Smooth particle lensing

We present a numerical technique to compute the gravitational lensing induced by simulated haloes. It relies on a 2D-Tree domain decomposition in the lens plane combined with a description of N-body particles as extended clouds with a non-singular density. This technique is made fully adaptive by the use of a density-dependent smoothing which allows one to probe the lensing properties of haloes from the densest regions in the centre or in substructures to the low-density regions in the outskirts. 'Smooth Particle Lensing' (SPL) has some promising features. First, the deflection potential, the deflection angles, the convergence and the shear are direct and separate end-products of the SPL calculation and can be computed at an arbitrary distribution of points on the lens plane. Secondly, this flexibility avoids the use of interpolation or a finite differentiation procedure on a grid, does not require padding the region with zeros and focuses the computing power on relevant regions. The SPL algorithm is tested by populating isothermal spheres and ellipsoids with particles and then comparing the lensing calculations to the classical fast Fourier transform based technique and analytic solutions. We assess issues related to the resolution of the lensing code and the limitations set by the simulations themselves. We conclude by discussing how SPL can be used to predict the impact of substructures on strong lensing and how it can be generalized to weak-lensing and cosmic shear simulations.