  The microphysical properties of the DM particle can, in principle, be
constrained by the properties and abundance of substructures in DM halos, as
measured through strong gravitational lensing. Unfortunately, there is a lack
of accurate theoretical predictions for the lensing signal of substructures,
mainly because of the discreteness noise inherent to N-body simulations. Here
we present Recursive-TCM, a method that is able to provide lensing predictions
with an arbitrarily low discreteness noise, without any free parameters or
smoothing scale. This solution is based on a novel way of interpreting the
results of N-body simulations, where particles simply trace the evolution and
distortion of Lagrangian phase-space volume elements. We discuss the advantages
of this method over the widely used cloud-in-cells and adaptive-kernel
smoothing density estimators. Applying the new method to a cluster-sized DM
halo simulated in warm and cold DM scenarios, we show how the expected
differences in their substructure population translate into differences in the
convergence and magnification maps. We anticipate that our method will provide
the high-precision theoretical predictions required to interpret and fully
exploit strong gravitational lensing observations.
