Recursive solution of light scattering problem
                 for multi-layered axisymmetric particles

                            V.G.Farafonov
          St.Petersburg University of Aerocosmic Instrumentation
                   St.Petersburg, 190000, Russia

                                and

                             V.B.Il'in
           Astronomical Institute, St.Petersburg University,
                    St.Petersburg, 198504, Russia


                              ABSTRACT

Light scattering by inhomogeneous (layered) particles is the problem
that often arises in optics of the atmosphere and ocean, biophysics,
astrophysics, etc [1]. To solve it, one usually applies the model
of concentric spheres or infinitely long circular cylinders.
However, real particles have a finite size and a non-spherical shape.

Recently, Gurwich et al. [2] have made an attempt to develop a recursive
solution of the problem for multi-layered spheroidal particles.
The authors were basing on the solutions for homogeneous (and core/mantle)
spheroids [3-4] and used the approach that had given satisfactory results
for multi-layered spheres [5] and infinite circular cylinders [6].
For spheroids, they obtained infinite systems of {\it non-linear}
algebraic equations, from which the coefficients of potential expansions
in terms of the spheroidal wave-functions could be obtained.
However, it looks rather difficult to realize this algorithm
as a computer code and to get numerical results.

In this paper we suggest a new recursive solution of the problem of
light scattering by multi-layered axisymmetric particles.
The algorithm utilizes the solution of the problem
for homogeneous axisymmetric particles developed in [7-9]
and has the following features (see also [10]).

The scalar potentials for each layer are represented by sums
of two potentials -- the first one is not singular at the
origin of the coordinate system, while the second one satisfies
the condition at infinity.
These new potentials are equal to surface integrals including only
the potentials for the previous layer.

The potentials of the internal field in the core (the innermost layer)
of a particle can be obtained from solution of integral equations
that are analogous to the equations for homogeneous particles.
The potentials of the scattered radiation are also determined
in a way similar to that for homogeneous particles.

All the potentials and the Green function are expanded in terms of the
spherical wave-functions.
After the substitution of the expansions into the integral equations,
one gets infinite systems of {\it linear} algebraic equations
for the expansion coefficients of the internal radiation in the core
and the scattered radiation.
The characteristics of radiation scattered by a multi-layered
particle are calculated from the same formula as for homogeneous
particles (see, e.g., [7]).

We have created a computer code realizing the described approach.
Test computations have demonstrated its high efficiency
for particles of various shapes and structure.

The work was partly supported by INTAS (grant 99/652).


                          References:

 1. Bohren C.F., Huffman D.R. (1983) Absorption and scattering of light
    by small particles. J.Wiley & Sons, NY.
 2. Gurwich I., Kleiman M., Shiloah N., Cohen A. (2000) Appl. Opt. 39, 470.
 3. Voshchinnikov N.V., Farafonov V.G. (1993) Astrophys. Space Sci. 204, 19.
 4. Farafonov V.G., Voshchinnikov N.V.,  Somsikov V.V. (1996) Appl.Opt. 35,
    5412.
 5. Wu Z.S., Wang Y.P. (1991) Radio Sci. 26, 1393.
 6. Gurwich I., Shiloah N., Kleiman M. (1999) J. Quant. Spectr. Rad. Transf.
    63, 217.
 7. Farafonov V.G., Il'in V.B., Henning T. (1999) J. Quant. Spectr. Rad.
    Transf. 63, 205.
 8. Farafonov V.G., Il'in V.B. (2000) in: W.L.Smith & Yu.M.Timofeyev (eds.),
    IRS 2000: Current Problems in Atmospheric Radiation, A.Deepack Publ.,
    Hampton, VA.
 9. Farafonov V.G., Il'in V.B. (2000) Opt. Spectr., submitted.
10. Farafonov V.G. (2000) Opt. Spectr., submitted.