Recursion relations for gravitational lensing

Abstract

The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting ‘roulette’ expansion generalises the notion of convergence, shear and flexion to arbitrary order. The independent coefficients of this expansion are screen space gradients of the optical tidal tensor which approximates to the usual lensing potential in the weak field limit. From lensed images, knowledge of the roulette coefficients can in principle be inverted to reconstruct the mass distribution of a lens. In this paper, we simplify the roulette expansion and derive a family of recursion relations between the various coefficients, generalising the Kaiser–Squires relations beyond the weak-lensing regime.