  Coronagraphic imaging in combination with moderate to high spectral
resolution may prove more effective in both detecting extrasolar planets and
characterizing them than a standard coronagraphic imaging approach. We envisage
an integral-field spectrograph coupled to a coronagraph to produce a 3D
datacube. For the idealised case where the spectrum of the star is well-known
and unchanging across the field, we discuss the utility of cross-correlation to
seek the extrasolar planet signal, and describe a mathematical approach to
completely eliminate stray light from the host star (although not its Poisson
noise). For the case where the PSF is dominated by diffraction and scattering
effects, and comprises a multitude of speckles within an Airy pattern typical
of a space-based observation, we turn the wavelength dependence of the PSF to
advantage and present a general way to eliminate the contribution from the star
while preserving both the flux and spectrum of the extrasolar planet. We call
this method `spectral deconvolution'. We illustrate the dramatic gains by
showing an idealized simulation that results in a 20-sigma detection of a
Jovian planet at 2 pc with a 2-m coronagraphic space telescope, even though the
planet's peak flux is only 1% that of the PSF wings of the host star. This
scales to detection of a terrestrial extrasolar planet at 2 pc with an 8-m
coronagraphic Terrestrial Planet Finder (TPF) in ~7 hr (or less with
appropriate spatial filtering). Data on the spectral characteristics of the
extrasolar planet and hence on its atmospheric constituents and possible
biomarkers are obtained naturally as part of this process.
