  It is shown which properties of a strong gravitational lens can in principle
be recovered from observations of multiple extended images when no assumptions
are made about the deflector or sources. The mapping between individual
multiple images is identified as the carrier of information about the
gravitational lens and it is shown how this information can be extracted from a
hypothetical observation. The derivatives of the image map contain information
about convergence ratios and reduced shears over the regions of the multiple
images. For two observed images, it is not possible to reconstruct the
convergence ratio and shear at the same time. For three observed images, it is
possible to recover the convergence ratios and reduced shears identically. For
four or more observed images, the system of constraints is overdetermined, but
the same quantities can theoretically be recovered.
