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.