  We present a far-infrared galaxy luminosity function for the local universe.
We have obtained 389 spectroscopic redshifts for galaxies observed at 90
microns in the AKARI Deep Field South, using the AAOmega fibre spectrograph via
optical identifications in the digitized sky survey and 4m-class optical
imaging. For the luminosity function presented in this paper, we have used
those galaxies which have redshifts 0<z<0.25, have optical magnitudes and are
not part of a newly discovered cluster of galaxies (giving a total of 130
sources). Infrared and optical completeness functions were estimated using
earlier Spitzer data and APM B-band optical data respectively, and the
luminosity function has been prepared using the 1/Vmax method. We also separate
the luminosity function between galaxies which show evidence of predominantly
star-forming activity and predominantly active galactic nucleus (AGN) activity
in their optical spectra. Our luminosity function is in good agreement with the
previous 90 micron luminosity function from the European Large Area ISO Survey,
and we also present a luminosity function with combined AKARI and ISO data. The
result is in reasonable agreement with predictions based on the earlier IRAS 60
micron PSC-z catalogue, and with a recent backward evolution model.
