  The direct detection of extrasolar planets by imaging means is limited by the
large flux of light from the host star being scattered into the region of
interest by a variety of processes, including diffraction. Coronagraphs are
devices that suppress the undesirable scattering of light caused by
diffraction. In a coronagraph the sensitivity limit for high dynamic range is
limited by the propagation of errors introduced by the imperfect optical system
to the final image. In this paper we develop theory and simulations to
understand how such errors propagate in a coronagraph. We describe the response
of classical and band-limited Lyot coronagraphs to small and large errors in
the placement of the central star, and identify ways of making such
coronagraphs more robust to small guiding errors. We also uncover features of
the decentered PSF that can lead to spurious detection of companions,
especially with aggressive, high dynamic range coronagraphs dedicated to
companion searches aimed at finding extrasolar terrestrial or Jovian planets.
