Optimal apodizers for the vector vortex coronagraph with on-axis telescopes

Phase mask coronagraphs such as the vortex coronagraph are meant to be used with the circular clear aperture of off-axis telescopes, and their performance is greatly reduced when used with on-axis telescopes. A possible solution to that problem consists in apodizing the entrance pupil plane of the coronagraph. Apodizers can be computed by solving a quadratic optimization problem in which the transmission of the apodizer is maximized under the constraint that the intensity of the electric field in the Lyot plane is less than an extremum value that is chosen to be small enough to sufficiently attenuate the starlight in the subsequent image plane. The transmission of the apodizer and the throughput of the system depends on the characteristics of the aperture and of the Lyot stop. We present apodizers optimally designed for the apertures of the Palomar telescope, the VLT, the E-ELT and the AFTA telescope, and for vortex phase masks with a topological charge of 4. Transmissions of 50 to 80% are found for mean contrast of 10^(-6) in the Lyot plane. The end throughput is between 16% and 55%, and mean contrast in the image plane at 2.5λ/D is between 3 × 10^(-8) and 3 × 10^(-9)