  5. K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles , M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic Press, 2000), pp. 323–354.
    [CrossRef]
  6. F. M. Kahnert, J. J. Stamnes, and K. Stamnes, “Application of the extended boundary condition method to homogeneous particles with point group symmetries,” Appl. Opt. 40, 3110–3123 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. W. Greiner and J. Reinhardt, Quantum Electrodynamics (Springer, 2008).
  14. T. Rother, Electromagnetic Wave Scattering on Nonspherical Particles (Springer, 2009).
    [CrossRef]
  15. F. M. Kahnert, J. J. Stamnes, and K. Stamnes, “Application of the extended boundary condition method to particles with sharp edges: a comparison of two different surface integration approaches,” Appl. Opt. 40, 3101–3109 (2001).
    [CrossRef]
  16. O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
    [CrossRef]
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    [CrossRef]

2011

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

2010

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

T. Rother and J. Wauer, “Case study about the accuracy behavior of three different T-matrix methods,” Appl. Opt. 49, 5746–5756 (2010).
[CrossRef] [PubMed]

2007

2006

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

T. Rother, K. Schmidt, J. Wauer, V. Shcherbakov, and J.-F. Gaeyt, “Light scattering on Chebyshev particles of higher order,” Appl. Opt. 45, 6030–6037 (2006).
[CrossRef] [PubMed]

M. Kahnert, “Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering,” Opt. Commun. 265, 383–393 (2006).
[CrossRef]

2005

2003

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1019–1029 (2003).
[CrossRef]

2001

1998

1965

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Aptowicz, K.

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Auger, J.-C.

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Cairns, B.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Chang, R.

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Dlugach, J. M.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Fernandes, G.

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Gaeyt, J.-F.

Greiner, W.

W. Greiner and J. Reinhardt, Quantum Electrodynamics (Springer, 2008).

Heckenberg, N. R.

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1019–1029 (2003).
[CrossRef]

Hovenier, J. W.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Jalava, J. P.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Kahnert, F. M.

Kahnert, M.

M. Kahnert, “Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering,” Opt. Commun. 265, 383–393 (2006).
[CrossRef]

M. Kahnert, “Irreducible representations of finite groups in the T matrix formulation of the electromagnetic scattering problem,” J. Opt. Soc. Am. A 22, 1187–1199 (2005).
[CrossRef]

Kiselev, N. N.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Liu, L.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Min, M.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Muinonen, K.

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles , M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic Press, 2000), pp. 323–354.
[CrossRef]

Muñoz, O.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Nieminen, T. A.

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1019–1029 (2003).
[CrossRef]

Pan, Y.-L.

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Petrov, D.

Reinhardt, J.

W. Greiner and J. Reinhardt, Quantum Electrodynamics (Springer, 2008).

Rosenbush, V. K.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Rother, T.

Rubinsztein-Dunlop, H.

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1019–1029 (2003).
[CrossRef]

Schmidt, K.

Schulz, F. M.

Shcherbakov, V.

Shkuratov, Y. G.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Shkuvatov, Y.

Stamnes, J. J.

Stamnes, K.

Tishkovets, V. P.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

van der Zande, W. J.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Videen, G.

Volten, H.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Waters, L. B. F. M.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

Wauer, J.

Appl. Opt.

Appl. Phys. B

J.-C. Auger, G. Fernandes, K. Aptowicz, Y.-L. Pan, and R. Chang, “Influence of surface roughness on the elastic-light scattering patterns of micron-sized aerosol particles,” Appl. Phys. B 99, 229–234 (2010).
[CrossRef]

Astron. Astrophys.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, “Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile,” Astron. Astrophys. 446, 525–535 (2006).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

M. I. Mishchenko, V. P. Tishkovets, L. D. Travis, B. Cairns, J. M. Dlugach, L. Liu, V. K. Rosenbush, and N. N. Kiselev, “Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions,” J. Quant. Spectrosc. Radiat. Transfer 112, 671–692 (2011).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1019–1029 (2003).
[CrossRef]

Opt. Commun.

M. Kahnert, “Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering,” Opt. Commun. 265, 383–393 (2006).
[CrossRef]

Proc. IEEE

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Other

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles , M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic Press, 2000), pp. 323–354.
[CrossRef]

W. Greiner and J. Reinhardt, Quantum Electrodynamics (Springer, 2008).

T. Rother, Electromagnetic Wave Scattering on Nonspherical Particles (Springer, 2009).
[CrossRef]

M. Kahnert, T. Nousiainen, and P. Mauno, “On the impact of small-scale surface roughness and non-sphericity on the optical properties of hematite aerosols,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

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Figures (4)

Fig. 1
Fig. 1

2D (left) and 3D (right) Chebyshev particle with polynomial order =45 and deformation parameter ε =0.05.

Fig. 2
Fig. 2

Top row: hh (left) and vv (right) components of the polarized differential scattering cross sections of 2D Chebyshev particles in a fixed orientation, computed with the group theoretical/perturbative T-matrix approach (black) and with mieschka (red). Bottom row: hh (left) and vv (right) components computed with mieschka for two different orientations.

Fig. 3
Fig. 3

Optical properties of spheres (dashed line), and 3D Chebyshev particles with ε =0.01 (blue) and A=0.11λ (red): ω (top left), g (top right), and C bak (bottom left). Also shown is the CPU time (bottom right) for computations using group theory (circles) and not using group theory (pluses).

Fig. 4
Fig. 4

Mueller matrix elements F 11 (left column) and –F 12 /F 11 (right column) of 3D Chebyshev particles (red) and spheres (blue) with particle radius 1 μm (top row) and 6 μm (bottom row).

Tables (3)

Tables Icon

Table 1 Reciprocity Test for 2D Chebyshev Particles

Tables Icon

Table 2 Reciprocity Test for 3D Chebyshev Particles with ε = 0.01

Tables Icon

Table 3 Reciprocity Test for 3D Chebyshev Particles with A = 0.11λ

Equations (16)

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

r ( θ ) = r 0 [ 1 + ɛ cos ( θ ) ] ,
Λ = 2 π r 0
A = ɛ r 0 .
r ( θ , ϕ ) = r 0 [ 1 + ɛ cos ( θ ) cos ( ϕ ) ] ,
T = U ( g ) T U 1 ( g ) ,
[ T , U ( g ) ] = 0 , g 𝒢
T n , m , τ , n , m , τ = 0 unless | m m | = 0 , , 2 ,
T n , m , τ , n , m , τ = ( 1 ) n + n T n , m , τ , n , m , τ
T n , m , τ , n , m , τ = 0 unless ( n + m + τ + n + m + τ ) . even
T = Rg Q Q 1 .
T ( Q 0 + Δ Q ) = R g Q .
T = ( Rg Q + T Δ Q ) Q 0 1 .
T ( 0 ) = Rg Q Q 0 1 .
T ( n ) = ( Rg Q + T ( n 1 ) Δ Q ) Q 0 1 .
( d σ d Ω ) α , β ( k ^ inc , k ^ sca ) = ( d σ d Ω ) β , α ( k ^ sca , k ^ inc ) .
( d σ d Ω ) α , β ( Θ = 90 ° ; θ p = 0 ) = ( d σ d Ω ) β , α ( Θ = 270 ° ; θ p = 90 ° ) .

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