Separability of rotational effects on a gravitational lens

We derive the deflection angle up to ${O(m}^{2}a)$ due to a Kerr gravitational lens with a mass m and specific angular momentum a. It is known that at the linear order in m and a the Kerr lens is observationally equivalent to the Schwarzschild one because of the invariance under the global translation of the center of the lens mass. We show, however, that nonlinear couplings break the degeneracy so that the rotational effect becomes in principle separable for multiple images of a single source. Furthermore, it is distinguishable also for each image of an extended source and/or a point source in orbital motion. In practice, the correction at ${O(m}^{2}a)$ becomes ${O(10\mathrm{}}^{-10})$ for the supermassive black hole in our galactic center. Hence, these nonlinear gravitational lensing effects are too small to detect by near-future observations.