  Two high performance coronagraphic approaches compatible with segmented and
obstructed telescope pupils are described. Both concepts use entrance pupil
amplitude apodization and a combined phase and amplitude focal plane mask to
achieve full coronagraphic extinction of an on-axis point source. While the
first concept, named Apodized Pupil Complex Mask Lyot Coronagraph (APCMLC),
relies on a transmission mask to perform the pupil apodization, the second
concept, named Phase-Induced Amplitude Apodization complex mask coronagraph
(PIAACMC), uses beam remapping for lossless apodization. Both concepts
theoretically offer complete coronagraphic extinction (infinite contrast) of a
point source in monochromatic light, with high throughput and sub-lambda/D
inner working angle, regardless of aperture shape. The PIAACMC offers nearly
100% throughput and approaches the fundamental coronagraph performance limit
imposed by first principles. The steps toward designing the coronagraphs for
arbitrary apertures are described for monochromatic light. Designs for the
APCMLC and the higher performance PIAACMC are shown for several monolith and
segmented apertures, such as the apertures of the Subaru Telescope, Giant
Magellan Telescope (GMT), Thirty Meter Telescope (TMT), the European Extremely
Large Telescope (E-ELT) and the Large Binocular Telescope (LBT). Performance in
broadband light is also quantified, suggesting that the monochromatic designs
are suitable for use in up to 20% wide spectral bands for ground-based
telescopes.
