Faraday Rotation Measure Synthesis for Magnetic Fields of Galaxies
  RM Synthesis was recently developed as a new tool for the interpretation of
polarized emission data in order to separate the contributions of different
sources lying on the same line of sight. Until now the method was mainly
applied to discrete sources in Faraday space (Faraday screens). Here we
consider how to apply RM Synthesis to reconstruct the Faraday dispersion
function, aiming at the further extraction of information concerning the
magnetic fields of extended sources, e.g. galaxies. The main attention is given
to two related novelties in the method, i.e. the symmetry argument in Faraday
space and the wavelet technique.
  We give a relation between our method and the previous applications of RM
Synthesis to point-like sources. We demonstrate that the traditional RM
Synthesis for a point-like source indirectly implies a symmetry argument and,
in this sense, can be considered as a particular case of the method presented
here. Investigating the applications of RM Synthesis to polarization details
associated with small-scale magnetic fields, we isolate an option which was not
covered by the ideas of the Burn theory, i.e. using quantities averaged over
small-scale fluctuations of magnetic field and electron density. We describe
the contribution of small-scale fields in terms of Faraday dispersion and beam
depolarization. We consider the complex polarization for RM Synthesis without
any averaging over small-scale fluctuations of magnetic field and electron
density and demonstrate that it allows us to isolate the contribution from
small-scale field.
