Abstract

We discuss, test, and compare two surface integration approaches that have been proposed for applying the extended boundary condition method (EBCM) to particles with sharp edges. One is based on approximating surface parameterization by a smooth function. By investigating the accuracy of this approach we find a quantitative condition for the radius of curvature of the approximate particle surface at the edge. The second approach is based on a special quadrature scheme for performing surface integration in the EBCM. For the simple test case of a cubic particle we find that the numerical advantages of the second method outweigh those of the first method, resulting in an overall reduction of computation time by a factor of 2. We conclude that the second method is preferable to the first when one is dealing with regularly shaped particles, for which the special quadrature scheme is reasonably simple to implement, and with particles with a relatively small number of sharp edges.

© 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. 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]
  3. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [Crossref] [PubMed]
  4. M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
    [Crossref]
  5. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [Crossref]
  6. M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 37, 1626–1629 (1998).
  7. W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” NASA Ref. Publ.1157, (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).
  8. 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]
  9. H. Laitinen, K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transfer 60, 325–334 (1998).
    [Crossref]
  10. T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
    [Crossref]
  11. 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]
  12. S. Havemann, A. J. Baran, “Extension of the T-matrix formulation to general 3D homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Scattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 107–110.
  13. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [Crossref]
  14. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
    [Crossref]
  15. P. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).
  16. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [Crossref] [PubMed]
  17. P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
    [Crossref]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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 Scattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.
  23. B. T. Draine, J. J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
    [Crossref]
  24. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [Crossref]
  25. 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]
  26. 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]
  27. 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]
  28. D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
    [Crossref] [PubMed]
  29. 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]
  30. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  31. 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]
  32. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).
  33. J. Ding, L. Xu, “Convergence of the T-matrix approach for randomly oriented, nonabsorbing, nonspherical Chebyshev particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 163–174 (1999).
    [Crossref]

2000 (1)

1999 (3)

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]

J. Ding, L. Xu, “Convergence of the T-matrix approach for randomly oriented, nonabsorbing, nonspherical Chebyshev particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 163–174 (1999).
[Crossref]

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]

1998 (5)

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 37, 1626–1629 (1998).

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

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]

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]

1997 (1)

1996 (6)

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]

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]

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]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (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]

1994 (3)

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. 405, 685–697 (1993).
[Crossref]

1991 (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, “Extension of the T-matrix formulation to general 3D homogeneous dielectric particles: examples of exact calculations for hexagonal ice columns and plates,” in Light Scattering 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).

Carlson, B. E.

Chen, Z.

Comberg, U.

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

Ding, J.

J. Ding, L. Xu, “Convergence of the T-matrix approach for randomly oriented, nonabsorbing, nonspherical Chebyshev particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 163–174 (1999).
[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 Scattering by Nonspherical Particles: Halifax Contributions (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. 405, 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. 405, 685–697 (1993).
[Crossref]

Havemann, S.

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

Hill, S. C.

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

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).

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.

Mackowski, D. W.

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]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[Crossref]

Mano, Y.

Mishchenko, M. I.

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 37, 1626–1629 (1998).

D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[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]

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]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[Crossref]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[Crossref]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[Crossref] [PubMed]

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]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[Crossref]

Mugnai, A.

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” NASA Ref. Publ.1157, (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

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.

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).

Stamnes, J. J.

Stamnes, K.

Sun, W.

Travis, L. D.

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]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[Crossref]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[Crossref]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[Crossref] [PubMed]

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).

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]

Wielaard, D. J.

Wiscombe, W. J.

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” NASA Ref. Publ.1157, (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

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 Scattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.

Xu, L.

J. Ding, L. Xu, “Convergence of the T-matrix approach for randomly oriented, nonabsorbing, nonspherical Chebyshev particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 163–174 (1999).
[Crossref]

Yang, P.

Yeh, C.

Appl. Opt. (9)

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]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[Crossref] [PubMed]

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 37, 1626–1629 (1998).

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]

D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[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]

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. 405, 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. 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 (4)

J. Quant. Spectrosc. Radiat. Transfer (5)

J. Ding, L. Xu, “Convergence of the T-matrix approach for randomly oriented, nonabsorbing, nonspherical Chebyshev particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 163–174 (1999).
[Crossref]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (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]

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]

Opt. Commun. (1)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[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 (7)

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).

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]

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 Scattering by Nonspherical Particles: Halifax Contributions (U.S. Army Research Laboratory, Adelphi, Md., 2000), pp. 83–86.

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

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

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of publications,” NASA Ref. Publ.1157, (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

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Figures (4)

Fig. 1
Fig. 1

Computational error of the first Mueller-matrix element for an approximate cube with smooth edges: left, as a function of the radius of curvature at the edges at a fixed refractive index and right, as a function of refractive index for a fixed radius of curvature.

