  The Hawaii Survey Field SSA22 is the fourth deepest Chandra X-ray field. To
allow for the fullest exploration of this field, we present new optical
spectroscopy from Keck/DEIMOS and Keck/LRIS, which, in combination with the
literature, brings the spectroscopic completeness of the 2--8 keV sample to
62%. We also make optical spectral classifications and estimate photometric
redshifts for the sources without spectroscopic redshifts. We then determine
hard X-ray luminosity functions (XLFs) for the full sample of Active Galactic
Nuclei (AGNs), as well as for the broad-line AGNs (BLAGNs) and the non-BLAGNs
separately. Our XLF for the full sample is in good agreement with the
literature, showing relatively strong evolution over the redshift range
$0.25\le z < 4$. The XLFs for the BLAGNs and the non-BLAGNs imply distinct
evolution with redshift, with BLAGNs becoming increasingly dominant at higher
redshifts and X-ray luminosities.
