**2.5. Scattering of Light by Small Particles:
An Essential Tool for Dust Studies**

Our knowledge about dust grains is mainly inferred from
their interaction with starlight: a grain in the line
of sight between a distant star and the observer reduces
the starlight by a combination of scattering and absorption;
the absorbed energy is then re-radiated in the IR.
For a non-spherical grain, the light of distant stars
is polarized as a result of differential extinction for
different alignments of the electric vector of the radiation.
Therefore, to model the observed interstellar extinction,
scattering, absorption, polarization and IR emission properties,
knowledge of the optical properties (extinction, absorption
and scattering cross sections) of interstellar dust is essential.
This requires knowledge of the optical constants of
the interstellar dust materials [i.e., the complex index of refraction
*m*() =
*m*^{'}()
- *i m*^{"}()],
and the dust sizes and shapes. Phrasing this differently,
to infer the size, morphology, and chemical
composition of interstellar dust, an important aspect
of the modelling of interstellar grains involves
the computation of extinction, absorption and scattering
cross sections of particles comprised of candidate materials
and in comparison with astronomical data.

During the recent years, dramatic progress has been made in measuring the complex refractive indices of cosmic dust analogues, e.g. by the Jena Group (Henning & Mutschke 2000) and the Naples Group (Colangeli et al. 1999). Interstellar particles would in general be expected to have non-spherical, irregular shapes. However, our ability to compute scattering and absorption cross sections for nonspherical particles is extremely limited. So far, exact solutions of scattering problems exist only for bare or layered spherical grains ("Mie theory"; Mie 1908; Debye 1909), infinite cylinders (Lind & Greenberg 1966), and spheroids (Asano & Yamamoto 1975; Asano & Sato 1980; Voshchinnikov & Farafonov 1993). For grains with sizes much smaller than the wavelength of the incident radiation, the dipole approximation can be used to evaluate cross sections for bare or coated spheroidal grains (van de Hulst 1957; Gilra 1972; Draine & Lee 1984; Bohren & Huffman 1983). The "T-matrix" (transition matrix) method, originally developed by Barber & Yeh (1975) and recently substantially extended by Mishchenko, Travis, & Mackowski (1996), is able to treat axisymmetric (spheroidal or finite cylindrical) grains with sizes comparable to the wavelength. The discrete dipole approximation (DDA), originally developed by Purcell & Pennypacker (1973) and recently greatly improved by Draine (1988), is a powerful technique for irregular heterogeneous grains with sizes as large as several times the wavelength. The VIEF (volume integration of electric fields) method developed by Hage & Greenberg (1990), based on an integral representation of Maxwell's equations, is physically similar to the DDA method. The microwave analog methods originally developed by Greenberg, Pedersen & Pedersen (1961) provide an effective experimental approach to complex particles. This method is still proving to be powerful (Gustafson 1999; Gustafson et al. 1999) as the needs still outstrip the capacities of computers.

Although interstellar particles are obviously non-spherical as evidenced by the observed polarization of starlight, the assumption of spherical shapes (together with the Bruggeman or the Maxwell-Garnett effective medium theories for inhomogeneous grains; Bohren & Huffman 1983) is usually sufficient in modelling the interstellar absorption, scattering and IR emission. For IR polarization modelling, the dipole approximation for spheroidal grains is proven to be successful in many cases. The DDA method is highly recommended for studies of inhomogeneous (e.g. coated) grains and irregular grains such as cometary, interplanetary, and protoplanetary dust particles.