  We propose the novel method of ``gravitational imaging'' to detect and
quantify luminous and dark-matter substructure in gravitational-lens galaxies.
The method utilizes highly-magnified Einstein rings and arcs as sensitive
probes of small perturbations in the lens potential (due to the presence of
mass substructure), reconstructing the gravitational lens potential
non-parametrically. Numerical simulations show that the implemented algorithm
can reconstruct the smooth mass distribution of a typical lens galaxy -
exhibiting reasonable signal-to-noise Einstein rings - as well as compact
substructure with masses as low as M_sub~10^-3 M_lens, if present.
``Gravitational imaging'' of pure dark-matter substructure around massive
galaxies can provide a new window on the standard cold-dark-matter paradigm,
using very different physics than ground-based direct-detection experiments,
and probe the hierarchical structure-formation model which predicts this
substructure to exist in great abundance.
