Model-independent characterisation of strong gravitational lenses
  We develop a new approach to extracting model-independent information from
observations of strong gravitational lenses. The approach is based on the
generic properties of images near the fold and cusp catastrophes in caustics
and critical curves. Observables used are the relative image positions, the
magnification ratios and ellipticities of extended images, and time delays
between images with temporally varying intensity. We show how these observables
constrain derivatives and ratios of derivatives of the lensing potential near a
critical curve. Based on these measured properties of the lensing potential,
classes of parametric lens models can then easily be restricted to such
parameter values compatible with the measurements, thus allowing fast scans of
large varieties of models. Applying our approach to a representative galaxy
(JVAS B1422+231) and a galaxy-cluster lens (MACS J1149.5+2223), we show which
model-independent information can be extracted in those cases and demonstrate
that the parameters obtained by our approach for known parametric lens models
agree well with those found by detailed model fitting.
