  In the strong lensing regime non-parametric lens models struggle to achieve
sufficient angular resolution for a meaningful derivation of the central
cluster mass distribution. The problem lies mainly with cluster members which
perturb lensed images and generate additional images, requiring high resolution
modeling, even though we mainly wish to understand the relatively smooth
cluster component. The required resolution is not achievable because the
separation between lensed images is several times larger than the deflection
angles by member galaxies, even for the deepest data. Here we bypass this
limitation by incorporating a simple physical prior for member galaxies, using
their observed positions and their luminosity scaled masses. This galaxy
contribution is added to a relatively coarse Gaussian pixel grid for modeling
the cluster mass distribution, extending our established WSLAP code (Diego et
al. 2007). We test this new code with a simulation based on A1689, using the
pixels belonging to multiply-lensed images and the observed member galaxies.
Dealing with the cluster members this way leads to convergent solutions,
without resorting to regularization, reproducing well the input cluster and
substructures. We highlight the ability of this method to recover dark
sub-components of the cluster, unrelated to member galaxies. Such anomalies can
provide clues to the nature of invisible dark matter, but are hard to discover
using parametrized models where substructures are defined by the visible data.
With our increased resolution and stability we show, for the first time, that
non-parametric models can be made sufficiently precise to locate
multiply-lensed systems, thereby achieving fully self-consistent solutions
without reliance on input systems from less objective means.
