We present a new approach to gravitational lens massmap reconstruction. Our
massmap solutions perfectly reproduce the positions, fluxes, and shears of all
multiple images. And each massmap accurately recovers the underlying mass
distribution to a resolution limited by the number of multiple images detected.
We demonstrate our technique given a mock galaxy cluster similar to Abell 1689
which gravitationally lenses 19 mock background galaxies to produce 93 multiple
images. We also explore cases in which far fewer multiple images are observed,
such as four multiple images of a single galaxy. Massmap solutions are never
unique, and our method makes it possible to explore an extremely flexible range
of physical (and unphysical) solutions, all of which perfectly reproduce the
data given. Each reconfiguration of the source galaxies produces a new massmap
solution. An optimization routine is provided to find those source positions
(and redshifts, within uncertainties) which produce the "most physical" massmap
solution, according to a new figure of merit developed here. Our method imposes
no assumptions about the slope of the radial profile nor mass following light.
But unlike "non-parametric" grid-based methods, the number of free parameters
we solve for is only as many as the number of observable constraints (or
slightly greater if fluxes are constrained). For each set of source positions
and redshifts, massmap solutions are obtained "instantly" via direct matrix
inversion by smoothly interpolating the deflection field using a recently
developed mathematical technique. Our LensPerfect software is straightforward
and easy to use and is made publicly available via our website.Comment: 17 pages, 18 figures, accepted by ApJ. Software and full-color
version of paper available at http://www.its.caltech.edu/~coe/LensPerfect