Abstract

The numerical evaluation of surface integrals is the most time-consuming part of the extended boundary condition method (EBCM) for calculating the T matrix. An efficient implementation of the method is presented for homogeneous particles with discrete geometric symmetries and is applied to regular polyhedral prisms of finite length. For such prisms, an efficient quadrature scheme for computing the surface integrals is developed. Exploitation of these symmetries in conjunction with the new quadrature scheme leads to a reduction in CPU time by 3 orders of magnitude from that of a general EBCM implementation with no geometry-specific adaptations. The improved quadrature scheme and the exploitation of symmetries account for, respectively, 1 and 2 orders of magnitude in the total reduction of the CPU time. Test results for scattering by rectangular parallelepipeds and hexagonal plates are shown to agree well with corresponding results obtained by use of the discrete-dipole approximation. A model application for various polyhedral prisms is presented.

© 2001 Optical Society of America

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References

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  1. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  2. N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
    [CrossRef] [PubMed]
  3. D. W. Mackowski, M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
    [CrossRef]
  4. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [CrossRef]
  5. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
    [CrossRef]
  6. P. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).
  7. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  8. P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
    [CrossRef]
  9. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
    [CrossRef]
  10. T. Rother, “General aspects of solving Helmholtz’s equation underlying eigenvalue and scattering problems in electromagnetic wave theory,” J. Electromagn. Waves Appl. 13, 867–888 (1999).
    [CrossRef]
  11. T. Rother, K. Schmidt, “The discretized Mie-formalism for plane wave scattering on dielectric objects with non-separable geometries,” J. Quant. Spectrosc. Radiat. Transfer 55, 615–625 (1996).
    [CrossRef]
  12. T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
    [CrossRef]
  13. T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
    [CrossRef]
  14. T. Wriedt, A. Doicu, “Novel software implementation of the T-matrix method for arbitrary configurations of single and clusters of composite nonspherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.
  15. H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
    [CrossRef]
  16. S. Havemann, A. J. Baran, “Extention of the T-matrix formulation to general 3d homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Stattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 107–110.
  17. B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 105, 685–697 (1993).
    [CrossRef]
  18. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  19. B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 131–144.
    [CrossRef]
  20. P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
    [CrossRef]
  21. W. Sun, Q. Fu, Z. Chen, “Finite-difference time domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999).
    [CrossRef]
  22. M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
    [CrossRef] [PubMed]
  23. Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
    [CrossRef]
  24. I. A. Zagorodnov, R. P. Tarasov, “Finite groups in numerical solution of electromagnetic scattering problems on non-spherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 99–102.
  25. C.-R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
    [CrossRef] [PubMed]
  26. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Point group symmetries in electromagnetic scattering,” J. Opt. Soc. Am. A 16, 853–865 (1999).
    [CrossRef]
  27. F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to particles with sharp edges: a comparison of two surface integration approaches,” Appl. Opt. (to be published). LP1734D.
  28. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  29. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  30. D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).
  31. T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
    [CrossRef]
  32. M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
    [CrossRef]
  33. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
    [CrossRef]

2000 (1)

1999 (3)

1998 (4)

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

1997 (1)

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

1996 (6)

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T-matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism for plane wave scattering on dielectric objects with non-separable geometries,” J. Quant. Spectrosc. Radiat. Transfer 55, 615–625 (1996).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
[CrossRef]

P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

1994 (1)

1993 (2)

M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
[CrossRef] [PubMed]

B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 105, 685–697 (1993).
[CrossRef]

1992 (1)

1991 (1)

1987 (1)

1979 (1)

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

1975 (1)

1970 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

1965 (1)

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

Baran, A. J.

S. Havemann, A. J. Baran, “Extention of the T-matrix formulation to general 3d homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Stattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 107–110.

Barber, P.

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

P. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bishop, D. M.

D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).

Chen, Z.

Comberg, U.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

Doicu, A.

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

T. Wriedt, A. Doicu, “Novel software implementation of the T-matrix method for arbitrary configurations of single and clusters of composite nonspherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 105, 685–697 (1993).
[CrossRef]

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 131–144.
[CrossRef]

Flatau, P. J.

Fu, Q.

Goodman, J. J.

B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 105, 685–697 (1993).
[CrossRef]

Havemann, S.

S. Havemann, A. J. Baran, “Extention of the T-matrix formulation to general 3d homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Stattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 107–110.

Herb, P.

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hu, C.-R.

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

Kahnert, F. M.

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to particles with sharp edges: a comparison of two surface integration approaches,” Appl. Opt. (to be published). LP1734D.

Kattawar, G. W.

Khlebtsov, N. G.

Lacis, A. A.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

Laitinen, H.

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Liou, K. N.

Lumme, K.

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Macke, A.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

Mackowski, D. W.

Mano, Y.

Mishchenko, M. I.

Parkin, M. E.

Rossow, W. B.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

Rother, T.

T. Rother, “General aspects of solving Helmholtz’s equation underlying eigenvalue and scattering problems in electromagnetic wave theory,” J. Electromagn. Waves Appl. 13, 867–888 (1999).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism for plane wave scattering on dielectric objects with non-separable geometries,” J. Quant. Spectrosc. Radiat. Transfer 55, 615–625 (1996).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
[CrossRef]

Schmidt, K.

