  Many high contrast coronagraph designs have recently been proposed. In this
paper, their suitability for direct imaging of extrasolar terrestrial planets
is reviewed. We also develop a linear-algebra based model of coronagraphy that
can both explain the behavior of existing coronagraphs and quantify the
coronagraphic performance limit imposed by fundamental physics. We find that
the maximum theoretical throughput of a coronagraph is equal to one minus the
non-aberrated non-coronagraphic PSF of the telescope. We describe how a
coronagraph reaching this fundamental limit may be designed, and how much
improvement over the best existing coronagraph design is still possible. Both
the analytical model and numerical simulations of existing designs also show
that this theoretical limit rapidly degrades as the source size is increased:
the ``highest performance'' coronagraphs, those with the highest throughput and
smallest Inner Working Angle (IWA), are the most sensitive to stellar angular
diameter. This unfortunately rules out the possibility of using a small IWA
(lambda/d) coronagraph for a terrestrial planet imaging mission.
  Finally, a detailed numerical simulation which accurately accounts for
stellar angular size, zodiacal and exozodiacal light is used to quantify the
efficiency of coronagraph designs for direct imaging of extrasolar terrestrial
planets in a possible real observing program. We find that in the photon noise
limited regime, a 4m telescope with a theoretically optimal coronagraph is able
to detect Earth-like planets around 50 stars with 1hr exposure time per target
(assuming 25% throughput and exozodi levels similar to our solar system). We
also show that at least 2 existing coronagraph design can approach this level
of performance in the ideal monochromatic case considered in this study.
