  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.
