  When light from a distant source object, like a galaxy or a supernova,
travels towards us, it is deflected by massive objects that lie on its path.
When the mass density of the deflecting object exceeds a certain threshold,
multiple, highly distorted images of the source are observed. This strong
gravitational lensing effect has so far been treated as a model-fitting
problem. Using the observed multiple images as constraints yields a
self-consistent model of the deflecting mass density and the source object. As
several models meet the constraints equally well, we develop a lens
characterisation that separates data-based information from model assumptions.
The observed multiple images allow us to determine local properties of the
deflecting mass distribution on any mass scale from one simple set of
equations. Their solution is unique and free of model-dependent degeneracies.
The reconstruction of source objects can be performed completely
model-independently, enabling us to study galaxy evolution without a lens-model
bias. Our approach reduces the lens and source description to its data-based
evidence that all models agree upon, simplifies an automated treatment of large
datasets, and allows for an extrapolation to a global description resembling
model-based descriptions.
