The Extended Soft Approximation for Spherical Particles

                         A.Y. Perelman
           St.Petersburg State Forest Technical Academy
                              and
                      N.V. Voshchinnikov
     Astronomy Department and Sobolev Astronomical Institute,
                   St.Petersburg University


                           Abstract

The soft approximation (SA) gives the possibility to obtain the different
optical characteristics of particles from the common point of view [1].
As for the Mie theory, they are expressed in terms of the scattering
coefficients $a_n$ and $b_n$. The SA is based on the assumption that the
denominators of $a_n$ and $b_n$ can be replaced by some expressions
independent of the subscript $n$ and, therefore, the SA cannot reproduce
the ripple structure arising because of the partial-wave resonances.
However, the SA reproduces quite well the behaviour of smoothed extinction
curves calculated  using the Mie theory for particles with refractive indices
up to 2.0 and more [2].

The SA can also serve as the source to derive the known approximations on the
basis of the formal mathematical calculations, and allows some conventual
approximations to be corrected by means of the utilization of their definitions
more carefully. In particular, within the framework of the Rayleigh-Gans theory,
the approximation for the extinction efficiency factor of absorbing particles
has been improved on the account of essential term which was earlier neglected.

The extended soft particles approximation (ESA) is constructed by the procedure
which may be considered as a specific form of analytical continuation of the SA.
This continuation is based on the short wavelength asymptotic of the considered
optical characteristics. The range of applicability of the ESA is studied in
detail for real and complex refractive indices.

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

References:

[1] A.Y. Perelman, Extinction and scattering by soft particles,
                   Applied Optics, 30, 475, 1991.

[2] A.Y. Perelman, N.V. Voshchinnikov, On the accuracy of the S-approximation
                   for dielectric particles, Journal of Quantitative
                   Spectroscopy and Radiative Transfer, 2000, submitted.