  Using 2 aspheric mirrors, it is possible to apodize a telescope beam without
losing light or angular resolution: the output beam is produced by
``remapping'' the entrance beam to produce the desired light intensity
distribution in a new pupil. We present the Phase-Induced Amplitude Apodization
Coronagraph (PIAAC) concept, which uses this technique, and we show that it
allows efficient direct imaging of extrasolar terrestrial planets with a
small-size telescope in space. The suitability of the PIAAC for exoplanet
imaging is due to a unique combination of achromaticity, small inner working
angle (about 1.5 $\lambda/d$), high throughput, high angular resolution and
large field of view. 3D geometrical raytracing is used to investigate the
off-axis aberrations of PIAAC configurations, and show that a field of view of
more than 100 $\lambda/d$ in radius is available thanks to the correcting
optics of the PIAAC. Angular diameter of the star and tip-tilt errors can be
compensated for by slightly increasing the size of the occulting mask in the
focal plane, with minimal impact on the system performance. Earth-size planets
at 10 pc can be detected in less than 30s with a 4m telescope. Wavefront
quality requirements are similar to classical techniques.
