  Properly apodized pupils can deliver point spread functions (PSFs) free of
Airy rings, and are suitable for high dynamical range imaging of extrasolar
terrestrial planets (ETPs). To reach this goal, classical pupil apodization
(CPA) unfortunately requires most of the light gathered by the telescope to be
absorbed, resulting in poor throughput and low angular resolution.
Phase-induced amplitude apodization (PIAA) of the telescope pupil (Guyon 2003)
combines the advantages of classical pupil apodization (particularly low
sensitivity to low order aberrations) with full throughput, no loss of angular
resolution and little chromaticity, which makes it, theoretically, an extremely
attractive coronagraph for direct imaging of ETPs. The two most challenging
aspects of this technique are (1) the difficulty to polish the required optics
shapes and (2) diffraction propagation effects which, because of their
chromaticity, can decrease the spectral bandwidth of the coronagraph. We show
that a properly designed hybrid system combining classical apodization with the
PIAA technique can solve both problems simultaneously. For such a system, the
optics shapes can be well within today's optics manufacturing capabilities, and
the $10^{-10}$ PSF contrast at $\approx 1.5 \lambda/D$ required for efficient
imaging of ETPs can be maintained over the whole visible spectrum. This updated
design of the PIAA coronagraph maintains the high performance of the earlier
design, since only a small part of the light is lost in the classical
apodizer(s).
