  The cosmic infrared background (CIB) consists of emission from distant,
dusty, star-forming galaxies. Energetically, the CIB is very important as it
contains as much energy as the extragalactic optical background. The nature and
evolutionary status of the objects making up the background are, however,
unclear. The CIB peaks at ~150 microns, and as such is most effectively studied
from space. The limited apertures of space-borne telescopes set the angular
resolution that can be attained, and so even Herschel, with its 3.5m diameter,
will be confusion-limited at this wavelengths at ~5mJy. The bulk of the
galaxies contributing to the CIB are fainter than this, so it is difficult to
study them without interferometry. Here we present the results of a preliminary
study of an alternative way of probing fainter than the continuum confusion
limit using far-IR imaging spectroscopy. An instrument capable of such
observations is being planned for SPICA - a proposed Japanese mission with an
aperture equivalent to that of Herschel and more than 2 orders of magnitude
more sensitive. We investigate the potential of imaging spectrometers to break
the continuum confusion limit. We have simulated the capabilities of a
spectrometer with modest field of view (2'x2'), moderate spectral resolution
(R~1-2000) and high sensitivity. We find that such an instrument is capable of
not only detecting line emission from sources with continuum fluxes
substantially below the confusion limit, but also of determining their
redshifts and, where multiple lines are detected, some emission line
diagnostics. We conclude that 3-D imaging spectrometers on cooled far-IR space
telescopes will be powerful new tools for extragalactic far-IR astronomy.
