Метод Т-матриц / Wriedt-superellipsoids-PartPartSystCharact-2002
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Part. Part. Syst. Charact. 19 (2002) 256 ± 268 |
Fig. 20: Shape of smooth (left) and rough (right) particles.
Fig. 21: Oriention-averaged differential scattering cross-section of smooth and rough particles, 1728 orientations, Nmax $ 20 Mmax $ 17, 20480 faces, M $ 1 5 $ 628 31 nm
6 Conclusions
An efficient way for computing scattering by nonaxisymmetric particles in the framework of the null-field method with discrete sources has been presented. The superellipsoid has been introduced to represent a wide range of realistic particle shapes. Additionally, reading a triangular surface patch model of a scattering particle has been implemented in the computational procedure.
Numerical experiments have been performed for superellipsoids representing a rounded dielectric cube and some realistically shaped particles. It has been demonstrated that this method is very well suited to compute the T-matrix for non-axisymmetric particles with an overall dimension of 4 m with a desktop computer. A Windows 9X program including graphical user interface for computing scattering by a superellipsoid is available from our web site [51].
The program has mainly been developed to investigate the effect of particle shape with various kind of methods and instruments in optical particle characterization such as intensity-based optical particle counters, intensity ratioing technique, visibility technique, phase Doppler anemometry, diffraction type of instruments, static light scattering, etc.
7 Appendix
The block elements of matrices A B and A0 are given by
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A11 |
$ S |
n 1 |
12 |
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1 |
A |
$ S |
n |
21 |
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1 |
A |
$ S |
n |
22 |
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1 |
A |
$ S |
n |
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3 # M n 1 3 |
dS |
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3 # M n 1 3 dS |
28 |
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3 # |
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1 |
3 |
dS |
! " |
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3 |
M n |
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1 |
3 |
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# M n dS
B11 $ jk2s
S
B12 $ jk2s
S
B21 $ jk2s
S
B22 $ jk2s
S
n 1 N 1 # M n 1
n 1 N 1 # M n 1
n 1 M 1 # M n 1
n 1 M 1 # M n 1
M 1 dS
M 1 dS
!29"
N 1 dS
N 1 dS
A011 |
$ S |
n M1 3 # n N1 3 dS |
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12 |
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1 |
3 |
1 |
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3 |
dS |
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A0 |
$ S |
n N |
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# n M |
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30 |
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21 |
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1 |
3 |
1 |
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3 |
dS |
! " |
A0 |
$ S |
n M |
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# n N |
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22 |
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1 |
3 |
1 |
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3 |
dS |
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A0 |
$ S |
n N |
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# n M |
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respectively. Here, M is the refractive index and is given
by M |
$ |
i s |
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8 Acknowledgement
We acknowledge support of this work by the Deutsche Forschungsgemeinschaft (DFG).
9 Symbols and Abbreviations
a, b, c |
bounds in x, y, z of the superellipsoid |
!a0 b0" |
expansion coefficients of the incident |
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field |
Dmn |
normalization constant |
enorth-south roundedness of superellip-
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|
soid |
E0 Es |
incident and scattered fields |
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! |
0 |
"0 |
surface current densities |
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e h |
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!f g " |
expansion coefficients of the scattered field |
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kwavenumber
Mmn1 3 Nmn1 3 |
localized vector spherical functions |
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1 3 |
1 3 |
distributed vector spherical functions |
mn |
mn |
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Part. Part. Syst. Charact. 19 (2002) 256 ± 268 |
267 |
1ni3 1ni31n 3 1n 3
M
n S
%T&
!x y z" x
n !x"
! "
0
vi
CAD
DDA
DSCS
DOS
DSM
FDTD FORTRAN MMP POV-Ray T-matrix VIEM VRML
magnetic and electric dipoles
vector Mie potentials
refractive index
east-west roundedness of superellipsoid particle surface
transition matrix cartesian coordinate position vector Green function Euler angles angular coordinates permittivity
wavelength in vacuum permeability
vertex points on particle surface
computer aided design discrete dipole approximation
differential scattering cross section disk operating system
discrete sources method finite difference time domain formular translator
multiple multipole program persistance of vision raytracer transition matrix
volume integral equation method virtual reality modelling language
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