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. The observables we 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 the parameter values that are compatible with the measurements, thus allowing fast scans of a large variety 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 each case and demonstrate that the parameters obtained by our approach for known parametric lens models agree well with those found by detailed model fitting.