| Model |
parameters |
LS method |
free codes |
speed |
accuracy |
range of applic. |
main purpose |
usage |
| H o m o g e n e o u s p a r t i c l e s |
| spheres |
x, m |
SVM (Mie theory) [1,2] |
many |
exteremely high |
very large |
no limits in x,m |
As a first approximation for scatterers of any shape,
structure, etc. |
most often |
| infinitely long circular cylinders |
x, m, alpha |
SVM [3-5] |
a few |
exteremely high |
very large |
no limits in x,m,alpha |
As a first approximation when one wants to learn possible effects of
nonsphericity of scatterers. |
seldom |
| prolate/oblate spheroids |
x, a/b, m, alpha |
SVM [6] / EBCM [16,17] |
several |
good |
very large / large |
certain limits in x,m
(see, e.g., our fig.) |
Study of shape effects
since spheroids with different semiaxis ratio
present a set of 2D shapes from needles to disks
(incl. spheres) |
often |
| Chebyshev particles |
x, e, n, m, alpha |
EBCM [16,17] |
several |
good |
large (?) |
certain limits in x,m |
Study of complex shape effects. |
seldom |
| superellipsoids |
a, b, c, e, n, orient.angles |
GMT [15] |
one |
|
|
certain limits in x,m |
Possible study of 3D shape effects. |
-- |
| C o r e - m a n t l e p a r t i c l e s |
| spheres |
xc, mc, xm, mm |
SVM [7-9] |
many |
very high |
very large |
no limits in x,m (?) |
Study of the simplest case
of inhomogeneity - two-layered particle. |
somethimes |
| infinitely long circular cylinders |
xc, mc, xm, mm, alpha |
SVM [10] |
DOP |
very high |
very large |
no limits in x,m (?) |
Study of the simplest case of inhomogeneity and nonsphericity -
two-layered non-spherical particle. |
very seldom |
| prolate/oblate confocal spheroids |
xc, a/bc, mc, xm, a/bm, mm, alpha |
SVM [11] / EBCM [13] |
a few |
good |
very large / large |
certain limits in x,m |
Study of the shape effects in the simplest case
of inhomogeneity - a set of two-layered non-spherical particles. |
seldom |
| M u l t i - l a y e r e d p a r t i c l e s |
| spheres |
{xi, mi}, i=1,N |
SVM [12] |
a few |
high |
very large |
some limits in x,m (?) |
Study of the inhomogeneity,
e.g. in the case of several well-mixed materials. |
seldom |
| axisymmetric particles |
alpha, {xi, a/bi, mi}, i=1,N |
EBCM [13] |
DOP |
|
|
certain limits in x,m |
Possible study of shape and structure effects. |
-- |
| I n h o m o g e n e o u s p a r t i c l e s |
| any shape particles with inclusions |
fi, ... |
EMT + basic LS method |
|
that of the LS method |
usually very low |
limited in x |
Consideration of shape and inhomogeneity effects. |
rather often |
| (fractal) aggregates |
x, m, D, rho, N, orient.angles |
DDA [14] |
a few |
very low |
low |
certain limits in x,m |
Study of structure and inhomogeneity effects. |
sometimes |
Parameters:
-- the size parameter x=2 pi r / lambda,
where r is the radius (for spheroids, e.g.,
the radius of the equivolume sphere), lambda
the wavelength of incident radiation;
-- m=n+ki is the complex rafractive index
(see corresponding
section
for more details);
-- alpha is the radiation incidence angle (usually between
a symmetry axis and the wavevector);
-- the aspect ratio a/b, where a,b
are the major and minor semiaxes;
-- The axisymmetric Chebyshev particles have the surface equation
R(theta) = r (1 + e cos(n*theta)), where r,e,n
are free parameters;
-- fi is the volume fraction of inclusions;
-- for the meaning of the parameters x, m, D, rho, N
see here;
-- for the meaning of the parameters a,b,c,e,n
see [15].
References:
[1] Mie G. (1908) Ann. Phys. 25, 377.
[2] Debye P. (1909) Ann. Phys. 30, 57.
[3] Lord Rayleigh (1881) Phil. Mag. 12, 81.
[4] Wait J.R. (1955) Can. J. Phys. 33, 189.
[5] Lind A.C., Greenberg J.M. (1966) J. Appl. Phys. 37, 3195.
[6] Asano S., Yamamoto G. (1975) Appl. Opt. 14, 29.
[7] Aden A.L., Kerker M. (1951) J. Appl. Phys. 22, 1242.
[8] Shifrin K.S. (1952) Izv. Acad. Nauk USSR N2, 15.
[9] Guettler A. (1952) Ann. Phys. 6, 65.
[10] Shah G.A. (1972) Mon. Not. Roy. Astr. Soc. 148, 93.
[11] Onaka T. (1980) Ann. Tokyo Obs. 18, 1.
[12] Wu Z.P., Wang Y.P. (1991) Radio Sci. 26, 1393.(?)
[13] Peterson B., Stroem S. (1974) Phys. Rev. D 10, 2670.
[14] Purcell E.M., Pennypacker C.R. (1973) Astrophys.J. 186, 705.
[15] Wriedt Th. (2002) Part. Part. Syst. Charact. 19, 256.
[16] Waterman (1971) Phys. Rev. D 3, 825.
[17] Barber P., Yeh C. (1975) Appl. Opt. 14, 2864.
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