  The vortex coronagraph is one of the most promising coronagraphs for high
contrast imaging because of its simplicity, small inner working angle, high
throughput, and clear off-axis discovery space. However, as with most
coronagraphs, centrally-obscured on-axis telescopes degrade contrast. Based on
the remarkable ability of vortex coronagraphs to move light between the
interior and exterior of pupils, we propose a method, based on multiple
vortices, that, without sacrificing throughput, reduces the residual light
leakage to (a/A)^n, with n >=4, and a and A being the radii of the central
obscuration and primary mirror, respectively. This method thus enables high
contrasts to be reached even with an on-axis telescope.
