2013A&A...551A..10C

Phase-mask coronagraphs can be seen as linear systems that spatially redistribute in the pupil plane the energy collected by the telescope. Most of the on-axis light must ideally be rejected outside the aperture so as to be blocked with a Lyot stop, while almost all of the off-axis light must go through it. The unobstructed circular apertures of off-axis telescopes make this possible but all of the major telescopes are on-axis, however, and the performance of these coronagraphs is dramatically reduced by their central obstructions. Their performance can be restored by using an additional optimally designed apodizer that changes the amplitude in the first pupil plane so that the on-axis light is rejected outside the obstructed aperture of the on-axis telescope. An apodizer is assumed to be located in a pupil plane, a phase mask in a subsequent image plane, and a Lyot stop in a reimaged pupil plane. The numerical optimization model is built by maximizing the apodizer's transmission while setting constraints on the extremum values of the electric field that the Lyot stop does not block. The coronagraphic image is compared to what a non-apodized phase mask coronagraph provides and an analysis is made of the trade-offs that exist between the transmission of the apodizer and the properties of the Lyot stop. The existence of a solution and the transmission of the mask depend on the geometries of the aperture and of the Lyot stop, and on the constraints that are set on the on-axis attenuation. The system's throughput is a concave function of the Lyot stop transmission. In the case of a VLT-like aperture, optimal apodizers with a transmission of 16% to 92% associated with a four-quadrant phase mask provide contrast as low as a few 10^–10 at 1λ/D from the star. The system's maximum throughput is about 64% for an apodizer with an 88% transmission and a Lyot stop with a 69% transmission. It is shown that optimizing apodizers for a vortex phase mask requires computation times much longer than in the previous case, and no result is presented for this mask. It is demonstrated that apodizers can be successfully optimized to allow phase mask coronagraphs to be used with the full aperture of on-axis telescopes while delivering contrast as low as, or even lower than what they could provide by themselves with off-axis telescopes.