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism for plane wave scattering on dielectric objects with non-separable geometries,” J. Quant. Spectrosc. Radiat. Transfer 55, 615–625 (1996).
[CrossRef]

Schulz, F. M.

Stamnes, J. J.

Stamnes, K.

Sun, W.

Tarasov, R. P.

I. A. Zagorodnov, R. P. Tarasov, “Finite groups in numerical solution of electromagnetic scattering problems on non-spherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 99–102.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

Waterman, P. C.

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

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

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

Wriedt, T.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

T. Wriedt, A. Doicu, “Novel software implementation of the T-matrix method for arbitrary configurations of single and clusters of composite nonspherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.

Yang, P.

Yeh, C.

Zagorodnov, I. A.

I. A. Zagorodnov, R. P. Tarasov, “Finite groups in numerical solution of electromagnetic scattering problems on non-spherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 99–102.

Appl. Opt. (8)

N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
[CrossRef] [PubMed]

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
[CrossRef]

W. Sun, Q. Fu, Z. Chen, “Finite-difference time domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999).
[CrossRef]

M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
[CrossRef] [PubMed]

Y. Mano, “Exact solution of electromagnetic scattering by a three-dimensional hexagonal ice column obtained with the boundary-element method,” Appl. Opt. 39, 5541–5546 (2000).
[CrossRef]

C.-R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

Astrophys. J. (1)

B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 105, 685–697 (1993).
[CrossRef]

J. Appl. Phys. (1)

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

J. Electromagn. Waves Appl. (2)

T. Rother, “General aspects of solving Helmholtz’s equation underlying eigenvalue and scattering problems in electromagnetic wave theory,” J. Electromagn. Waves Appl. 13, 867–888 (1999).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
[CrossRef]

J. Geophys. Res. (2)

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

J. Mod. Opt. (1)

T. Wriedt, A. Doicu, “Formulations of the extended boundary condition method for three-dimensional scattering using the method of discrete sources,” J. Mod. Opt. 45, 199–213 (1998).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transfer (3)

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism for plane wave scattering on dielectric objects with non-separable geometries,” J. Quant. Spectrosc. Radiat. Transfer 55, 615–625 (1996).
[CrossRef]

H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

Proc. IEEE (1)

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

Other (8)

P. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).

S. Havemann, A. J. Baran, “Extention of the T-matrix formulation to general 3d homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Stattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 107–110.

T. Wriedt, A. Doicu, “Novel software implementation of the T-matrix method for arbitrary configurations of single and clusters of composite nonspherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 131–144.
[CrossRef]

D. M. Bishop, Group Theory and Chemistry (Dover, Mineola, N.Y., 1993).

F. M. Kahnert, J. J. Stamnes, K. Stamnes, “Application of the extended boundary condition method to particles with sharp edges: a comparison of two surface integration approaches,” Appl. Opt. (to be published). LP1734D.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

I. A. Zagorodnov, R. P. Tarasov, “Finite groups in numerical solution of electromagnetic scattering problems on non-spherical particles,” in Light Stattering by Nonspherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chýlek, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 99–102.

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Figures (10)

Fig. 1
Fig. 1

Essential symmetry elements of a pentahedral prism.

Fig. 2
Fig. 2

Illustration of the surface parameterization r(θ, ϕ), its projection ρ(ϕ) into the xy plane, distance a from the center to the corner of the polygonal facets, and height h of the prism.

Fig. 3
Fig. 3

Periodicity of the surface parameterization of a hexagon.

Fig. 4
Fig. 4

Additional symmetry of the D 3h group compared with the C 3h group.

Fig. 5
Fig. 5

Symmetry-reduced integration range of a regular hexahedral finite prism.

Fig. 6
Fig. 6

Top facet of a trihedral prism, illustrating method C. The polar quadrature points are marked on the horizontal axis. For each polar quadrature point the range of the azimuthal integration is shown: For those polar quadrature points that lie inside the inscribed circle, the corresponding ϕ integration extends from 0 to π/3. For those polar quadrature points θ that lie outside this circle, the corresponding ϕ integration extends from 0 to ϕ c (θ).

Fig. 7
Fig. 7

Comparison of Mueller matrix elements of a cube (as explained in the text) computed with the DDM (circles) and the EBCM implementation reported here (solid curves).

Fig. 8
Fig. 8

Same as Fig. 7 but for a hexahedral prism (as explained in the text).

Fig. 9
Fig. 9

Mueller matrix elements for trihedral prisms (solid curves), tetrahedral prisms (dashed curves), and hexahedral prisms (dotted curves).

Fig. 10
Fig. 10

Same as Fig. 9, but for decahedral prisms (solid curves), 15-hedral prisms (dashed curves), and 30-hedral prisms (dotted curves).

