Lens equation of axisymmetric lenses. Solid lines represent the right-hand side of Eq. (7) for five lenses with different density profiles. Given a source at position β, its lensed images form at the values of θ where the solid line intersects a horizontal line located at β on the vertical axis. Dotted lines represent positions of the radial caustics. Sources located within the radial caustic of a given lens produce three images. The lens models used in this simulation consist of a stellar component and a dark matter halo, as described in Sect. 3.1. Their density profile is plotted in Fig. 4.