  We propose a new, two-stage algorithm for inverting strong gravitational
lenses. The key to the algorithm is decoupling the effects of lens
magnification and intrinsic structure in the background source in the
appearance of lensed arcs. First, the distribution of mass on the deflector
plane and the geometry of the source-deflector-observer optical system are
established. This is done by numerically simulating the lensing of light past a
parametric mass model, and adjusting the handful of model parameters to match
the positions and shapes of the observed and simulated lensed arcs. At the same
time, this determines the magnification of the background source induced by the
lensing process. The predicted magnification is then removed from the data to
reveal the intrinsic, though still distorted, background distribution of light.
After tracing each lensed ray back to the source plane, the data are combined
to produce a surface brightness distribution of the source. This two-stage
inversion scheme produces a parametric model of the deflector and a pixelized
rendering of the background source which together mimic the observed
gravitationally lensed features. We test the viability of scheme itself on a
well-studied collection of lensed objects in the galaxy-cluster MS 2137.
Confident in the algorithm, we apply it second time to predict the distribution
of mass in the galaxy-cluster MS 1455 responsible for an observed triplet of
lensed arcs. Our predictions about the lens in MS 1455 make it particularly
interesting, for a single background source is responsible for both tangential
arcs and a radial arc.