Tables (5)

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Table 1 CPU Time (in Seconds) for a Cubea

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Table 2 CPU Time (in Seconds) for a Hexahedral Prisma

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Table 3 CPU Time (in Seconds) for a Cube for Computing Matrices RgQ and Q and for the Whole EBCM Computationa

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Table 4 CPU Time (in Seconds) for a Hexahedral Prisma

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Table 5 CPU Time (in Seconds) for Three Hexahedral Prisms of Finite Length Computed with Methods B and C

Equations (52)

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Ei=n=1m=-nnan,m1Mn,m1kr+an,m2Nn,m1kr,
Es=n=1m=-nnpn,m1Mn,m3kr+pn,m2Nn,m3kr,
Eint=n=1m=-nncn,m1Mn,m1ksr+cn,m2Nn,m1ksr.
a=Q·c,
p=-Rg Q·c,
p=T·a,
T=-Rg Q·Q-1.
Q1,1=J1,2+nsJ2,1,
Q1,2=J2,2+nsJ1,1,
Q2,1=J1,1+nsJ2,2,
Q2,2=J2,1+nsJ1,2,
Jn,m,n,m1,1=--1mSMn,-m3kr×Mn,m1ksr·nˆdS,
Jn,m,n,m1,2=--1mSNn,-m3kr×Mn,m1ksr·nˆdS,
Jn,m,n,m2,1=--1mSMn,-m3kr×Nn,m1ksr·nˆdS,
Jn,m,n,m2,2=--1mSNn,-m3kr×Nn,m1ksr·nˆdS.
Jn,m,n,m1,2=-1m+m dndn02πdϕexpim-mϕ×0πdθunkrjnksrr2b0,mnθb0,mnθ×sinθ+mmd0,mnθd0,mnθ/sin θ+nn+1k hnkrjnksr×rθ d0,mnθb0,mnθsin θ+im rϕ d0,mnθd0,mnθ/sin θ.
Tn,m,n,mk,k=0 |m-m|0, N, 2N, 3N,
Tn,m,n,mk,k=0 n+n+m+m+k+k odd,
Tn,-m,n,-mk,k=-1k+kTn,m,n,mk,k.
Tn,-m,n,-mk,k=-1m+m+k+kTn,m,n,mk,k
02πdϕ expim-mϕfr, rθ, rϕ=N 02π/Ndϕ expim-mϕf r, rθ, rϕ.
d0,mnθ=-1n+md0,mnθ-π,
b0,mnθ=--1n+mb0,mnθ-π.
0πdθ=20π/2dθ
rθ, 2π/N-ϕ=rθ, ϕ,rθ, 2π/N-ϕ/θ=rθ, ϕ/θ,rθ, 2π/N-ϕ/ϕ=-rθ, ϕ/ϕ.
02π/Ndϕr2θ, ϕfrθ, ϕexpim-mϕ=2 0π/Ndϕr2θ, ϕfrθ, ϕcosm-mϕ,
02π/Ndϕ rθ, ϕθ frθ, ϕexpim-mϕ=2 0π/Ndϕ rθ, ϕθ frθ, ϕcosm-mϕ,
02π/Ndϕ rθ, ϕϕ frθ, ϕexpim-mϕ=2i 0π/Ndϕrθ, ϕϕ frθ, ϕsinm-mϕ.
ϕ 0, 2π/N,ϕ 2π/N, 4π/N,
ϕ 2π-2π/N, 2π
θ 0, θ0ϕ,θ θ0ϕ, π-θ0ϕ,
θ π-θ0ϕ, π,
0γdϕsinm-mϕ=1/m-m1-cosm-mγmm0m=m,
0γdϕcosm-mϕ=1/m-msinm-mγmmγm=m.
Rθ=h tan θ
tan θm=ρπ/Nh/2=2ahcosπ/N-cot α sinπ/N1-sin2π/Nsin2ααπN12 cosπ/Nα=πN.
Rθ=ρϕc.
sin4 ϕc+A0tan θsin3 ϕc+B02tan2 θ-2sin2 ϕc+C0tan θsin ϕc+D01-2tan2 θ=0,
rθ, ϕ=h/2cos θθ 0, θ0ϕρϕsin θθ θ0ϕ, π2.
ρϕ=a cos ϕ-cot α sin ϕ1-sin2 ϕ/sin2 αϕ 0, 2πN{α}a2 cos ϕϕ=α
α=πN-2/2N
tan θ0ϕ=ρϕ/h/2,
rθ, ϕθ=h sin θ2 cos2 θθ 0, θ0ϕ-ρθ, ϕsin θ tan θθ θ0ϕ, π2,
rθ, ϕϕ=0θ 0, θ0ϕ1sin θdρϕdϕθ θ0ϕ, π2,
dρϕdϕ=a2ρϕ/asin ϕ cos ϕ-sin2 αsin ϕ+cot α cos ϕsin2 α-sin2 ϕϕ 0, 2πN{α}tan ϕρϕϕ=α.
rθπ-θ1=-rθθ1,
rθϕ1+2k-π=rθϕ1,
rϕπ-θ1=rϕθ1,
rϕϕ1+2k-π=rϕϕ1,
θ10, π/2,
ϕ1[0, 2π/N),
k1, 2,, N-1.

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