Fig. 2
Fig. 2

Cross sections in the θ = π/2 plane through approximate cubes of various radii of curvature at the edges. The three approximate cubes correspond to an expansion order in relation (22) of N = 24, 52, and 180 from left to right.

Fig. 3
Fig. 3

Positions of the azimuthal quadrature points in methods A and B (as explained in the text).

Fig. 4
Fig. 4

Elements of the Mueller matrix calculated with the method of Laitinen and Lumme (circles) and the EBCM implementation reported in this paper (solid curves) for a cube of side length kl = 10 and a refractive index of 1.5 + 0.005i.

Tables (1)

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Table 1 CPU Time (in seconds) for a Cube of Side Length kl for Methods A and B

Equations (51)

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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.
an,mk=n=1m=-nnk=12 Qn,m,n,mk,kcn,mk,
pn,mk=-n=1m=-nnk=12 Rg Qn,m,n,mk,kcn,mk,
pn,mk=n=1m=-nnk=12 Tn,m,n,mk,kan,mk,
a=Q·c,
p=-Rg Q·c,
p=T·a,
T=-RgQ·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,
rθ, ϕ=rθ, ϕxˆ sin θ cos ϕ+yˆ sin θ sin ϕ+zˆ cos θ
=rˆrθ, ϕ,
Jn,m,n,m1,1=--1m02πdϕ 0πdθMn,-m3krθ, ϕ×Mn,m1ksrθ, ϕ·rθ×rϕ,
rθ, ϕa00+n=1Nm=0n an,md0,mnθcos mϕ,
xϕ=rπ/2, ϕ,
κs=dtsds
ts=dxsds
s=0ϕdxϕdϕdϕ
Rc=x2+x23/2x2+2x2-xx,
δN=0πdΘM11Θ; RcN0πdΘM11Θ; Rc-1×100%,
|m|kRc2.0δ,
rθ, ϕ=l2 cos θ0θθ0ϕρϕ; lsin θθ0ϕθπ/2,
rθ, ϕ+nπ/2=rθ, ϕ and n=1, 2, 3
rπ-θ, ϕ=rθ, ϕ θ, ϕ,
ρϕ; l=l cos ϕ-sin ϕ1-2 sin2 ϕϕπ/4l2 cos ϕϕ=π/4
tan θ0ϕ=ρϕ/l/2.
xi=b-a2 xi+b+a2,
wi=b-a2 wi.
δN=0πdΘM11NΘ0πdΘM11N-1Θ-1×100%,
nˆdS=rθ×rϕdθdϕ=rˆr2 sin θ-θˆr sin θ rθ-ϕˆr rϕdθdϕ,
Mn,m3kr, θ, ϕ=-1mdnhnkrCn,mθexpimϕ,
Nn,m3kr, θ, ϕ=-1mdnnn+1kr hnkrPn,mθ+unkrBn,mθexpimϕ,
Bn,mθ=θˆb0,mnθ+ϕˆ imsin θ d0,mnθ,
Cn,mθ=θˆ imsin θ d0,mnθ-ϕˆb0,mnθ,
Pn,mθ=rˆd0,mnθ,
b0,mnθ=ddθ d0,mnθ,
unx=1xddxxhnx,
dn=2n+14πnn+11/2.
Jn,m,n,m1,1=--1m+midndn02πdϕ expim-mϕ×0πdθhnkrjnksrr2md0,mnθb0,mnθ+mb0,mnθd0,mnθ,
Jn,m,n,m1,2=-1m+mdndn02πdϕ expim-mϕ×0πdθunkrjnksrr2b0,mnθb0,mnθ×sin θ+mmd0,mnθd0,mnθ/sin θ+nn+1k hnkrjnksr×rθ d0,mnθb0,mnθsin θ+im×rϕ d0,mnθd0,mnθ/sin θ,
Jn,m,n,m2,1=--1m+mdndn02πdϕ expim-mϕ×0πdθnn+1ks hnkrjnksr×rθ b0,mnθd0,mnθsin θ-im rϕ d0,mnθd0,mnθ/sin θ+hnkrvnksrr2b0,mnθb0,mnθsin θ+mmd0,mnθd0,mnθ/sin θ,
Jn,m,n,m2,2=--1m+mdndn02πdϕ expim-mϕ×0πdθiunkrvnksrr2md0,mnθb0,mnθ+mb0,mnθd0,mnθ+nn+1ks×unkrjnksrim rθ d0,mnθd0,mnθ+rϕ b0,mnθd0,mnθ+nn+1k hnkrvnksrim rθ d0,mnθd0,mnθ-rϕ d0,mnθb0,mnθ.
vnx=1xddxxjnx.

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