# CAOSP abstracts, Volume: 34, No.: 3, year: 2004

*Author(s):* Kocifaj, M.
*Journal:* Contributions of the Astronomical Observatory Skalnaté Pleso, vol. 34, no. 3, p. 141-156.
*Date:* 10/2004
*Title:* Interstellar dust extinction problem: benchmark of (semi)analytic approaches and regularization method
*Keyword(s):* interstellar dust, extinction, inverse problems
*Pages:* 141 -- 156

**Abstract:**
Interstellar extinction curves have a typical so-called bump at a constant wavelength of
about 220 nm. This indicates that cosmic dust particles distributed in space must be
quite small in comparison with the wavelengths of visible radiation. The well-known Mie theory,
or its approximations, are usually employed to simulate an interaction of electromagnetic
radiation with such particles. However, the conventional Mie theory is applicable only for
spherical and homogeneous particles, and, as known, the spherical geometry is very rare in
space. Utilization of any approximation in solving the inverse problem for interstellar
extinction may therefore lead to questionable results. To evaluate possible differences
between retrieved size distributions, we performed a benchmark of three various techniques.
The first one is based on the anomalous diffraction approximation and offers a semi-analytical
solution. The profile of an extinction curve is scalable: a simple parametrization uses
the modified gamma function as a substitute for the real distribution. The second approach
extends the first one, but the distribution function is not expressed in an analytical
form. The final profile of size distribution is computed using Mellin's transform of kernel
of the integral equation. The third solution follows the modified Tikhonov's regularization
and can be applied to both spherical and non-spherical particles. There is no requirement
placed on a distribution function. It is shown that direct consequences of the above discussed
approximations are: i) underestimation of the amount of large particles, ii) a reduced value
of the modal radius of the retrieved size distribution, and iii) quite narrow distrubution
functions.

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