Image Rotation from weak Lensing
  Forthcoming radio surveys will include full polarisation information, which
can be potentially useful for weak lensing observations. We propose a new
method to measure the (integrated) gravitational field between a source and the
observer, by looking at the angle between the morphology of a radio galaxy and
the orientation of the polarisation. For this we use the fact that, while the
polarisation of a photon is parallel transported along the photon geodesic, the
infinitesimal shape of the source, e.g. its principal axis in the case of an
ellipse, is Lie transported. As an example, we calculate the rotation of the
shape vector with respect to the polarisation direction which is generated by
lensing by a distribution of foreground Schwarzschild lenses. For radio
galaxies, the intrinsic morphological orientation of a source and its polarised
emission are correlated. It follows that observing both the polarisation and
the morphological orientation provides information on both the unlensed source
orientation and on the gravitational potential along the line of sight.
