High resolution VLBI polarisation imaging of AGN with the Maximum
  Entropy Method
  Radio polarisation images of the jets of Active Galactic Nuclei (AGN) can
provide a deep insight into the launching and collimation mechanisms of
relativistic jets. However, even at VLBI scales, resolution is often a limiting
factor in the conclusions that can be drawn from observations. The Maximum
Entropy Method (MEM) is a deconvolution algorithm that can outperform the more
common CLEAN algorithm in many cases, particularly when investigating
structures present on scales comparable to or smaller than the nominal beam
size with "super-resolution". A new implementation of the MEM suitable for
single- or multiple-wavelength VLBI polarisation observations has been
developed and is described here. Monte Carlo simulations comparing the
performances of CLEAN and MEM at reconstructing the properties of model images
are presented; these demonstrate the enhanced reliability of MEM over CLEAN
when images of the fractional polarisation and polarisation angle are
constructed using convolving beams that are appreciably smaller than the full
CLEAN beam. The results of using this new MEM software to image VLBA
observations of the AGN 0716+714 at six different wavelengths are presented,
and compared to corresponding maps obtained with CLEAN. MEM and CLEAN maps of
Stokes $I$, the polarised flux, the fractional polarisation and the
polarisation angle are compared for convolving beams ranging from the full
CLEAN beam down to a beam one-third of this size. MEM's ability to provide more
trustworthy polarisation imaging than a standard CLEAN-based deconvolution when
convolving beams appreciably smaller than the full CLEAN beam are used is
discussed.
