size also allows higher contrast observation by better concentrating planet light over the speckle halo background, and the gain in collecting area enables spectroscopic characterization. It is therefore essential to identify and develop coronagraph concepts which can deliver high performance on centrally obscured and/or segmented apertures.

Coronagraph designs for centrally obscured and/or segmented apertures have been proposed by several authors, offering a wide range of solutions and approaches:

-   [[**Lyot-type coronagraphs with amplitude masks.**]{} Most studies of coronagraph designs for obscured and/or segmented apertures considered Lyot-type coronagraph optimized for high contrast by either apodization of the entrance pupil (APLC concept introduced by [@2003AA...397.1161S]) or apodization of the focal plane mask (Band-limited coronagraph concept introduced by [@2002ApJ...570..900K]). For the apodized pupil Lyot coronagraph (APLC), [@2005ApJ...618L.161S] and [@2009ApJ...695..695S] showed that the entrance pupil apodizer can be optimized for centrally obscured pupils. Using this technique, [@2007AA...474..671M] studied the APLC for ELTs, finding high throughput solutions offering better than 1e-5 contrast at and beyond 3 $\lambda$/D separation. [@2010AA...519A..61M] proposed using a multistage apodized pupil Lyot coronagraph (APLC) to mitigate central obstruction limitations. While central obstruction can be mitigated in the Lyot-type coronagraph design, [@2005ApJ...633..528S; @2005ApJ...626L..65S] showed that spiders and gaps in APLC and band-limited 